WO2006023012A2 - Distance division multiplexing - Google Patents

Abstract

General method for extracting an electromagnetic or other wave-propagated signal of a desired source from the overall received waveform containing the sum of signals from a multiple of such sources comprising the steps of first expanding the spectrum of the received sum of signals in proportion to their source distance so as to spectrally isolate the signal from the desired source, selecting the signal spectrum and spectrally compressing the selected signal back to its original band of frequencies. The distance dependent expansion is performed by scanning the space gradient of the signal spectrum.

Description

Distance division multiplexing

BACKGROUND OF THE INVENTION

Technical field

This invention generally pertains to communication of information between a source and a receiver More particularly, it concerns the use of source distance information at the receiver to ensure maximum bandwidth of communication and avoid noise and interference from other sources operating over the same frequencies

Brief description of the prior art

Tn his classic paper titled "A mathematical theory of communication" (Bell System Technical Journal, vol 27, pages 379-423,623-656, 1948), Claude E Shannon defined the object of communication technology as enabling the transfer of information from a source to a receiver A perfect receiver should be accordingly defined ab one that could receive an arbitrary signal /(r, £) from a transmitter at a relative distance r without noise, distortion or interference from any other bource Such an ideal receiver is unachievable by Shannon's theory, but current technology is especially worse off with respect to the criterion of interference, because it splits the available physical bandwidth in some way to keep the signals from multiple sources separate all the way The separation techniques include frequency division multiplexing (FDM) used in radio and television broadcast, wavelength division multiplexing (WDM) and mode separation in optical fibres, spread-spectrum encoding or code division multiple access (CDMA), or time division multiplexing (TDM) and its asynchronous variant, the Ethernet Recent variations of this theme include blind signal processing as discussed in the book titled Adaptive Blind Signal and Image Processing (Wiley, 2002, authors A Cichocki and S Amaπ), which uses statistical analysis to cope with the distortion of the original separation parameters by the wireless channel, and autocorrelation matching, in which a "prefilter" is applied at the source, as described by R Liu, H Luo, L Song, B Hu and X Ling m their paper titled "Autocorrelation - a new differentiating domain for multiple access wireless communication" , in the Proceedings of ISCAS, 2002 All of these techniques effectively share the channel capacity corresponding to the usable physical bandwidth Lately, another such idea, using multiple transmitting and receiving antennae in parallel, is called space division multiplexing (SDM), as in the articles "Reduced complexity space division multiplexing receivers" by G Awater, A van Zelst and R van Nee in the Proceedings of IEEE Vehicular Technology Conference, May 2000, and "Channel Estimation and Signal Detection for Space Division Multiplexing in a MIMO-OFDM System" , by Y Ogawa, K Nishio, T Nishimura and T Ohgane in IEICE Transactions on Communications, VoI E88-B, No 1, January 2005 The usage is debatable, since it concerns merely using a larger antenna cross section to achieve a correspondingly larger channel, i e there is no actual division of space whatsoever, even though the parallel antennae could be using complementary polarizations, which, if used to transmit different channels, would have qualified as a form of space division multiplexing However, it would still be far ambitious than the objects and motivation of the present invention, as follows If only we could string separate cables or fibres between each receiver and its selected source the sharing of the channel capacity would become unnecessary, and the entire capacity of the cable or fibre link would become available to each receiver and its respective source It is desirable to have a similar capability for wireless technology, which is being steadily pushed into increasingly higher frequency bands for bandwidth as channels compete withm the same frequency bands over the same physical space The mam challenges are directivity and range selection The first is partly addressed by using high operating frequencies so that the wavelengths are comparable to or less than the receiver dimensions, and partly by phased array technology, which enables source direction selection without physically moving an antenna There has been no practical solution for the second, although as range and angle are mutually complementary as physical dimensions of space, and on that basis, a similar, receiver-side technology could have intuitively thought possible The present invention is a solution based on a method for enabling a receiver of electromagnetic or other waves to determine the distance r to the source of the waves by modifying a receiver parameter, as described in copending application titled "Passive distance measurement using spectral phase gradients" , filed 2 July 2004, number 10/884,353, incorporated here m its entirety by reference The method involves varying an instantaneous frequency selector ω at the receiver at a rate a, whereby frequency shifts δω become induced in the received waves in proportion to ar, so that r can be computed from a and δω This method avoids round trip timing (RTT) and coherent phase reference requirements, but it depends on the phase distribution, which is already utilized in current technology For example, o any kind of modulation as such involves a nonzero bandwidth spread, and frequency modulation (FM) especially relates to phase modulation (PM), o PM itself is also in use, for instance, in data modems as quadrature phase shift keying (QPSK), and for the encoding of colour in PΛL and SECAM broadcast television formats, and o in any case, all signal processing, including the autocorrelation matching and the blind signal processing methods mentioned above, involve manipulation of the signal phase

