Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L27/00—Modulated-carrier systems
  • H04L27/18—Phase-modulated carrier systems, i.e. using phase-shift keying
  • H04L27/22—Demodulator circuits; Receiver circuits
  • H04L27/233—Demodulator circuits; Receiver circuits using non-coherent demodulation
  • H04L27/2332—Demodulator circuits; Receiver circuits using non-coherent demodulation using a non-coherent carrier
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03D—DEMODULATION OR TRANSFERENCE OF MODULATION FROM ONE CARRIER TO ANOTHER
  • H03D1/00—Demodulation of amplitude-modulated oscillations
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L7/00—Arrangements for synchronising receiver with transmitter
  • H04L7/0016—Arrangements for synchronising receiver with transmitter correction of synchronization errors
  • H04L7/002—Arrangements for synchronising receiver with transmitter correction of synchronization errors correction by interpolation
  • H04L7/0029—Arrangements for synchronising receiver with transmitter correction of synchronization errors correction by interpolation interpolation of received data signal
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L7/00—Arrangements for synchronising receiver with transmitter
  • H04L7/02—Speed or phase control by the received code signals, the signals containing no special synchronisation information
  • H04L7/033—Speed or phase control by the received code signals, the signals containing no special synchronisation information using the transitions of the received signal to control the phase of the synchronising-signal-generating means, e.g. using a phase-locked loop
  • H04L7/0334—Processing of samples having at least three levels, e.g. soft decisions
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L7/00—Arrangements for synchronising receiver with transmitter
  • H04L7/04—Speed or phase control by synchronisation signals
  • H04L7/10—Arrangements for initial synchronisation
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L27/00—Modulated-carrier systems
  • H04L27/0014—Carrier regulation
  • H04L2027/0044—Control loops for carrier regulation
  • H04L2027/0046—Open loops
  • H04L2027/0048—Frequency multiplication
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L27/00—Modulated-carrier systems
  • H04L27/0014—Carrier regulation
  • H04L2027/0083—Signalling arrangements
  • H04L2027/0085—Signalling arrangements with no special signals for synchronisation
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L7/00—Arrangements for synchronising receiver with transmitter
  • H04L7/04—Speed or phase control by synchronisation signals

Definitions

• the present invention relates to digital demodulators used, for example, in burst communications applications. More specifically, the invention relates to such demodulators which perform demodulation without the use of a synchronization preamble attached to data bursts.
• burst communications has usually required a synchronization preamble for the acquisition of carrier synchronization and symbol synchronization prior to synchronous, coherent detection of the modulation symbols in the data burst.
• a preamble is ordinarily employed for burst communications even when a digital demodulator is used for reception.
• U.S. Patent No. 4,466,108 describes a preamble- less approach to digital satellite burst communications that uses either binary phase-shift keying (BPSK) or quaternary phase-shift keying (QPSK) modulation and time division multiple access (TDMA) by some N transmitting stations to share the same satellite transponder sequentially.
• BPSK binary phase-shift keying
• QPSK quaternary phase-shift keying
• TDMA time division multiple access
• the carrier frequency is assumed to be known with sufficient accuracy initially so that carrier frequency acquisition is not required.
• burst communications In burst communications, overhead in the form of a preamble is usually employed to allow carrier synchronization and symbol synchronization to be acquired prior to data detection. If the bursts are short, however, it is desirable to omit the synchronization preamble in order to have a reasonable access efficiency. When there is no preamble for carrier synchronization and symbol synchronization, these synchronizations must be acquired from fully modulated or suppressed-carrier transmissions. Furthermore, the demodulator must process the burst several times to obtain all synchronization functions and then finally to make bit decisions on the burst sequence. A demodulator concept is presented herein that utilizes digital processing for the reception of preamble-less burst transmissions.
• burst transmissions without preambles for acquiring carrier synchronization and symbol synchronization could be for thin-route systems that carry a few voice and/or data channels or short messages, such as in low-rate TDMA or random-access packet communications. These applications are likely to employ earth stations that use antennas with small apertures. It is assumed that modulations of quaternary phase-shift keying (QPSK) and binary phase-shift keying (BPSK) are used at transmission speeds that are sufficiently low (upper bound of perhaps 20 Msymbol/s) so that digital processing is feasible for the demodulator.
• QPSK quaternary phase-shift keying
• BPSK binary phase-shift keying
• All required demodulator operations are performed sequentially by repeated digital processing of the stored complex signal samples for the received burst.
• Algorithms are defined for each processing step.
• the first processing is for the detection of burst presence and the acquisition of coarse frequency, which resolves the uncertainty in carrier frequency to a small fraction of the modulation symbol rate.
• Digital processing is then utilized to perform matched filtering,- which increases the signal-to-noise power ratio (S/N) of the complex signal prior to further processing.
• S/N signal-to-noise power ratio
• the complex samples are processed to obtain symbol synchronization.
• sample interpolation is used to obtain one complex sample for each modulation symbol at the appropriate timing instant for making bit decisions.
• an algorithm for carrier synchronization is utilized to acquire fine frequency and carrier phase on the single samples of the modulation symbols.
• UW detection defines the starting location of the random modulation, the data portion of the burst.
• the UW is a known sequence with good distinguishability that provides low probabilities of both false detection and missed detection.
• the required length of the UW is short compared to the duration of most data bursts.
• the UW is also employed as an aid in acquiring coarse fre ⁇ quency. Knowledge of the UW modulation sequence is the factor that makes the UW valuable in this additional role.
• Synchronization algorithms according to the present invention are designed to function very reliably at moderate carrier-to-noise (C/N) per modulation symbol, that is, E s /N 0 values of 7 to 10 dB.
• Computer simulations are necessary to evaluate the reliability of the synchronizations and the overall demodulator concept for low E s /N 0 values between 3 and 6 dB.
• FEC coding forward error correction
• Fig. la shows a BPSK Signal Constellation
• Fig. lb shows a QPSK Signal Constellation
• Fig. 2a shows a BPSK Signal generator
• Fig. 2b shows a QPSK Signal generator
• Fig. 3a shows a burst format with a synchronization preamble
• Fig. 3b shows a burst format without a synchronization preamble, this format being applicable to the present invention
• Fig. 4 shows a block diagram of the circuity required to obtain baseband samples
• Fig. 5 shows a block diagram of a digital demodulator according to the present invention
• Fig. 6 shows a diagram for performing energy measurement at a particular frequency f
• Fig. 7 shows a block diagram for the processing of complex samples to obtain coarse frequency acquisition on a fully modulated BPSK or QPSK transmission signal
• Fig. 8 shows the operational relationship between a matched filter, an interpolation filter and a symbol synchronizer
• Fig. 9 shows plots of Nyquist responses involved in matched filtering
• Fig. 10 shows the location of poles and zeros for an equalized Butterworth filter used to approximate a square root Nyquist response with 40% rolloff.
• the modulation for the transmission bursts is assumed to be either BPSK or QPSK.
• the carrier frequency, f c ⁇ c /2 ⁇ r
• f n is the phase angle for the nth modulation symbol and ⁇ c is some constant carrier phase angle.
• n can take on only the two values of 0 and IT radians.
• A. represent an amplitude coefficient for BPSK that yields the desired phases.
• a n has values of +1 and -1 in accordance with:
• the BPSK transmission may be represented as a carrier with binary-antipodal amplitude modulation.
• the modulation phase angle, f n can take on the four values of +0.25 ⁇ r, +0.75 ⁇ , -0.25T ⁇ , -0.75T ⁇ radians. It is convenient to use a trigonometric identity in order to represent the QPSK transmission in the alternative form of the sum of binary amplitude modulated quadrature carriers:
• Signal constellations for BPSK and QPSK are shown in Figures la and lb, respectively.
• the two BPSK signal points lie along the X axis, which represents amplitude modulation of the cosine carrier.
• QPSK has binary modulation of the cosine and the sine carriers, the signal points are ' the resultant of projections on both the X and the Y axes. Consequently, the four QPSK signal points of Figure lb have X and Y components of equal magnitudes. Therefore, the signal points are on a circle of radius Vc * (also equal to E S ) at locations midway between the X and Y axes.
• Unfiltered BPSK and QPSK transmissions would have constant envelopes. Filtering on the transmit end is often necessary to reduce the signal bandwidth and thereby obtain reasonable spectral efficiency. Such filtering results in envelope variations of the transmission.
