JPH1022873A - Symbol timing estimating method for spread spectrum signal - Google Patents

Abstract

PROBLEM TO BE SOLVED: To find symbol timing with a software at high accuracy in a short time. SOLUTION: The mutual correlation between a complex base-band signal r(k) of QPSK, with which a spread spectrum signal from a terminal 11 is detected, and demodulated data e(-jθk) from a terminal 26 is calculated (25), and filtering processing is performed to this mutual correlation by filters 28a, 28b and 28c. These filters are coefficients am , bm and cm approximating Nyquist filters at the respective time as secondary formulas at symbol timing τ. While using the result of this filtering processing, the τ is calculated (29).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention
The present invention relates to a method for estimating a symbol timing of a spread spectrum signal used in (code division multiple access).

[0002]

2. Description of the Related Art It is necessary to estimate a symbol timing for measuring each parameter in a transmitter or a receiver of spread spectrum communication. Conventionally, the symbol timing is estimated by M from the input spread spectrum signal.
A complex baseband signal of phase (M is an integer of 2 or more) PSK is obtained, and demodulated data (phase data) obtained by demodulating the complex baseband signal and the complex baseband signal are used as shown in FIG. I was going.

A complex baseband signal r (t) of, for example, QPSK detected from an input terminal 11 to a baseband signal
Is supplied to the sampling circuit 12 and the differentiating circuit 13, and the sampling circuit 12 outputs the voltage control clock (VCC) 1
4 and the output of the differentiating circuit 13 is also sampled by the output of the voltage control clock 14.
Sampled at Each sampling output of the sampling circuits 12 and 20 is multiplied by an ideal signal (reference signal) exp (-jθk) (θk is the k-th phase of the demodulated data) from the signal generator 17 by multipliers 15 and 16, respectively. These multiplied outputs, that is, deviations from the ideal data, are added by accumulators (integrators) 18 and 19, that is, averaged. The outputs of the accumulators 18 and 19 are multiplied by a multiplier 21, and The deviation from the symbol timing is detected, the real part is detected by the circuit 22, and the detected output controls the clock signal of the voltage control clock (VCC) 14,
The output of the VCC 14 is synchronized with the symbol timing.

Hereinafter, it will be described that the symbol timing of a complex baseband signal of QPSK can be estimated by the maximum likelihood estimation method according to this conventional technique. This is described in the document "Digital Communications".
Proakis McGraw-Hill issued. , But will be briefly described below. First, the log likelihood function ∧ _L (φ, τ) can be set as follows.

∧ _L (φ, τ) = Re [exp (−jφ)
{R (t) R ^* (t−τ) dt] where r (t) is the received signal (complex baseband), R
(T) is a reference signal, τ is a time delay, φ is an initial phase of a carrier, T is a measurement time, ∫ is from 0 to T, and * is a complex conjugate. In the maximum likelihood estimation method, this log likelihood function ∧ _L
Τ is determined so that (φ, τ) is maximized.

[0006] In other words, to erase the full to φ the _{∂∧ L / ∂φ = 0 ∂∧ L} / ∂τ = 0, solve for τ. From the above equation, τ is determined so as to satisfy the following equation. Re [Z (τ) · (∂Z ^* (τ) / ∂τ)] = 0 (1) where Z (τ) = ∫r (t) R ^* (t−τ) dt (2) ∫ is from 0 to T, and R ^* (t−τ) = Σg (t−τ−kT _c ) exp (−jθk) (3) g (t) is the impulse response characteristic of the Nyquist filter (g (t) = 0 for | MTS |> 0), θ _k
K th phase of demodulated data, T _c is the chip interval, T _s
Is a sampling period, and Σ is from k = 0 to a value corresponding to T. Therefore, when these are substituted into the equation (1), the following is obtained.

[0007] Re [Z (τ) · ∂Z * (τ) / ∂τ] = Re [Σ {exp (-jθk) · Yk (τ)} · Σ {exp (-jθ k) ∂Y k (τ ) / {Τ}] = 0 (4) where Y _k (τ) = {r (t) g (t−τ−kT _c ) dt (5), and ∫ is from 0 Up to T.