It has not been obvious, therefore, that this method can be used for source selection without being impacted by modulation or signal processing, and without interfering with these operations Moreover, in the presence of a modulating signal, a received carrier is no longer an almost pure sinusoid, as would appear to be assumed in the copendmg application, so that even the inferred distance r{ω) would vary significantly over the received modulated carrier bandwidth

It is in fact generally unobvious how any form of distance determination could help in signal selection or source isolation An independent review of the copendmg application method observed, for example, that timing or coordinate information from the global positioning system (GPS) could be encoded in transmitted signals to enable source distance determination without RTT or coherent phase reference While the method could have other applications, it would be specific to signals actually bearing the encoded coordinate or timing information and thus less than general The encoded information would be generally available only after the signals are separated, and would be thus useless for the separation itself

A hitherto unaddressed need exists, therefore, for a method that can separate signals from multiple sources, that does not interfere with the signal phase distribution or depend on the signal form or content, and would enable the entire physical bandwidth available from a source to be utilized for communication with only that source, without interfering with signals from another source Such a separation is available for sources located at different directions from the receiver using phased array antennae as remarked, but not for sources along roughly the same direction and differing only in distance It would be also desirable to have a method that ran be applied over a large gamut of operating wavelengths, for example, from radio waves to ultraviolet frequencies, and even to acoustic waves It would be additionally desirable for the method to be also useful for detecting the presence of multiple sources, i e of interference, so as to enable a receiver to lock on to and track a selected source SUMMARY OF THE INVENTION

Accordingly, a primary object of the present invention is to provide a very general mechanism, whirh would be largely independent of signal form and content, for separating signals from multiple sources even when the sources are located along roughly the same direction from the receiver Another object is to enable, at a receiver, most if not the entire physical bandwidth between a source and the receiver to be made available for communication between them, without interfering with communication from other sources or receivers A secondary object is to provide a general means for detecting such interference and determining the causative source distance distribution

Principle of operation This ob]ect, and others which will become apparent, are achieved in the present invention, within a receiver receiving an overall waveform comprising a combination of signals J^ F₃ (ω) from a multitude of sources S₃ at distinct respective distances r₃, by applying a succession of transformations to the received combination of signals, as will be shortly described The notations £[] and TL\\ will be used to denote the lower and upper frequency bounds, respectively, relative to a predefined threshold amplitude a_th, i e

|F»|² < |α_tΛ|² if ω < L[F₃] or ω > H[F₃] (1)

Correspondingly, W₃ = Η[F₃] — L[F₃] will denote the respective bandwidths, so that

[H - £) [F₃ (ω)] ≡ H [F₃ («)] - L [F₃ (ω)] < W₃ (2)

A nominal bandwidth W > W₃ can be assumed as non overlapping portions of the spectra would be separable by filters The inventive procedure for extracting a specific signal F₁ then comprises the steps of A optionally first splitting the combined received signal into n > 1 subbands of successive widths β_\W , βiW , β_πW , i e into subbands n— 1 n

[£ + ∑ β»W, L + ∑ β_μW), μ = l n (3) μ=l /1=1 using a set of subband filters S_μ, so that ∑^ βμ = 1, and, writing {F₃} as short for ∑₃ F_{j >} ^we would have

C[S_μ{F₃}] = C[{F₃ }] + ∑ β_μW and Η[S_μ{F,}] = C[S_μ{F₃ }] + β_μW; (4) μ= l

B. applying to each subband S_μ{F_j } of the input signal [F₃ } a time- varying sampling or frequency selection mechanism as described in the copending application, characterized by a parameter α_μ independent of the source, and hence of the subscript j, to cause the subband spectrum to be linearly shifted to

H(a_μ)F_μ] (ω) = F_μJ (ω[l +

where F_μj ≡ S_μF_}, i.e. by shilts δω₃ ≡ ωa_μry, (5)

C. then applying a selection filter G_μι to the resulting shifted spectral sum to particularly select H_μF_μτ = H(a_μ)F_μt(ω) and reject H_μF_μj for all j φ ι, i.e.