• Nyquist filtering as described in (R.W. Lucky, J. Salz, and E. J. Weldon, Jr., "Principles of Data Communication.” New York: McGraw-Hill Book Company, 1968, pp. 43-54) may be used so as to create nulls in intersymbol interference (ISI) at detection sampling instants. In such a case, the filtering will be split between the transmit end and the receive end equally as square-root Nyquist responses. This receiver filtering matched to the transmit pulse shape maximizes the S/N in detection.
• ISI intersymbol interference
• the transmit section must contain a response compensa ⁇ tion equal to ( ⁇ f/R s )/sin( ⁇ f/R s ) in addition to the square-root Nyquist response.
• Signal generation arrangements for both BPSK and QPSK are illustrated in Figures 2a and 2b, respectively.
• the modem transit filters 220, 280 and 290 are represented at baseband.
• the signal is generated by modulating, at modulator 230, the cosine carrier generated by carrier generator 240 with a filtered version of the sequence of modulation coefficients. A-., produced by Binary Source 210.
• QPSK generation in Figure 2b separate transmit filters 280 and 290 are required for the two baseband sequences of B n and A-, modulation coefficients produced by Binary Sources 260 and 270, respectively.
• the QPSK signal is actually the sum of two BPSK transmissions, for which the carriers have a quadrature phase relationship, such a quadrature phase relationship is provided by a 90° - phase-shifter 202 which receives a carrier signal produced by carrier generator 294. The output of the phase-shifter 202 goes to a modulator 201.
• Such a signal generation of QPSK produces Gray encoding as described in (Members of BTL Technical Staff, Transmission Systems for Communications. Bell Telephone Laboratories, Fourth Edition, 1970, pp. 589- 591) of bits onto the QPSK vector, which has the desirable property of adjacent signal vectors differing in only one bit position. During any data burst, the modulation sequence appears as a random sequence.
• the overhead can cause a significant loss in access efficiency.
• the UW must always be included, in order for the burst location during reception to be determined accurately and reliably. Usually, the UW length does not exceed 32 modulation symbols, and is therefore fairly short compared to the burst duration.
• the required preamble length for reliable acquisition of carrier synchronization and symbol synchronization may be a significant fraction of the burst duration.
• access efficiency can be greatly degraded by the overhead preamble required for synchronization acquisition. It follows that the access efficiency could be improved significantly for short burst transmissions by the elimination of the synchronization preamble.
• Burst formats with and without synchronization preambles are illustrated in Figures 3a and 3b, respectively.
• the data burst has some length, N D measured in modulations symbol intervals.
• both formats have a UW requirement of some length, N 0 .
• timing uncertainty necessitates a guard space of some N G symbol intervals to prevent possible time overlap of bursts received from different transmit locations.
• the synchronization preamble has a required length of some N p symbol intervals.
• Figure 3b has all of the same requirements, except that the synchronization preamble is eliminated.
• Access efficiency for burst transmission is defined by the fraction of available time allocation for the burst that is used to transmit data.
• the overhead for guard space, synchronization preamble, and UW represent potential waste of available time and power for purposes other than to transmit message bits or data.
• N H denote the total overhead measured in modulation symbol intervals. Then, access efficiency is given by:
• Access efficiency with a synchronization preamble is only about 0.60 for the illustrative example.
• Elimination of the synchronization preamble for this example allows the access efficiency to be increased to approximately 0.85.
• Algorithms are described later that can acquire very accurate carrier synchronization from the stored samples of a preamble-less burst even when the initial frequency uncertainty of ⁇ F/2 is larger than the modulation symbol rate, R s . It should be noted that an extremely long preamble, such as 500 or more symbol intervals, would be necessary to acquire carrier synchronization in real time when the frequency error is not small compared to R s .
• FIG. 4 is a block diagram of the circuitry required to obtain the baseband samples.
• the received BPSK or QPSK transmission on line 401 has an occupied bandwidth of B 0 , some nominal carrier frequency of f 0 , and a frequency uncertainty of ⁇ F/2 about f 0 .
• Complex sampling by means of A/D converters 402 and 403, at a rate of f s - sR s set by sampling clock 404, or s complex samples per symbol interval, is employed to obtain an adequate description of the received burst transmission.
• Digital processing of all the burst samples is utilized to perform the required demodulator functions of various synchronizations, filtering, and data detection as will be described below.
• the number of complex samples required per modulation symbol interval is related to the range, F, of carrier frequency uncertainty, occupied bandwidth, B 0 , and modulation symbol rate R s by: F B 0 + F s ⁇ RT s " -* R s
• Figure 5 is a block diagram of the digital demodulator.
• the complex samples are stored in a memory 501. Sequential operations are used for coarse frequency acquisition and correction, by means of blocks 502 and 503, respectively, matched filtering, by means of blocks 504 and 505, symbol synchronization by means of block 506, sample interpolation by means of block 507 to the correct symbol timing, and carrier synchronization by means of block 508 to acquire fine frequency and carrier phase.
• bit decisions are made by blocks 510 and 511 on the components of the complex samples for the modulation symbols. Also, UW detection by block 512 is included.
• burst presence is declared when a detection threshold is exceeded at any of the M tones.
• the threshold for burst presence may be exceeded at more than one tone.
• the threshold may be exceeded at two or more time locations for some of the M sliding-block correlations. Time and frequency locations are noted for the largest correlation above threshold. Coarse frequency is based upon the frequency cell at which the maximum occurred. Because the UW is employed in the detection, burst synchronization is provided from the time location of maximum correlation.
• burst synchronization provided by the time location of the maximum of the correlations above threshold, any further processing of the complex samples can be restricted to those samples within the UW and the data burst.
• the knowledge of burst location thus avoids including samples of noise only, which would degrade the S/N of synchronizations by processing samples of noise outside of the burst locations.
• One of the important functions of the demodulator is matched filtering of the received modulation symbols which takes place at blocks 504 and 505. Matched filtering is used to maximize the S/N at the correct time location for modulation decisions. Effective matched filtering is possible only when the residual frequency error, f ⁇ , after coarse frequency acquisition is much smaller than R s , the modulation symbol rate. With ⁇ ⁇ R s /8 spacing for the correlation tones used in coarse frequency acquisition, then f e ⁇ R s /16 when coarse frequency is correctly acquired. This accuracy is adequate for matched filtering to be employed. Furthermore, some filtering is necessary to increase the sample S/N prior to processing for symbol synchronization and carrier synchronization. Thus, matched filtering performed right after coarse frequency is acquired avoids the necessity of other filtering operations.
• Symbol synchronization performed at block 506, determines the one time location per symbol that should maximize the symbol S/N so as to minimize the error probability for decisions on the modulation bits. Therefore, interpolation at block 507, of the matched filter output is necessary after symbol synchronization to determine the complex sample values at the appropriate sampling times for bit decisions. Then, only one complex sample per modulation symbol is employed for further processing after symbol synchronization, using the samples obtained by interpolation.
• carrier synchronization at block 508 on the complex samples obtained by interpolation is employed to estimate fine frequency and carrier phase.
• Fine frequency refers to the residual small frequency error, f e , remaining after coarse frequency acquisition.
• the complex samples are corrected at block 509 for phase rotation in accordance with the estimates of errors in fine frequency and carrier phase.
• Total time for all demodulator processing of a burst can be allowed to exceed the burst duration.
• the maximum allowable processing time per burst is equal to the average burst length divided by the duty factor for the bursts that must be demodulated at the receiving earth station.
• the matched filter output is recomputed to interpolate the sample values to the desired timing instants for bit decisions.
• the recommended method of calculating the complex samples at the desired mid-symbol locations is to employ an interpolation filter following the matched filter.
• FIG. 5 illustrates UW detection after bit decisions are made. This is the usual method, but UW detection for the digital demodulator is actually combined with the initial synchronization algorithm for detecting burst presence, estimating coarse frequency, and determining coarse burst location. The UW can be detected again after bit decisions are made as a means to resolve any phase ambiguity in carrier synchronization.
• the demodulator concept is intended for applications to communications at sufficiently low speed (perhaps less than 10 Msymbol/s) so that only a few DSP chips are required for the digital processing.