That is, Σ ｛exp (−jθk) · Y _k
(Τ)｝ corresponds to the output of the circuit 18 in FIG.
xp (−jθk) {Y _k (τ) / {τ} corresponds to the output of the circuit 19, the VCC 14 is controlled so that the real part of the product of these outputs becomes zero, and the symbol of the input QPSK complex baseband signal From the timing, the sampling circuits 12, 20
Is estimated as the sampling timing.

In the configuration shown in FIG. 2, the symbol timing is estimated by the maximum likelihood estimation method.

[0010]

The conventional method shown in FIG. 2 is a method configured by hardware. When this method is realized by software, a highly accurate solution can be obtained because the input signal is a discrete time signal. I can't. Further, in order to obtain a highly accurate solution, the sampling rate (sampling speed) must be increased, so that the amount of calculation by the interpolation filter increases and the processing time becomes longer.

[0011]

According to the present invention, a cross-correlation between a complex baseband signal and demodulated data is calculated, and the three Nyquist filter characteristics approximated to the cross-correlation as a function of the symbol timing τ are calculated. , And the symbol timing is calculated using the three filter processing results.

A description will now be given of how symbol timing can be estimated by such a method. _{Let the} sampling period T _S be T
_When equal to _C / 8 (T _C : chip period), the reference signal can be expressed by the following equation from the equation (3). R ^* a _{(nT s -τ) = Σ k} = 0 g ({8k-n} T S + τ) exp (-jθk) ··· (6) where the Nyquist filter characteristic g (t), as follows Is approximated as a quadratic expression related to τ.

[0013] _{g (mT S + τ) =} a m + b m τ + c m τ 2 ··· (7) provided that m = 8k-n. Equation (2), Equation (6),
Substituting equation (7) into equation (1) yields the following. Re [Z (τ) · (∂Z ^* (τ) / ∂τ)] = T _s ² Re [A · B ^* + (| B | ² + 2A · C ^* ) τ
+ (B ^* · C + 2B · C ^* ) τ ² +2 | C | ² τ ³ ] = 0 Here, since τ is a very small value, ignoring the second-order and higher-order terms substantially satisfies the expression (1). Symbol timing τ
Is determined by τ = −Re [A · B ^* ] / (| B | ² + 2Re [A · C ^* ]) (8) _{However, A = Σ m a m D} m ··· (9) B = Σ m b m D m ··· (10) C = Σ m c m D m ··· (11) D m = Σ k r _8k-m exp (−jθ _k ) (12) r _8k−m = r (｛8 km−T _s ) This equation (12) gives the input complex baseband signal r
(K) and the cross-correlation between the demodulated data e (−jθk).

Next, as shown in the equation (7), the coefficients a _m , b _m , c of the Nyquist filter approximated as a quadratic equation of τ
_Here is a method to find _m . First, the Nyquist filter to be originally required time from the apex of the impulse response so as not occur intersymbol interference to the first zero point must be T _C. If the roll-off coefficient is α, the impulse response of this filter is

[0015]

(Equation 1) Becomes Then, the impulse response characteristics of the Nyquist filter are approximated by equation (7), and the coefficients a _m , b _m ,
Find _cm . Here, as an approximation method, the Nyquist filter is set in the section ｛(n−0.5) T _S to (n + 0.5)
T _S ｝, (n = −M, −M + 1,..., M−1, M)
And the least square method is used in each range. (All outside the section are set to 0.) As described above, the Nyquist filter is approximated by a quadratic expression relating to τ. However, as an approximation method, it can be approximated by a third or higher order expression relating to τ. However, even if the approximation is performed by the third or higher order, the result is exactly the same as the case of the second approximation. It is τ
This is because the second and higher-order terms are ignored at the end of obtaining. Therefore, it is meaningless to approximate the Nyquist filter with a third-order or higher-order expression related to τ.