G_μιH_μ ∑ F_μ, ∞ H_μδ_t3 ∑ F_μ, = H_μF_μx , where δ_tJ ≡ \ * ^ ^{~ j)} (6) i { 0 (i ≠ j)

and is approximate because the stop band rejection of real filters cannot be unity, so that

G_μιH_μ s= H_μG_μιδ_l:) , (7)

where G_μt ≡ G_μ denotes corresponding baseband filters of bandwidths β_μW;

D. applying the reverse mechanism H^~l ≡ H^~1 (a_μ) — H(-a_μ) to shift the result H_μF_μτ back to F_μt;

E and lastly, putting the subbands F_μι back together, in reverse to Step A, to obtain F₁

Note that Steps D and E can be interchanged, i.e. the subbands can be summed before applying the reverse mechanism, if the a_μ are equal. These steps form successive stages of signal processing in the receiver. The essence of the separation, contained in Steps B through D, is summarized by the following process flow:

{F_M} → H_μ{F_μ]} -≤^!→- G_μxH_μ{F_M} « H_μG_μtδ_tJ{F_μ,} * H_μF_μ "→^] F_μτ , (8) and may be alternatively summarized as a product of operations of the form

F₁₁₁ ^ H-¹ {a_μ) G_μ,H{a_μ) J2 F_μJ (9)

corresponding to the orthogonality relation

H-¹ {a_μ) G_μxH(a_μ) ^ δ_ιi. (10)

The utility of the method lies in the fact that the H operations depend only on α_μ which are independent of the signal sources, the latter being distinguished by the indices i or j in the above equations. The separation is obtained spectrally via the transformed filters G_μx ~ H_μG_μι (equation 7), applied in the transformed space as H^~i G_μιH_μ, per equation (9), instead of baseband filters G_μ, which per se cannot provide the separation. The design of G_μτ can be derived from that of G _μ by frequency scaling it by a_μr_x using known principles of filter design, the estimation of r, for this purpose will be described shortly.

The utility of subband processing is as follows. Consider that in its absence, amounting to taking n = 1 and β = 1, only a single parameter α would be applied at the receiver. If r, < r₁₊₁, the following general inequality must hold using the short notation H₁ for H[F₁] and L_x for .C[F₁]:

(l + αr,)W, < (l + αr_t+1)£,₊₁. (11 )

Solving for a from the first inequality yields

nr > ^{Hl ~ £}'⁺¹ H2Ϊ

which simplifies, for the common case of sources with identical component bandwidth allocations, to

^αr* ^≥ (Sr_t/rjC- W ⁼ [T71 ^{" 1}] ^{• (13)}

This bound diverges at small C, being positive only if

r_x W C > -J-W, or, equivalently, Jr₁ > T_x-, (14) but no choice oi a will suffice if L is less than this value

For example, at C = 0, the bound will be negative, but the foregoing procedure cannot possibly separate the bignals because the d c (ω = 0) components will not be shifted at all, as H(a)F₃ (0) = F₃ (0[l + (Xr₃]) = F₃ (0) by equation (23) The problem is that the lower bound and the spread W ≡ Ti — C are also scaled by H(a), so that the lower part of the signal spectrum tends to remain in the "spectral shadow" of any nearer sources This is not a special limitation of the method - very low frequencies as such generally pose problems such as the ratings of reactive elements needed for d c isolation, due to which baseband audio and video systems are invariably designed with lower frequency bounds well above 0 With modulated radio frequency signals, the limiting constraint becomes the physical source separation Sr₁, instead of C For any given C and W , there would thus be a sizeable range of δr_% over which a complete separation of signals would be impossible However, if C > 0, partial separation of a fraction β 6 [0, 1] of the bandwidth becomes possible, with the lower bound on a set by the condition

\δr_τ C I ^"1 W ar_τ > — 7^7 - 1 requiring only Or₁ > βr_τ — (15)

(_ r_t p w J L.