• the demodulator concept is described for only one frequency channel of burst communications, extension to multiple channels can be accommodated by the use of additional DSP chips.
• Use of well-known FFT (fast Fourier transforms) techniques (B. Gold and C . Rader, Digital Processing of Signals. McGraw-Hill Book Co., 1969, pp. 173-201) can be utilized to reduce the time requirements for some of the digital processings operations, especially if it is desired to demodulate burst transmissions from multiple sources that may employ different carrier-frequencies.
• Digital processing requirements are simplified by use of -the lowest sampling rate that can represent the signal without distortion over the total range, F t , of signal spectrum plus initial frequency error.
• the range, F, of carrier frequency uncertainty can be divided into M frequency cells of width ⁇ each.
• Energy measurements over a sliding time interval of N modulation symbols are made in parallel at M tones that are located at the centers of the frequency cells.
• burst presence is declared.
• energy measurements may also exceed the detection threshold at other times and frequencies.
• Coarse frequency is determined by the frequency cell at which the maximum occurs, and the time location of the maximum yields coarse burst synchronization. Therefore, one processing operation combines the three functions of burst presence detection, coarse frequency estimation, and coarse burst timing.
• burst time location (burst synchronization) allows samples of noise only preceding and following the burst to be discarded. Hence, all further processings are restricted to only the complex samples from the burst transmission (including UW) . These samples are corrected for phasings in accordance with the estimated error in coarse frequency. Correction of the phases of complex samples based on the coarse frequency estimation completes the process of coarse frequency acquisition.
• Coarse frequency estimation is made much more difficult by the omission of a synchronization preamble.
• the modulation For coarse frequency to be acquired the modulation must be removed. Squaring for BPSK and quadrupling for QPSK are necessary for modulation removal in a simple manner. However, these operations complicate the processing.
• mth-power operations for m-ary PSK expand the frequency scale by a factor of m. Both the sampling rate, f s , and the number M of frequency correlations must be increased by the factor m. This increases the processing complexity for acquiring coarse frequency, especially for QPSK.
• An even greater problem is the required length N of the observation interval. The S/N is lowered by a factor of 1/m for mth-power modulation removal. With this loss, a large N is required for sufficient S/N to provide reliable burst detection and coarse frequency acquisition.
• m 4 results in a requirement on N that may exceed the burst length.
• Removal of the known UW pattern does not cause the S/N loss associated with modulation removal by squaring or quadrupling.
• carrier synchronization can also be performed reliably on the UW if its length is sufficient.
• Another advantage of the UW for synchronization is that a fixed number of transitions in the UW pattern can assure that coarse symbol synchronization will be obtainable. Therefore, the UW can serve extra duty by being employed as a substitute for a coarse synchronization preamble.
• a binary UW should be used even when the data modulation is QPSK, with the binary elements of the UW mapped into two antipodal vectors of the QPSK signal constellation. Probabilities of false detection and missed detection are investigated in this section on coarse frequency acquisition.
• a suitable UW sequence of length N 16 is proposed. If operation at very low E s /N 0 is desired, N may have to be increased to 24 or 32.
• the frequency separation With a total of M complex correlators at frequencies equally spaced over the total range, F, of frequency uncertainty, the frequency separation will be denoted by ⁇ . Assuming that the two outer correlations are located at ⁇ /2 each from the two ends of the bands of width F, the frequency spacing is:
• the actual frequency of the received transmission can be no further away from one of the frequencies for power measurement than ⁇ /2.
• M must be selected to be sufficiently large so that the correlation loss is small for a frequency error of ⁇ /2.
• correlation with a frequency error of f e Hz results in a power loss factor of: sin-2 ( ⁇ f ⁇ T)
• ⁇ can be selected to place an upper bound on L e .
• 8/ ⁇ r is chosen for the lower bound on the power loss factor, L e .
• the spacing ⁇ - between correlation frequencies is:
• the carrier frequency can be no further from the reference frequency of one of the power measurements than:
• the equivalent of this sliding window is effected by the use of a noise bandwidth equal to the inverse of T for the continuous signal in each of the M frequency slots.
• the number M of frequency terms is equal to the number of time samples in the FFT block.
• the frequency spacing for an observation interval of T is 1/T rather than the 1/(2T) spacing for the M power measurements.
• M 2N time samples in the interval T.
• the frequency spacing would be the inverse of this " extended interval of 2T. Because the artificial second half of this extended observation interval contains no information on burst presence and coarse frequency, the frequency estimation has a 3-dB deficiency in S/N with respect to that which could be obtained from an actual observation interval of 2T. That is, S/N is still based upon the true observation interval of T.
• An energy threshold, E t for the detection of burst presence should be set so as to approximately balance P m and P f at the lowest E s /N 0 at which reliable detection is required.
• E s may be based upon an E s /N 0 of perhaps 4, or a 10 log E s /N 0 of 6 dB.
• E m /N 0 denote the minimum value of E s /N 0 for which burst detection is designed. Note that the total signal energy in the N symbol intervals of the observation interval is given by:
• Approximate balancing of P m and P f is achieved when the detection voltage threshold is set at one-half of the total. Then, for the energy threshold.
• the noise envelope has a Rayleigh density function, g(v) , where:
• Miss probability is determined from the Ricean density function of the envelope of signal plus noise.
• E/N 0 must be large in the interval T.
• P m is approximated by the effect of in-phase noise alone in causing the energy level of signal plus noise to drop below E t .
• the optimum threshold results in P 1 slightly greater than the miss probability, P m .
• false detection probability, P f dominates with respect to errors in the detection of burst presence.
• P, l ⁇ "14 , however, P f is likely to still be very small, such as 10 -9 or less.
• One approach is to define the desired resolution for coarse frequency first.
• An appropriate solution would be to make the maximum error, f e , in carrier location to be one-sixteenth of the modulation symbol rate, which is accurate enough to allow matched filtering to be implemented.
• the spacing of frequency cells will be one-eighth of R s
• Low-pass filtering with a cutoff frequency of F/2 Hz is employed on the quadrature components prior to sampling and analog-to-digital (A/D) conversion to obtain the P + Q values.
• the sampling rate must be increased by a factor of m to represent an expanded frequency range of mF Hz.
• the additional samples can be obtained either from interpolation of samples taken at a rate of s per symbol interval, or by increasing the initial sampling rate to provide ms samples of R per symbol interval.
• t 0 is the time interval between samples and is the inverse of the increased sampling rate.
• a vector Z n is defined by the components X n and Y n .
• modulation removal consists of taking the mth power of Z n at the block 703 to obtain a new vector, w n , where n n JY and
• the components u and v for the vector w represent the quadrature components at the mth harmonic of f + f..
• squaring yields the following components at 2f 0 + 2f s :
• quadrupling for QPSK modulation removal yields components at 4f 0 + 4f f
• T NTs-, of some N modulation symbols.
• the range of frequency uncertainty is expanded for BPSK by squaring to 2F t , and quadrupling for Qx-3K expands the frequency range to 4F t . This expansion of the range of frequency uncertainty similarly expands the number of tones at which the energy calculations must be made for determining burst presence and coarse frequency.
• Frequency resolution is inversely related to the interval over which coherent addition is performed before the energy computation is made. It is desirable to estimate carrier frequency coarsely in the initial frequency acquisition, in order to reduce the number of tones at which the energy computations are performed.
• the envelopes of the N 2 blocks would then be computed and summed to yield the total envelope in each frequency cell. Energy in the frequency cell is proportional to the square of the total envelope.
• N- — 8 is selected as the minimum number of symbol intervals for coherent addition of the quadrupled QPSK signal. It follows that the spacing of frequency cells will be:
• the maximum error in frequency between the closest frequency cell and the fourth harmonic of the carrier is:
• r n r n . k + 7 n
• Burst presence is declared when the square of r n for any of M frequency cells exceeds the energy threshold, E t .
• Coarse frequency is based upon selecting the frequency cell at which the threshold is exceeded. If the metric threshold is met for more than one frequency cell, the frequency choice is based upon the cell with the greatest value of T n . Also, the time location at which the maximum metric value occurs yields coarse burst synchronization.
• E m /N 0 represent the lowest E s /N 0 at which very reliable determinations of burst presence and coarse frequency are required.