(The quadratic term is related because τ in the equation
This is because there is a first derivative with respect to. However, if we change to an algorithm that does not ignore terms of second or higher order at this end, the result should be different. Naturally, it seems that the higher the order of approximation, the higher the accuracy. However, it is necessary to finally solve a higher-order expression related to τ, and the second-order approximation to τ is sufficient even from the required accuracy.

[0017]

FIG. 1 shows an embodiment of the present invention.
First, the cross-correlation calculator 25 receives the received complex baseband signal r (k) and the demodulated data exp (−jθ) from the terminal 26.
Using k), the cross-correlation value D _{m is obtained} by the following equation, that is, equation (12).

[0018] _{D m = Σ k r 8k-} m exp (-jθk) the cross-correlation value D _m, by entering coefficients a _m, b _m, a c _m filter 28a with each, 28b, to 28c (9) Expressions A, B, and C in Expressions (10) and (11) are obtained. Finally, the symbol timing calculation unit 29 calculates Expression (8) from A, B, and C to obtain τ.

Next, a comparison will be made between the case where the conventional method is realized as it is by software and the method of the present invention. Regarding accuracy Conventional method Since the input to VCC14 is only the sampling interval, the obtained estimated value has no resolution higher than the sampling interval. That is, the sampling rate is 9.830M, for example.
In the case of Hz, the error is about 100 nS. Actually, since there is an error due to the differentiation processing corresponding to the differentiation circuit 13,
More than that.

Since the method of the present invention approximates the characteristics of the Nyquist filter and mathematically finds the solution, the solution can be obtained with high accuracy. According to actual measurements, the error was as small as about 10 nS. Calculation time Conventional method If high resolution is desired, interpolation must be performed to shorten the sampling interval, which takes time.

Since the interpolation method is not particularly necessary, the calculation can be performed in a short time. That is, if the conventional method is calculated with the same level of accuracy as the method of the present invention, the input signal must be sampled at a sampling rate 10 times or more than that of the present method. In the method of the present invention, four correlation calculations are performed. Therefore, the conventional method requires at least 10/4 = 2.5 times or more the calculation amount.

[0022]

As described above, according to the present invention, the symbol timing can be estimated with high accuracy and in a short time by the arithmetic processing.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a functional configuration of an embodiment of the present invention.

FIG. 2 is a block diagram showing a conventional symbol timing estimation method.

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[Procedure amendment]

[Submission date] October 29, 1996

[Procedure amendment 1]

[Document name to be amended] Statement

[Correction target item name] 0006

[Correction method] Change

[Correction contents]

[0006] In other words, to erase the full to φ the _{∂∧ L / ∂φ = 0 ∂∧ L} / ∂τ = 0, solve for τ. From the above equation, τ is determined so as to satisfy the following equation. Re [Z (τ) · (∂Z ^* (τ) / ∂τ)] = 0 (1) where Z (τ) = ∫r (t) R ^* (t−τ) dt (2) ∫ is from 0 to T, and R ^* (t−τ) = Σg (t−τ−kT _c ) exp (−jθk) (3) g (t) is the impulse response characteristic of the Nyquist filter (g (t) = 0 for | MT _S | > 0), θ _k
K th phase of demodulated data, T _c is the chip interval, T _s
Is a sampling period, and Σ is from k = 0 to a value corresponding to T. Therefore, when these are substituted into the equation (1), the following is obtained.

Claims (1)

[Claims] 1. An M-phase signal from an input spectrum signal.
A complex baseband signal of SK (M is an integer of 2 or more);
A method of obtaining the demodulated data and estimating the symbol timing of the complex baseband signal by using the data; and calculating a cross-correlation between the complex baseband signal and the demodulated data. A symbol timing estimation method for a spread spectrum signal, comprising: a step of performing a filtering process using three Nyquist filter characteristics approximated as functions; and a step of calculating a symbol timing using the three filtering results. .