Although β signifies a compromise on the full separation of the signal spectrum, the separation is nevertheless useful as the separated parts comprise t he lower frequency band [C, C + βW] from the nearer source and the higher frequency band [H - βW, Ti] from the farther source, which will likely contain much of the information In particular, if the signal is preconditioned for separation by autocorrelation, the separated high frequency band \Η - βW, H] would serve as a strong reference tor autocorrelative separation of the remainder of the signal bandwidth [C, Η — βW) With subband processing, however, the conditions (15) become

°>^r _* ≥ T¹ FlF ^{~ X} requiring only Sr₁ > β_μτ_ι — , (16)

L ^"1 Pμ '^v J ^L-μ where C_μ is the lower frequency bound of the /ith subband These conditions are weaker than (13) and (14) by the factor β_μ, and assure separability for all subbands μ > 1 even at C = 0, as the subband lower bounds are raised to C_μ ≡ C + Y^Z₁ β_μW per equation (3)

Thus, with subband processing, near perfect separability can be assured in all cases, without a fundamental need for autocorrelation or other techniques that would involve signal modulation or content It is generally desirable, however, to keep the subbands as wide and as few in number as possible, however, because each subband entails shifting, filtering and reverse shifting operations, adding linearly to the complexity of the receiver It would be generally preferable, therefore, to keep n small, and indeed as close to 1 as possible

The secondary object of detecting interference and estimating the source distribution may be achieved by a simple variation of this procedure, comprising, after Step B, the alternative steps of

C measuring the lower bound C[H (a_μ)S_μ[F_j)] to compute the distance r_mln of the nearest source as

_(μ) (C[H{a_μ)S_μ{F,}] _ \

obtained from the relation

C[H(a_μ)S_μ[F₃}] = (1 + a_μr_x) C[S₁₁[F₀)], (18)

identifying the minimum of the μ-th subband of the shifted combined spectrum with the shifted lower frequency bound of that subband - the result will be nonzero if either C > 0 or μ > 1,

D and likewise measuring the upper bound Ti[H (a _μ) S₁₁[F_j)] to compute the distance r_max ol the farthest source from the corresponding relation

_r(μ) ₌ (H[H(a_μ)S_μ{F₃}) _ \ ^μ \ U[S₁₁[F₁)] ¹J ' ⁽¹⁹⁾

so that the spread of sources would be given by the vector of distance intervals [δi ^) where

In the numerators of equations (17) and (19), C and Ti are measured from the spectra, whereas in both the denominators of these equations and in Steps A-E of the mam inventive piocedure, C and Ti are likely to be known parameters of design The bound measurements may be performed in reverse order Importantly, as they concern derivatives of spectral distributions, thee measurements would be difficult if the specti a are discontinuous Smoothening, mterpolative and correlative techniques may be accordingly employed The maximum and minimum spread can be clearly estimated from these subband-specific values as

<5r_max = - ^mm{^r _ml) and <5r_mm = - rnaxjr^}, respectively (21)

The likelihood of detecting interference and separating the interfering sources would clearly improve with narrower subbands, as the interference might occur within the signal bandwidth W, and not affect the ends of the signal spectrum, i e dr^ > 0 for only some indices μ such that 1 < μ < n Tins would not be an issue for interfering sources of similar band spreads However, the technique would be also useful for eliminating narrow band noise or other narrow band signals that happerib to occur within the desired signal spectrum, for this, a large n, or small β_μ, would be required

Tf the object is to merely detect all such mterfeience, it would be more productive to use a single, sufficiently large shift factor α and a single tunable subband filter S(Q) of a variable centre frequency ω and a narrow pass-band δW <ε W, in order to periodically scan the received signal spectrum for interference The modified procedure m this case would be

A* applying the tunable filter S(Q) to the total received signal F(ω) (corresponding to [F₁]), for which