• the total S/N in the observation interval of N modulation symbols is:
• N 2 the required number of blocks of length N, is given by:
• N 2 I In 10 - 2.3 I Also a total observation interval of N symbols is required, where
• Omission of the synchronization preamble for improving the access efficiency implies that the message bursts are not very long.
• the burst length places an upper bound on the available observation interval for coarse frequency acquisition. From Table 4-1 it is seen that large observation intervals, N (measured in modulation symbols) , are required if the probability, P t , of false detection is to be very low.
• An alternative method of burst detection and frequency acquisition will be investigated next that avoids quadrupling for modulation removal and the consequent large requirement on N.
• the UW pattern allows modulation removal in a form similar to decision feedback (DFB) of modulation decisions.
• the vectors, Z n are multiplied by a known vector sequence in place of squaring or quadrupling.
• Multiplication of the signal by the known UW pattern does not expand the frequency scale or require an increased sampling rate, as does squaring and quadrupling. It follows that the number of frequency cells required for estimating coarse frequency is reduced by avoiding either squaring or quadrupling.
• the UW may be binary by using only two antipodal vectors of the QPSK constellation. With the binary UW, modulation removal is effected by convolution of the discrete signal for each frequency cell with a known UW sequence of +1 and -1 values.
• Multiplication of the signal at each tone by the UW effects modulation removal only near the correct time/frequency locations.
• the operation is linear, however, and the phase angle is not magnified by the process.
• the linear operation does not cause any second-order noise terms. Consequently, filtering prior to modulation removal is unnecessary.
• Matched filtering must be employed at some point to maximize the S/N at the detection instants for bit decisions. Such matched filtering need be performed only for the winning tone in coarse frequency acquisition. Therefore,* filtering requirements are reduced by avoiding filtering prior to modulation removal and performing matched filtering after coarse frequency is acquired.
• the vector W n is used to form a noncoherent metric, y n .
• the total metric r n for the observation interval of N symbols is the sum of ⁇ n values for the N 2 blocks.
• False detection of a burst presence can be caused only by noise. Although the UW may be falsely detected before it is in the correct time location, use of a suitable UW will yield a larger correlation when the alignment is achieved.
• a UW pattern should be chosen that has low autocorrelation for all time displacements relative to the correlation when aligned. Then, maximum correlation should occur at worst only a sample or two away from correct time alignment. With such resolution of a fraction of a modulation symbol interval in coarse burst synchronization, fine burst alignment will be obtained when symbol synchronization is acquired on the output of the matched filter. It is assumed that there will be no time overlap of transmission bursts. Also, the burst length will be known.
• the receiving station will have acquired any previous burst and know where that burst ends. Consequently, the memory of the energy measures for the M frequency cells can be zeroed prior to arrival of the new burst. This memory erasure prevents problems of false detection of the present burst from energy in the preceding burst.
• the UW detection for burst presence and estimation of coarse frequency should have a low value of P m .
• the pattern of the UW is not very critical for P-., but the UW pattern must be known and be of sufficient length, N, to provide a low value of P m .
• Use of a pseudo-random pattern or a Barker sequence for the UW is necessary to improve its autocorrelation properties so as to make a less coarse resolution of burst time location and yield a low probability P f of false detection.
• the metric threshold for UW detection is based on some minimum value of E--/N 0 for the ratio E s /N 0 of signal energy per modulation symbol to noise power density.
• E s /N 0 the ratio of signal energy per modulation symbol to noise power density.
• optimization of the detection threshold is often based upon minimizing the sum P 1 + P m , where P t is the false detection probability at one frequency/time location when the signal is absent, and P m is the miss probability in the correct frequency/time slot when the signal is present.
• the UW must have a fairly high S/N, , in order for reasonably low values of P, and P m to be achieved.
• the optimum threshold is approximately at 0.5 r s , where r s is the UW detection value from signal alone with perfect alignments in both frequency and time.
• P, and P m may be approximated as follows:
• P is one order of magnitude larger than P f . It is desirable for P, to be much smaller than P m , as will now be explained.
• P f denote the overall probability of false detection over some M tones and N a symbol intervals of signal absence prior to burst arrival. It is reasonable for the threshold to be set to balance P f and P m .
• the total probability of false detection may be approximated by its union bound of:
• Table 4-2 gives P, and P m values as a function of UW length N.
• the pattern removal of the UW serves as modulation removal, so that the necessity of squaring is avoided. Removal of the known UW pattern, therefore, improves the performance of carrier synchronization because it does not lower the S/N as does squaring and quadrupling. Multiplication of the signal with its delayed replica is necessary in symbol synchronization rather than pattern removal.
• Use of a pseudorandom UW with N/2 transitions provides a good pattern for reliable symbol synchronization.
• the detection threshold could be exceeded when there are small errors in both time and frequency. Therefore, the time/frequency accuracy of detection is improved by selecting the combination of time and frequency cells that yields the largest metric. Furthermore, coarse burst synchronization is based upon the time location of the maximum metric. Therefore, continued metric determinations and metric 11605
• comparisons should be performed over frequency and time for an interval of one UW length after the initial detection of burst presence.
• the UW detection threshold was a fixed value based upon some E m /N 0 , the minimum value of E s /N 0 for which highly reliable synchronization is required.
• the false detection probability, P for any frequency/time cell during signal absence is a constant.
• E s /N 0 increases above its minimum value, however, the miss probability in the correct frequency/time cell is lowered dramatically.
• P m becomes much smaller than P f when E /N is several dB above the assumed minimum.
• Previous transmission bursts from the same source may be monitored to estimate the received signal level.
• an adaptive UW threshold can be employed.
• the adaptive threshold would be related to the signal energy level per symbol, E s .
• E s the signal energy level per symbol
• P f and P m would both be decreased with increasing E s /N 0 , and remain fairly balanced at all signal levels.
• any adaptive UW threshold must be based upon the level of the present reception.
• This adaptive threshold technique is termed CFAR for "constant false alarm rate.”
• the detection threshold is increased with signal energy, so that P m only has a moderate decrease as E s /N 0 is increased.
• a UW pattern must be chosen that has very low autocorrelation for any time displacement from correct alignment.
• the shortened correlation intervals and ⁇ noncoherent combining make the UW sequence selection more difficult for achieving the desirable autocorrelation properties.
• Low overall metrics for the UW detection must be achieved for any timing error of one or more symbol intervals.
• the stored complex signal will have some small residual frequency error, f. Because the spacing ⁇ of the correlation tones for estimating coarse frequency is less than or equal to one-eighth of the modulation symbol rate, R , I it follows that
• matched filtering can be employed prior to other demodulator processing.
• Processing of the filtered samples by the symbol synchronizer yields an estimate of the desired sampling times for bit detection. Only one complex sample per symbol is used in processing after symbol synchronization. These sample values must be obtained from the output of the matched filter by interpolation that yields one complex sample per modulation symbol interval at the timing location obtained from symbol synchronization. Both matched filtering and sample interpolation will be examined in this section of the disclosure.
• Outputs for the interpolation filter are computed only at the sampling instants (one per symbol) defined by the timing phase from the symbol synchronizer.
• Figure 8 depicts the configurations of matched filtering by block 801, symbol synchronization by block 803, and sample interpolation by block 802.
• Overall Nyquist filtering as described in the Lucky et al reference discussed above, is desired so that no intersymbol interference (ISI) occurs at the detection sampling instants.
• ISI intersymbol interference
• the interpolation filter In order not to change the overall response, the interpolation filter has a flat response over the signal bandwidth, and the amplitude then rolls off gradually to zero before the end points of +f s /2 for the sampling spectrum.
• the interpolation process could be considered as an inherent part of symbol synchronization, but interpolation will be treated here as a separate process associated with filtering after a timing estimate is provided by the symbol synchronizer.
• Matched filtering with a square-root Nyquist function has an infinite impulse response. Use of only the significant portion of the impulse allows an FIR implementation using direct convolution. Truncation of the impulse response does cause some spectral distortion, but this distortion is very small if most of the energy is conveyed by the finite " portion of the impulse response that remains after truncation. Also, the impulse response should be truncated equally to both sides of its main time lobe, so as to have symmetry about the point of mean delay. Such symmetry avoids delay distortion.
• Recursive implementation of digital filtering is appropriate when the filter response is based upon the poles and zeros of the frequency response function.
• the square-root Nyquist response ideally has no delay distortion, it can be approximated by designs based on poles and zeros of the transfer function. Locations of poles and zeros are given in (J.J. Poklemba, "Pole-Zero Approximations for the Raised Cosine Filter Family," COMSAT Technical Review. Vol. 17, No. 1, pp. 127-157) for excellent approximations to square-root Nyquist filters of various rolloff factors from 0.1 up to 1.0. Hence, recursive techniques may be employed for digital implementation of these filter designs.
• the recursive implementation yields an output that is impulse invariant with respect to the analog filter function.
• the recursive representation of filtering yields an output, Z, as a function of input z in accordance with the following equation:
• a total Nyquist frequency response with a rolloff factor of p would ideally have flat delay over the entire band and flat amplitude out to ⁇ (1 - p)R s /2 from band center.
• the rolloff of amplitude has skew symmetry about ⁇ R s /2, with total cutoff occurring at ⁇ (1 + p)R s /2 from band center.
• the total bandwidth for non-zero amplitude is R s (1 + p) .
• the low-pass amplitude response (that for positive frequencies) is given for cosinusoidal rolloffs by
• This approximation consists of a delay- equalized four-pole Butterworth response that has a 3- dB cutoff at ⁇ 0.5 R s about band center.
• a simple delay equalization is provided by a single pole/zero pair on the real axis at distances of ⁇ 1.2 (0.5 R s ) from the origin.
• This useful filter may be readily implemented using the recursive technique.
• One advantage to use of a truncated impulse response and direct convolution is that the filter is represented exactly over the finite region. The amplitude function of frequency for a square-root Nyquist approximation is then completely symmetrical, and there is no delay distortion. Consequently, ISI will be zero at the correct sampling instants for bit decisions.
• Sample interpolation is simplified by the use of a filter with a finite impulse response of short duration and implementation by direct convolution.
• Another requirement on the interpolation filter is for its amplitude to be flat over the signal spectrum.
• the impulse response is not truly finite, truncation of the impulse response to only its main lobe and two sidelobes on each side will convey all the significant response. With its mean delay represented at the delay origin, the impulse response for this interpolation filter is expressed as
• T, 1/B 1 is the "Nyquist" interval for this interpolation filter—the pulse interval that would produce samples without ISI.
• B is the Nyquist bandwidth between the two half-amplitude points, as
• the output of the matched filter would be computed once per symbol interval as a function of its input, which has four or more samples per symbol interval. Because the matched filter has a narrower bandwidth than the response just proposed, the width of the impulse response measured in symbol intervals must be increased, which requires more terms to represent the truncated impulse response. Therefore, it is recommended that a separate filter following matched filtering be employed for interpolation.
• the output of the matched filter at s > 4 complex samples per symbol constitutes the input to the interpolation filter. In accordance with the timing estimate from the symbol synchronizer, one output complex sample per symbol is computed for the interpolation filter.
• Quadrature timing references with frequencies of R s and some arbitrary phase delay of ⁇ are used to obtain correlations U and V with the envelope squared of the samples from the matched filter. These correlations are used by the symbol synchronizer to obtain an estimate ⁇ of the actual signal timing phase and the amount ⁇ by which the delay of the reference timing should be increased.
• the required additional delay is the difference between ⁇ and f, as
• the output complex samples of the interpolation filter would be defined in terms of its truncated impulse response by a center term and some number, n.-, of terms to the left and right of center.
• Z(4nT + 2.07) ⁇ h(kT * 0.57)
• z denotes the input sample values and Z the output values for the interpolation filter.
• the truncated impulse response is represented relative to its mean delay so that h(iT) is symmetrical about its relative delay origin.
• n, 4
• For digital implementation of filtering, must be quantized into some number m, of input sample intervals of T plus a fraction of T expressed as m 2 t 0 .
• the delay t 0 represents the resolution for symbol synchronization, which should be perhaps 256 timing steps per modulation symbol interval, or
• a 1 is defined as
• n is the greatest integer, positive or negative, that does not exceed A-, as given by
• the integer m 2 for quantizing into timing steps of t 0 is given by the closest integer to A 2 , as
• the m,T portion of the timing shift can be effected in the convolution by shifting the time indices of the input samples by m,.
• the m 2 t 0 portion of the timing shift must be represented, however, by a shift of delay for the impulse response.
• burst synchronization after matched filtering is retained either by accounting for the group delay introduced by filtering or by performing UW detection on the output of the filter. It follows that the entire burst (except for a very small guard space for time uncertainty) can be processed to obtain symbol synchronization.
• the only signal attributes useful to symbol synchronization are provided from symbol transitions.
• the UW has transitions in symbol values exactly one-half of the time. Because these transitions are always present in the UW, the UW can provide a good pattern for acquiring symbol synchronization.
• the data have an average transition probability of one-half, but can have long intervals without transitions. On the average, the transitions in the data will aid in symbol synchronization.
• a nonlinear operation (such as squaring) is necessary to obtain symbol synchronization from the complex samples out of the matched filter. The operation can be the same for any portion of the burst, including the UW. Therefore, the UW and the data burst can both be used in obtaining symbol synchronization.
• Two modes of synchronization are usually employed in burst communications: acquisition and tracking.
• symbol synchronization is acquired during the preamble. Then the timing estimate is maintained with continued tracking by the symbol synchronizer throughout the data burst following the preamble.
• either the UW or the entire burst can be used for the acquisition of a coarse timing estimate.
• a second processing of the same burst may be employed to refine the estimate of symbol timing.
• fine resolution of symbol timing can be achieved by a two-step processing of the entire burst. This second step in symbol synchronization that is used to obtain a fine timing estate does not constitute a tracking mode of synchronization, but is merely a second step in acquisition.
• the recommended method achieves a timing estimate in one step, without the necessity of an initial acquisition of coarse frequency.
• the algorithm is effective for either BPSK or QPSK.
• timing jitter will not cause a significant loss in detection performance.
• the analysis of timing jitter is for continuous signals, but is applicable to the discrete case if the sampling rate is sufficient to derive the Fourier components without distortion from undersamp1ing. Description of Symbol Synchronization
• Symbol synchronization is achieved by processing the complex samples obtained from the output of the matched filter.
• two complex samples per symbol are adequate to obtain symbol synchronization from a band-limited signal.
• the algorithms for symbol synchronization can utilize two or more complex samples per symbol interval. It is not known whether the accuracy in symbol synchronization will be sufficient on two samples per symbol unless the timing estimate is further refined by an additional stage of processing of new samples from the matched filter after the first timing correction. Consequently, it may be desirable to use four samples per symbol to avoid the necessity of a repeated stage of synchronization for improving the fine timing estimate.
• the input of the matched filter must be determined for the complex samples at the new timing.
• the maximum signal-to-noise power ratio (S/N) is achieved for the samples located near the middle of each modulation symbol.
• the optimum sampling point is precisely at midsymbol. Only the one sample per symbol at the midsymbol location should be computed from the output of the matched filter to be used in further processings after symbol synchronization is obtained.
• this stage may consist of two steps.
• the first step is to acquire coarse timing.
• Coarse timing merely groups the complex samples correctly so that, for a rate of s complex samples per modulation symbol, each group of s samples lies within the same symbol interval.
• fine timing is obtained. Fine timing consists of estimating where, between adjacent samples of different symbols, the symbol boundary is located. In the estimations of symbol timing, an average over some number N of symbols is- required to reduce the estimation errors introduced by signal disturbances from additive noise and sometimes by intersymbol interference (ISI) .
• ISI intersymbol interference
• the overall relative accuracy of the source for clock frequency will ordinarily be l ⁇ "5 or better.
• the mean time for frequency error in symbol timing to accrue a significant phase error would be on the order of several thousand symbol intervals. Avoiding preamble overhead to increase access efficiency is meaningful only when the bursts are short, at the most only a few hundred symbol intervals. Therefore, an estimate of timing phase obtained from any portion of a burst is applicable for the entire burst.
• s 2 complex samples per symbol.
• the samples may be categorized as being even or odd on the basis of subscript numbers.
• the even sample is denoted by an index or subscript of 2n.