£[S(Q)F(ω)] = Q - δW/2 and TC[S(Q)F(ω)} = Q + δW/2, (22)

to obtain the filtered subband S(ω)F(ω) ≡ (S o F) (ω) ~ F(Q) at Q and vanishing outside of Q ± δW/2,

B* applying to the filtered subband (SoF)(ω) a time- varying sampling or frequency selection mechanism as described in the copending application, characterized by a parameter a, to cause the filtered subband's spectrum to be linearly shifted to

W(Q)(5 O F)(ω) = ^] F(ω[l + ar]) a ^] F(C[I + αr]) i e by shifts δω « Qar (23) r r for each contributing noise or signal source at respective distance r,

C* and measuring the lower and upper bounds C[H(a)(S o F)(ω)] and H[H (a) (S o F) (ω)], respectively, of this shifted subband in order to compute the minimum and maximum contributing source distances

"^n(ω) - ^Ω V S - δW/2 ¹J ~ V 2 - δW/2 ¹J and r_max(ω) = a _₁ f n[H(a)(S o F)(ω)} \ Q - δW/2 - 1 * α -i f tt[∑_r JXS[I + HH _ ^ ⁽²⁴⁾ I, Q - δW/2 respectively, as a function of the subband centre frequency ω We may likewise compute

δr_mΑX{δW) = max r_max(ω) - minr_mln (ω) and όr_mm(δW) = mm r_max(ω) - max r_mm(ω) (25)

corresponding to equation (21), but generally representative of the filter bandwidth δW chosen, or other statistics from the r_mm(ω) and r_max(ω) distributions depending on the application

Implementation

The above inventive procedures are independent of the physical nature of the signals and their wavelength range An equally general method for inducing the frequency shifts in the received waveforms, per equation (23) and orthogonally to their modulated information so as to be suitable for the objects of this invention, is provided by the copending application as mentioned The method concerns the spectral phase distribution of a signal, which can be obtained using any appropriate spectrometπc means, such as resonant cavities or circuits, diffraction gratings for optical signals, and digital signal processing for electronic media Specifically, as stated in the Background, it involves scanning the gradient of this phase distribution over the signal spectrum by continuously varying the instantaneous tuning ω of the resonant cavity or circuit, the intervals d ≡ nλsm θ (for any given diffraction angle θ) of the giating, or the sampling interval T ≡ 1/ω of the digital processing system, each at the same normalized rate ω^~1dω/dt ≡ \^~Λ dλ/dt ≡ T^~ldT/dt equal to cα (or ca_μ), where c denotes the wave speed It is shown in the copending application that linear frequency shifts obeying equation (23) result without otherwise affecting amplitude or phase The reverse mechanism in Step D follows from the shift formula ω → ω(l + ar) The formula also permits negative choices for a, but only positive values widen the spectrum, which is necessary for the inventive procedures Orthogonality to the signal content comes from the fact that the distance information in the phase gradient is an inherently spatial contribution, derived from the spatial contribution k r in the expression φ = k r—ωt for the total instantaneous phase of a travelling wave, whereas signal content and modulation ordinarily refer strictly to the temporal term ωt If r were to vary so as to interfere with the signal contribution, the variation would be in the form of a Doppler shift, which would not be new, and can be corrected for where necessary If the r variation were instead random or oscillatory, at frequencies comparable to that of the signal, it would as such interfere with the leception, even in absence of other sources So the distance information r can be exploited to separate or extract a set of signals by this method if they can at all be individually received A modulated signal may be conversely viewed as a jitter in the carrier's source distance indication, which makes the shifted modulated carrier frequency uncertain relative to the shifted unmodulated carrier, by a spread ot {ω_c(l + ατi), ω_c(l + 0112)}, where r\ and r-_± are the minimum and the maximum values for r, respectively, revealed by the spectral phase gradient, and ω_c is the carrier frequency Its spectral footprint is then the interval [C[IIF], H[HF]] = H[L[F], H[F]], 1 e H times the unshifted original footprint oi the modulated carrier, due to the linearity of H By the principles of Fourier analysis, these spectral bounds are simply equivalent to indefinitely stationary sinusoidal components including the result of modulation, and involve no extra uncertainty

Embodiments In general, a receiver embodying the present invention would thus generally include

• zero or more optionally tunable input filters {S_μ} and at least one optionally tunable selection filter G,