• the odd sample will be given a subscript of 2n+l. It will be assumed that some number N + 1 of symbol intervals are used in the processing, with symbol subscripts n from 0 to N, which results in N symbol boundaries with subscripts n from 1 to N.
• the first of a pair of complex samples has a subscript of 2n+i and the second complex sample has a subscript of 2n+i+l.
• g n denote the binary coefficient (+l or -1) of the nth symbol of the UW. Because carrier phase synchronization has not been obtained, each of the components (x and y) has coherent addition, and the metric is then equal to the envelope. Hence, the squares of the two timing metrics are given by
• V 4n «i " y 4n ⁇ i + y 4n+ifl * y 4n*W2 * y 4n + i-*3
• the metrics are based on the average of the absolute values of the sums of grouped samples. This algorithm does not need any information as to the symbol coefficients and can thus be used over the data burst as well as the UW. Also, with separate additions over the components x and y of the complex signal z out the matched filter, the metric is based upon an envelope. It follows that the metrics ⁇ ,- will give excellent measures of the correct sample grouping for either BPSK or QPSK modulations. The largest metric of s timing positions indicates the grouping that yields the largest envelope for the total averaging interval of N symbols.
• i 0, 1, 2, and 3.
• the selected i for coarse timing is based upon the largest of the four r,-, values that which denotes the best timing boundaries for grouping the four consecutive samples of each modulation symbol.
• the method that uses absolute values of sums is preferred.
• the UW length may be inadequate for reliable symbol synchronization. Therefore, a technique is preferred that can be used over the entire burst if necessary. As stated previously, this method is applicable to both BPSK and QPSK modulations.
• the s complex samples per symbol are located symmetrically within a symbol interval.
• the two center samples are assumed to lie at +T s /2s about the middle of the modulation symbol interval, and the outer two samples are assumed to be located at T s /2s from the symbol boundaries.
• the two center samples that are assumed to be located at points T s /4 from the middle of the symbol are the same as the two outer samples that are assumed to lie at T s /4 from the symbol boundaries.
• the purpose is to achieve a finer estimate of the sample locations than given by the coarse estimate from the first step of synchronization.
• phase angle of the sample at time t b is II/s + e n relative to the symbol boundary, where
• the preceding sample point of the (n-l)th BPSK symbol at time t a is located just prior to the boundary of the (n-l)th and nth symbols at a phasing location of ⁇ /s - Cn .
• Timing error be denoted by ⁇ .
• the residual phase error after coarse timing is achieved is related to the fractional timing error by:
• R s 1/T S is the BPSK modulation symbol rate.
• Positive values of ⁇ and e correspond to late sampling instants, while negative values denote early sampling times.
• a polarity transition of the bandlimited signal results in an approximately sinusoidal shape for its envelope with a peak at 0.5T S from the boundary.
• the phase angle of this sinusoidal shape would have a ⁇ /2 value for a sample distance of 0.5T S from the boundary, corresponding to a period of 2T S , two BPSK symbol intervals.
• ⁇ denote the sample distance from the boundary, where ⁇ ⁇ 0.5T.
• the envelope value may thus be approximated by:
• timing phase error e is based on a symbol timing period of T s .
• the timing error relative to the 2T S period of the sinusoidal envelope shape in the vicinity of a bit transition is actually 0.5e.
• points a and b are located from the symbol boundary by the following distances (time offset from boundary) :
• envelope values for samples a and b when a bit transition occurs may be approximated by:
• a gating function G is used to yield a unity value when a binary symbol transition is detected, and a zero value in the absence of a transition. The function is obtained for the boundary between the (n - l)th and nth symbol as follows:
• G n 0.5 - 0.5 sgn (x a x b + y a y b )
• An error detector for symbol timing is obtained from the product of G n and the conditional error detection function d n .
• This conditional error detector is a function of the component pairs x a , y a and x b , y b , as
• N d is the number of detected symbol transitions for the N symbol boundaries, as N
• the estimator of timing phase error based on s 2 complex samples per BPSK symbol is given for the nth boundary (between symbols n-l and n) by the expression below - ⁇ ⁇ - 2 ⁇ ?,a ⁇ ctan l(r b -rJKr b +rj
• the arctan function is approximately equal to its argument and the timing error estimate is thus roughly proportional to the difference of the envelope values at points b and a.
• the two QPSK symbols of interest must be represented by vectors. These two symbols, with indices n and n + 1, will be denoted by z n « X n * JY n » A n e J n
• Vector components X and Y are determined from the average of the two center samples of a QPSK symbol.
• a reference vector for the differential phase is desired.
• the reference is obtained from the Z n .. vector with a phase rotation of -7T/4 radians.
• the reference vector for the nth symbol is thus given by:
• the signal vector Z n for the nth symbol is the product of the reference vector R.. and the differential vector W n for the transition in the nth boundary region, between symbols n - l and n, as
• the components of the nth isymbol vector are related to components of R.. and W n as follows:
• the differential vector has a phase angle ⁇ n and some magnitude of K n , as where
• the reference vector W is determined.
• the signal vector for the nth symbol is obtained.
• the differential vector is calculated. It is the binary components of the differential vector that are most useful. A positive value for U n or V n indicates no transition for that component of the differential vector, while a negative value indicates a transition.
• U H - K n cos ( ⁇ adj) V. Y Q V. n n
• Transition detectors for the two binary differential components are defined by
• Each detector yields unity gain when a transition is detected and zero gain for no transition.
• the detector gain is multiplied by factors d n and e n that are roughly proportional to the timing error. For the nth transition region,
• each component (U or V) of the differential vector W at points b and a time instants t b and t a ) may be used to roughly estimate the timing phase error when a transition occurs.
• the component amplitudes may be approximated at points a and b in terms of some constants K, and K 2 by:
• the timing estimates from N total transition regions are averaged to reduce the effect of signal distortion and additive noise. Only some N d binary transitions will be detected, and the average timing error is estimated from N N
• Determination of Fourier components at a frequency of R s for the squared envelope allows symbol synchronization to be applicable to either BPSK or QPSK. Such a technique is, therefore, highly desirable for the burst communications that may employ either of those modulations.
• the transition regions have waveforms corresponding to a frequency of R s /2.
• the phasing of the frequency components at R s /2 from envelope variations at symbol transitions is equally likely to be constructive or destructive; that is, the expected value of the Fourier component at R s /2 is zero.
• the frequency is doubled and the phasing is always constructive. Therefore, there is an expected value of the Fourier component at R s for the squared waveform that has a magnitude proportional to the number of transitions.
• R s ⁇ n carrier phase for the quadrature demodulation during the nth symbol interval.
• the waveform frequency is R s /2, but the polarity is dependent on ⁇ n . Also, there is a phasing difference of i ⁇ radians for odd and even symbols. Thus, there would be no average Fourier spectral component at R s /2.
• the waveform has a much more complicated shape than that given by the preceding equation. There are, however, some components of cos (2 ⁇ rR-.t- ⁇ ) associated with all symbol transitions. It is these components that can be used to obtain fine symbol timing for either BPSK or QPSK.
• the frequency of the reference generators is R,. Because coarse timing is not required, the phase is arbitrary, with some unknown value of ⁇ .
• the quadrature references for obtaining spectral components at R are:
• references P and Q have some unknown timing phase ⁇ .
• the Fourier components can be used to estimate the difference between the timing phase ⁇ of the complex samples Z and the phase ⁇ .
• ⁇ refers to the initial phase error in sampling time.
• ⁇ is not the same as e in the previous two-step synchronization, for which e referred to the residual timing phase error after the first step of coarse synchronization.
• e ⁇ - W ⁇ will be used to denote the residual timing error after the one-step synchronization is acquired.
• N total number of symbols included in processing
• Quadrature timing references may be generated using either of two methods.
• these references are derived from samples of the output of a continuous generator with frequency R s and some unknown constant phase ⁇ .
• P(nt 0 ) is obtained directly from the generator output, while Q(nt 0 ) is obtained for a 90° shift of the output.
• the second method there is no continuous generator. Instead, P(nt 0 ) and Q(nt 0 ) for different n are obtained directly as discrete values from two stored sequences. Then, the reference phase angle can be selected to yield only specific values at nt 0 times, such as +1.
• phase ⁇ of the squared waveform is considered to be the standard.
• the timing error ⁇ of the references P and Q may be determined from the Fourier coefficients, U and V.
• P(nt 0 ) and Q(nt 0 ) are derived from a continuous generator, it may be desirable to provide a new reference with the correct phase, ⁇ .
• Quadrature references, P' and Q 1 for this new timing generator are represented as follows.
• V K s sin
• the new timing references may be generated as linear combinations of the old quadrature references in accordance with
• N s s N samples to process.
• Fourier components of cos (2 ⁇ rR s t - ⁇ ) and sin (2 ⁇ rR s t - ⁇ ) can be obtained from the N s samples of the envelope squared by the following equations:
• V ⁇ nt > sin (2 ⁇ Rj ⁇ t 0 - ⁇ )
• ⁇ r (nt 0 ) 2 ⁇ rR s nt 0 - ⁇
• Timing accuracy for the fine symbol synchronization is dependent upon both the pulse shapes (after matched filtering) and the number s of samples per symbol interval.
• An upper bound on synchronization performance can be made, however, based upon continuous waveforms, ideal pulse shapes, and a linear channel that is corrupted only by additive white Gaussian noise (AWGN channel) .
• AWGN channel additive white Gaussian noise
• ISI causes perturbations of the waveform positions about the mean value.
• ideal waveforms it is meant that such pattern-induced timing jitter from ISI does not occur, and that the waveform shapes in an interval of ⁇ T s /2 about a symbol transition have a sinusoidal shape at a frequency of R s /2 and a phase angle of ⁇ /2.
• Additive Gaussian noise ⁇ with zero mean and a variance of ⁇ 2 will also cause an in-phase timing component.
• a.noise variable j8 with zero mean and variance ⁇ will cause a quadrature timing component.
• the total signal plus noise at baseband may be represented by
• the timing variance of interest is for the doubled frequency term at R s after squaring.
• the residual phase error is e and its variance is
• the UW has transitions at one-half of the symbol boundaries.
• the variance of the residual timing phase error after correction by the symbol synchronizer would be: a " HE ⁇ / o
• the required N may be doubled.
• E s /N 0 10.
• the required number of symbol intervals for the desired timing accuracy is then about 100:
• the complex samples may be repeatedly processed to obtain the required synchronizations and finally to achieve data detection and UW detection. It is assumed jthat detection of burst presence and coarse frequency synchronization have been obtained first. Then, matched filtering is performed. After matched filtering, the complex samples " are then processed to achieve symbol synchronization.
• Coarse symbol synchronization provides the timing resolution necessary for the correct grouping of samples so that each member of a group of s samples falls within the same modulation symbol interval. The symbol boundaries lie somewhere between the consecutive samples from adjacent symbols.
• the second step in symbol synchronization is to obtain the fine timing that establishes where between the samples the symbol boundaries lie. Information from waveform shapes by symbol transitions is used to estimate the boundary locations.
• metrics are formed for i different timings or partitionings of the samples into groups of s consecutive samples.
• the Fourier technique is applicable to both BPSK and QPSK. Although this method can provide fine timing after coarse timing has been obtained first, the first step is unnecessary. Therefore, the step for obtaining coarse timing can be omitted. Consequently, symbol synchronization based upon obtaining Fourier components of the squared envelope appears to be indeed the simplest of the methods that were studied.
• the estimated timing phase error is defined by the notation X.
• a simple explanation of symbol synchronization is as follows.
• the detection loss caused by rms timing error will probably be negligible.
• the equations for timing jitter are based upon continuous rather than discrete signals.
• Use of filtering that limits the signal spectrum to less than 2R S total width should be employed. For instance, Nyquist filtering with a rolloff factor of p results in a total bandwidth of R s (1 + p) , and squaring of the envelope doubles the bandwidth.
• Carrier synchronization is investigated in this section of the disclosure for burst communications without a synchronization preamble to facilitate acquisition.
• the only burst overhead is a unique word (UW) that is necessary to define the location of the start of the data or message portion of the burst.
• UW unique word
• All of the required synchronizations for the demodulator are acquired sequentially by repeated processings of the stored complex samples of the received transmission burst.
• Knowledge of the UW pattern is taken advantage of in using the UW as an aid in acquiring some of the synchronizations.
• Detection of burst presence and the estimation of coarse frequency were described above. Because the UW is used in the correlations at different tones to determine coarse frequency, coarse burst synchronization is also provided by the same operation. As also described above, matched filtering is employed after coarse frequency synchronization. Then, as further described above, symbol synchronization is acquired on the output samples from the matched filter. After the estimation of symbol timing, interpolation of the output samples of the matched filter is employed to compute one complex sample per modulation symbol at the appropriate timing instant for bit decisions to be made. For the assumed symmetrical pulse shapes, the correct sampling times correspond to mid-symbol locations. Any further processings for carrier synchronization and data detection are then performed only on these samples at nominal mid-symbol locations.
• Synchronization performance is affected by intersymbol interference (ISI) and additive noise. Averaging over the total burst to increase the signal- to-noise power ratio (S/N) is very effective in reducing the errors in frequency and phase caused by ISI, because the variance of the phase jitter produced by ISI is inversely proportional to the square of the averaging interval. Phase jitter from noise has a variance that is inversely related to averaging time and is therefore dominant. Synchronization performance is analyzed for the recommended methods of frequency estimation and phase estimation. Formulas of the error variances are given as functions of E s /N 0 and the total burst length N in symbol intervals.
• Carrier synchronization is referred to here as the estimation of fine frequency and carrier phase.
• the two estimators are made from the mid-symbol samples of the stored burst record of some N modulation symbols. Then, the complex samples are corrected for phase to values corresponding to coherent detection. Finally, bit decisions are made on these corrected samples.
• the phase angle of the sample is given by:
• ⁇ n arctan (y ⁇ x,,)
• N 0 the noise power density.
• E s denote the received signal energy per modulation symbol. If E s /N 0 is sufficiently large, then the envelope must be considered to be quasi-constant with a mean of Vie. Also, the variance of the phase error ⁇ n will be approximated by:
• the phase error is a linear function of quadrature noise level, and is therefore a Gaussian variable.
• the phase angles of the N symbols can be processed rather than the quadrature components without any loss of optimality.
• ⁇ n - ⁇ n + ⁇ n arctan (Y../X.,) where the sampled components, including noise, are X n and Y n .
• phase angles are random.
• Pairs of samples of ⁇ +n and ⁇ . n can be averaged to obtain N/2 estimates of the phase at burst center. This is evident by noting that the effect of phase rate is equal and opposite for ⁇ n .
• ⁇ -. -m ⁇ t + m ⁇ command + m ⁇ -, + ⁇ ⁇ - ⁇
• Each individual phase estimate is a white Gaussian variable with mean of m ⁇ p and the same variance about the mean. This variance is given by: ⁇ 2 -, m£ ⁇ 2 ⁇ n 2 °>n
• phase variance per modulated sample is:
• a carrier reference for coherent demodulation requires an estimate of phase rate ⁇ in addition to the estimate of ⁇ 0 .
• the estimated phase correction prior to coherent detection is - ⁇ n for BPSK and + ⁇ n for QPSK, where
• phase rate is equal to phase shift divided by the time interval.
• nth individual estimate of ⁇ is for positive n given by:
• phase rate or radian frequency is obtained from a weighted average of the N/2 individual estimates of ⁇ .
• g n used to denote the weighting coefficient for the nth individual estimate
• the overall estimate of phase rate is expressed by:
• ⁇ e is the equivalent number of total individual estimates given by:
• the weighting coefficients correspond to tap gains for a digital filter with a finite impulse response (FIR filter) .
• FIR filter finite impulse response
• the S/N for ⁇ is maximized by "matched filtering," in which each gain term, g n , is directly proportional to the S/N of the individual estimate, ⁇ n , or inversely proportional to its variance. Note that:
• N e The normalizing term, N e , is given by:
• the average phase angle is determined for the first and second halves of the burst.
• carrier phase and phase rate are estimated from linear combinations of the averages of carrier phase for the two halves of the burst.
• Phase rate ⁇ causes ⁇ b to differ from m ⁇ 0 , the phase at burst center, by +m ⁇ (N/4) T s .