• and one or more fixed or variable mechanisms for shifting H(a) and reverse shifting H(-a) as explained The receiver would additionally include either

• a fixed or vaiiablc means for setting either a or G, or both, in order to select a desired signal F₁ and reject interfering signal or noise sources, according to Steps A through E, or

• low and high spectral bound detector means for determining L and H particularly of the shifted spectra, H_μ{F_μj} ≡ H(a_μ)S_μ{F_:l} in Steps C and D', along with optional means for varying one or more of the subbaπd filters S, so as to vary the coi responding subband mteivals and to thus detect interference within the signal spectrum, according to the alternative Steps C and D' in the inventive procedure Alternatively, a receiver may use a single tunable subband filter S(ω) and one set of spectral bound detector means applied to H(a)(SoF)(ω) per equation (24) to continually scan the entire signal bandwidth W using the modified inventive procedure oi Steps A* through C*

Both of the inventive functions, of separating the signal from a desired source and of detecting interference withm the signal band, may be implemented within a given receiver, for use one at a time or in parallel The spectral bound detectors may be also applied to the unshifted spectra for accuracy of measurement, in which case the same threshold a_th (equation ]) must be employed In principle, the subband filters should suffice to ensure that spectral discontinuities withm a subband do not matter - it should be sufficient to scan inward from the extremities of the spectrum to the first crossing of the threshold magnitude ±o_t/, However, as noise can generate false threshold crossings, one or more of the following schemes ould be generally necessary set the threshold above a sufficiently high empirically determined value, compare several successive samples to skip over narrower noise spikes, or average over several successive frames, which is common in spectral measurements More sophisticated techniques involving smoothening, interpolation or autocorrelation over the spectrum may also be used None of these schemes is usually an option for Steps C and D for selecting a desired signal, however

Λ basic receiver need not employ subbaπdmg at all, and thus skip Steps A and E A more sophisticated receiver may use subbanding, and would need a multitude ol input subband filters {S_μ} With subbanding, it would be often also useful to use a smaller a_μ for the higher subbands, while using sufficiently high values for the low subbands, so as to keep the shifted spectra within the handling range of the circuits, this would not be a concern with digital signal processing The shift parameter a may be alternatively fixed at a large enough value for the intended operating distance range Large values of a can be achieved using bhort time frames in the shifting mechanism, as also described in the copending application The desired signal F₁ can then be selected by varying G, or switching between a set of fixed filters (G₁) The alternative would be to use a single fixed selection filter G, and to vary α in order to bring F₁ into the pass band of G In either case, the variation may be performed manually through suitably implemented controls or knobs, or automatically by scanning the combined shifted spectrum { H [a) F₃) for a signal matching some selection criteria, such as a spread-spectrum code, a specific subcarner, a signature pattern, etc that could be predefined, interactively set or acquired from a previously selected signal, so as to lock on to that source

These selection and detection functions may also be combined m a receiver, by the use of separate detection and source separation modules, each containing its own instances ot both the subband filters 5 and the frequency spreading shift mechanisms H In such a receiver, the detection module may use relatively narrow subbands to dynamically determine the coarsest subband partitioning of the signal spectrum to simplify the operating configuration of source selection module, and to thus ensure better performance or lower the total power consumption Another variation would be to keep the inventive selection module on standby, so as to only activate it in the presence of interference The onset of interference may be detected aut omat ically using the inventive Steps C and D', simplistically without partitioning into subbands, or more particularly with subbands, or more accurately using a single scanning subband, as in Steps A* through C* An alternative arrangement could also be employed for the interference detection in order to activate the inventive source selection procedure In the case of audio or video communication, the inventive signal selection procedure may even be manually activated or turned off based on perception of interference If multiple antenna or aperture feeds are available, c g as stereoscopic or array antennae or microphones, the range separation can be combined with the angular information from the feeds to determine the source locations over two or three dimensional space, as opposed to the one dimensional range distribution of sources that can be determined using a single feed In all of these cases, the determined spatial distribution of sources can be displayed to the user to allow visual perception of interference and interactive selection