• ⁇ a differs from m ⁇ 0 by -m ⁇ (N/4) T s in the absence of noise. Note that the effects of ⁇ on phase are equal in magnitude and opposite in sign for the average phases for the two halves of the burst. Thus, an estimate of m ⁇ 0 is obtained from the averages of X a and
• the variance of the achieved phase estimate of ⁇ 0 is only a fraction 1/N of the phase variance for each complex sample representing one modulation symbol.
• the estimate is asymptotically optimum at high E s /N 0 and given by:
• phase rate the phase rate after coarse frequency acquisition can be as large as ⁇ /8 radians per symbol interval.
• a two-step approach to carrier synchronization is proposed to avoid the problems associated with excessive phase rate.
• an estimate will be made of the initial phase rate, ⁇ e , by processing only complex samples for the U u symbols of the UW.
• the UW is a known binary sequency with modulation coefficients A., of +1 and -1 values, multiplication by m is not required for modulation removal. Instead, the complex sample for each modulation symbol is multiplied by its known modulation coefficient to recover an unmodulated set of N. j complex samples.
• ⁇ e of phase rate is used to correct the phase values of the complex samples of all N modulation symbols
• the average phase of the UW samples is computed.
• this average phase, ⁇ 0 corresponds to that of the carrier at the middle of the UW.
• This phase estimate of ⁇ 0 is obtained without ambiguity, and will be used to resolve the phase ambiguity of the carrier reference obtained in the second step of carrier synchronization.
• the second estimate that of ⁇ c at the middle of the data burst
• its rms error is much smaller than that for the first estimate because the burst length, N D far exceeds the length, N u , of the UW.
• the phase rate, ⁇ remaining after the first frequency correction is estimated.
• ⁇ 0 After initial correction of symbol polarities for the UW, its unambiguous estimate of carrier phase at UW center is recomputed as ⁇ 0 .
• the new phase estimate, ⁇ c calculated for the center of the data burst has an m-state ambiguity, it has a small rms error.
• ⁇ c and ⁇ 0 should be identical except for the phase ambiguity of ⁇ c . Therefore, ⁇ c is compared to ⁇ 0 to resolve the m-state phase ambiguity. Then, ⁇ c is used as a coherent reference to correct the phases of all modulation symbols, that is, to effect coherent demodulation.
• i has values of -2, -1, +1, and +2.
• each frequency estimate is defined by:
• the overall estimate is obtained by a weighted average of the two individual estimates of phase rate.
• the variance of the estimate is:
• the overall estimate of phase rate has a variance of:
• t n denoting the time location relative to burst center for the nth symbol, its phase correction based on the estimation of phase slope is:
• phase estimate ⁇ 0 at the middle of the UW has been described for the first step of carrier synchronization. This estimate was without ambiguity for a point (N D + N practical)/2 symbol intervals prior to burst center.
• the phase estimate for the second processing has an m-state ambiguity, which can be resolved by comparing it to that of the unambiguous estimate of ⁇ 0 .
• Modulation removal must be effected before coherent addition can be performed.
• w n (z radical) m (-1) ( "- 2 ⁇
• phase angles for these N 2 complex samples are defined by:
• the average phase at burst center is calculated from:
• Phase rate is given by the difference in phase divided from the time interval between the two samples. Division by m is required to offset the phase multiplication by m.
• An overall estimate of phase rate is then obtained from the weighted average of frequency estimates.
• N 2 is related to the burst length, N D , by:
• the variance of the overall estimate of phase rate is related to that of ⁇ , by:
• the ⁇ ., estimate of phase rate has an rms error of: a- - R ⁇ * — R s*—
• the overall phase estimate has its variance reduced by a factor of N e from that for ⁇ -. Therefore ,
• the rms error of the phase at mid-burst is: ax _
• the unambiguous phase estimate, d 0 at the middle of the UW is recalculated after the phase correction of the N JJ symbols of the UW.
• the accurate but ambiguous phase estimate, ⁇ c obtained from the N D burst symbols in the second step ,of carrier synchronization is compared with d 0 to remove the phase ambiguity.
• Estimated phase, 0 C at the center of the data burst is used to correct the modulation symbols for coherence prior to bit decisions.
• coherent vectors Z are obtained from the vectors z prior to phase correction by:
• Carrier Synchronization methods have been investigated for the estimation of phase rate and carrier phase for burst communications that do not employ synchronization preambles. Elimination of burst preambles is for the reduction of overhead, so that the access efficiency for burst communications via satellite will be high even for fairly short bursts.
• Some overhead of approximately 16 modulation symbols is necessary for a UW that defines the starting point of the data or message portion of the burst.
• the data modulation can be either BPSK or QPSK.
• a binary UW is assumed in both cases, which for QPSK is achieved by using two antipodal signal points of the 4-ary constellation.
• the modulation must be removed to obtain unmodulated samples for estimating carrier phase and phase rate.
• the binary UW sequence is known.
• symbol synchronization and burst location have already been determined prior to carrier synchronization. Therefore, multiplication of phase by m is not required; instead, the modulation removal on the UW is achieved simply by multiplication by the known binary UW sequence of modulation coefficients, which have values of +1 and -1.
• Carrier synchronization is based upon the mid ⁇ symbol complex samples of all N modulation symbols after matched filtering. All algorithms shown for estimating carrier phase and phase rate are applicable to both BPSK and QPSK. Some of the algorithms, however, are reliable only when E s /N 0 is very large, such as 17 dB or higher. Therefore, algorithms that are asymptotically optimum at high E s /N 0 are not recommended because of possible poor performance at low to moderate E s /N 0 . Instead, a method of carrier synchronization is recommended that will be very reliable at moderate E s /N 0 values, such as 7 dB for BPSK and 10 dB for QPSK.
• a two-step processing is recommended to overcome the problem of excessive phase rate.
• a carrier phase estimate without ambiguity is also obtained for the mid-point of the UW, with the phase designated as ⁇ 0 .
• the N D symbols of the data burst are processed. Multiplication of phase by m for modulation removal reduces the effective E s /N 0 by a factor of m.
• the effective E/N 0 per complex sample is very large, so that phase estimation is highly reliable in the second step.
• a new phase estimate, ⁇ c for the middle of the UW is calculated after the phase corrections. Multiplication of phase by m for modulation removal in the data burst necessitates division by m later, with an m-state phase ambiguity occurring from the division.
• This ambiguity for the very accurate carrier reference, ⁇ c from the second step of carrier synchronization is resolved by comparing this ambiguous estimate with the unambiguous phase estimate, ⁇ 0 , obtained in the first processing step.
• Performance formulas are given for carrier synchronization as functions of burst length N and E s /N 0 .
• N D 128 symbols and an E s /N 0 of 10 dB
• the phase estimate at burst center has an rms error of only 1.3°.
• the estimate of phase rate has an rms error of about 0.0006 R s .
• Use of both estimates is necessary to estimate phase for the N different symbols in the burst. Symbols near both ends of the burst have the worst phase estimates, but even there the rms error in less than 2.6°.
• the modulation is contained only in the real component, X, of the complex signal, Z.
• a bit decision is therefore made on the nth symbol vector in accordance with
• A-- sgn (X n ) These bit decisions have only +1 and -1 values.
• the received transmission consists of a modulation bit variable A multiplied by a cosine carrier plus another modulation variable B multiplied by a sine carrier. Therefore, two bit decisions are made on each modulation symbol, with these decisions made on the two components, X and Y, of the complex signal Z.
• nth QPSK symbol For the nth QPSK symbol,
• the effect of imperfect synchronization upon detection performance is not simple to calculate.
• the effect is merely a lowering of the available signal voltage by a factor of cos ⁇ . Therefore, the BPSK conditional error probability for a fixed ⁇ and an AWGN channel is:
• BPSK has only one bit per symbol and QPSK has two bits per symbol.
• the UW is detected after bit decisions are made on the N ⁇ symbols of the UW.
• UW detection has already been included in the algorithm to detect burst presence and estimate coarse frequency. It is also possible, if so desired, to utilize UW detection after bit detection to resolve the ambiguity in carrier phase synchronization. In the recommended two-step method of carrier synchronization, however, the unambiguous phase estimate, d 0 , at the center of the UW is used to resolve the m-state ambiguity in the accurate estimate, d c , of the carrier phase at the center of the data burst.

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  • 1992-11-27 WO PCT/US1992/010018 patent/WO1993011605A1/fr not_active Ceased
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