More particularly, the inventive interference detection procedure of Steps C and D' or Steps A* through C* ib not necessary in these cases With stereo- or quadraphonic acoustic feeds, the two or three dimensional spatial distribution of the sources would be revealed by a diagram of circles, or spherical surfaces, drawn with radii corresponding to the peaks in the shifted spectrum and centred on the geometrical representations of the feeds or microphones, with intensities proportional to the (analogue) energy distribution of the shifted spectrum II(a)S{F_j}, i e \H(a)S{F₃ }\² Correspondingly an automatic (non interactive) source selection system may use the phase differences between the feeds to discriminate in direction as well as distance

Variations

Numerous variations of the inventive procedures are possible and are intended within the present invention For example, prcfiltering may be also employed to alter the spectral profile over the desired band in order to simplify, or correct for limitations in, the design of the selection filter G₁ The prefilteπng could include compressing the signal spectrum, using frequency modulation say, and Step D could likewise be accomplished by "mixing" , i e by multiplying with a generated intermediate frequency signal, or by frequency modulation If the same value of α is used for each of the subbands in Step B, Step E could be performed before Step D, as mentioned, with the advantage that only one reverse shitting mechanism is needed, though it must then handle the combined shifted bandwidth of all of the subbands

Further, the input signal spectrum may be expanded before Step B using frequency modulation to limit noise arising in the subsequent stages The final stage may likewise comprise a more complex combination of mixing and spectral expanding or compacting Additionally, a receiver needing to monitor multiple sources may be designed using a common shift mechanism in Step B and multiple selectors G₁, each differently designed and fed the same shift mechanism output in parallel, or using identical selectors but fed by differently designed or tuned shift mechanisms, the latter being each fed the same input combination of signals

Other objects, features, applications, variations and advantages of the present invention will be apparent when the detailed description of the preferred embodiment is considered m conjunction with the drawings, which should be construed in an illustrative and not limiting sense

Brief Description of Drawings

Fig 1 illustrates the separability of wave-propagated signals from two or more sources at different distances irom the receiver, using a distance-dependent frequency shifting mechanism at a receiver Fig 2 summarizes the simplified inventive procedure for selecting a desired signal in the scenario of Fig 1 Fig 3 demonstrates the problem of spectral shadow that occurs with closely located sources, or signals with low frequency content, or with inadequate distance-dependent frequency shifting

Fig 4 illustrates separability of the lower half of the signal bandwidth in the scenario of Fig 3 Fig 5 illustrates separability of the upper half of the signal bandwidth in the scenario of Fig 3 Fig 6 summaπzes the inventive procedure for selecting a desired signal in the scenaiio of Fig 3 Fig 7 is a block diagram for a receiver implementing the inventive piocedure of Fig 6 Fig 8 is a block diagiam for a simpler version of the receiver of Fig ύ

Fig 9 is a block diagram for a receiver implementing the simplified inventive procedure of Fig 2 Fig 10 shows the alternative steps in the simplified mvenl ive procedure to determine the spread of sources Fig 11 shows the modified inventive procedure for measuring the spread of sources using a scanning filter Fig 12 is a block diagram for a receiver implementing the modified inventive procedure of Fig 11 Fig 13 illustrates the "scatter plot" approach for displaying the spread of sources

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Fig 1 illustrates the inventive procedure for separating signals received from sources at different distances irom the receiver, using a graph of the spectral shift as a function of distance Incoming signals of spectia F(ω) and F'(ω), from sources [520] and [530] at distances r and r' = r + δr, respectively, from the receiver [600] located at the origin of the graph are assumed to ordinarily occupy the same frequency band W The two signals would ordinarily be received together as the combined signal J^ F₃ (ω) ≡ [F₃) [100] and interfere with each other's reception at the receiver By applying Step B of the inventive procedure as given in the Summary the receiver causes the spectra of these component signals to be shifted in proportion to the source distances using the method described in the copendmg application, i e by frequency factors (1 + αr) [220] and (1 + ατ¹) [230] The component spectra then occupy the shifted bands F₁ (W₁) = //(Q)F₁ (W) = HF₁ [320] and F₂(W₁) ≡ H{a)F₂(ω) = HF₂ [330], respectively If the shifted component spectra no longer overlap, as shown, either signal can be separated by applying a suitable band-pass filter G₁ [420] or G₂ [430], according to Step C, to correspondingly select either HF₁ [320] or HF₂ [330], respectively This extracted signal, say HF₁ ≡ G₁H ∑ F₃, has to be shifted back to its original band as F₁ ^) [120] to be usable This shift would be best done using the reverse shift mechanism H^~λ {a) ≡ H(—a), according to Step D The above steps form the basic inventive procedure, and are summarized in Fig 2 as a time sequence of operations applicable to narrow band sources with sufficient distances between them As mentioned in the Summary, frequency modulation or mixing with intermediate frequency signals can be additionally applied in Steps B and D and the return shift operation H^~Λ of Step D can be replaced by these methods

Fig 3 illustrates the problem of spectral shadow, which arises whenever the sources are too close (δr, <ε r,), the applied temporal parallax (a) is too small, or the signal contains very low frequencies (£ « HOr £ s; 0), so that equation (13) is not satisfied The figure shows that under any of these conditions, the shifted spectra overlap and cannot be separated using a band-pass filter If, further the sources are of nearly equal strength, the shifted spectrum of the nearer source, F_i (ω₁) [320], in effect casts a shadow [322] over the shifted spectrum F₂(w₂) [330] of the farther source, i e that portions of the latter, F2(w2) [330], that fall within this shadow will suffer interference from the nearer source If the signals are frequency or spread-spectrum modulated for which a receiver typically recovers the carrier coherently using a phase-lock circuit, the faithcr or otherwise weaker source would be likely rejected altogether, regardless of which source was desired Further, Fig 3 also illustrates the spectral widening property of the H operators, which exacerbates the shadow problem Widening occurs because the lower bound [321] of the shifted spectrum would have been shifted by (1 -\- ar)C, which is less than the shift (1 + ar)Ti. contained in the upper bound [323] of the shifted spectrum, so that the shifted bandwidth is itself greater than W , and the spectral shadow [322] cast by the source becomes greater than W by the same factor (1 4- or), as shown The inventive solution for the spectral shadow problem, as formally treated in the Summary, is to partition the incoming combined signal into two or more subbands, to then apply the procedure of Fig 2 separately to each of the subbands, and lastly, recombine the subbands to obtain the separated signal spectrum In the example of Fig 3, since the shadow [322] covers roughly half of the second source spectrum [330], separation can be achieved by partitioning the input signal into two subbands, as illustrated in Figs 4 and 5, showing the results of applying Step B to the lower and the upper subbands, respectively As shown in Fig 4, the lower subband So ∑^ F₃ [105] of the combined incoming signal, obtained from the lower subband filter S₀ in Step A separates, under the inventive operation H (a), into the shifted component spectra SQHF_I [325] and SQHF₂ [335] If just separated, the shifted lower bound [331] of the second signal will coincide with the shifted upper bound [327] of the first The lower subbands become separable because the lower subband of the first source no longer casts a shadow on the lower subband of the second though both are shifted by the same parallax factor α

Fig 5 shows the corresponding separation of the upper subband Si ∑_j F₃ [106] of the combined incoming signal, obtained from the lower subband filter S_\ in Step A, into the shifted component spectra SiHFi [326] and SiHF₂ [336] Again, if just separated, the shifted lower bound [337] of the second signal will coincide with the shifted upper bound [323] of the first The shadow would range from the shifted lower bound [327] to the shifted upper bound [323], and fails to cover the shifted subband [336] of the second source

Fig 6 summarizes the complete inventive procedure including the separation into lower [105] and upper [106] subbands in Step A, by means of the lower and the upper subband filters [400] and [402,] respectively, to eventually obtain the extracted lower [125] and upper [126] subbands of the desired signal Fj [120] from the first source, and recombination of these extracted subbands in Step E As mentioned in the Summary, Step E, recombination, can be pel formed before applying the reveise shift, i e before Step D, which would be useful for reducing the number of operations The figure incidentally also illustrates that narrower filters could be used for the source selection, in the place of Gi [420], and that a could be made smaller as well

Fig 7 is a block diagram of a receiver incorporating the complete inventive procedure described in Fig 6 It shows incoming electromagnetic (or acoustic) waves [610] being collected by an antenna (or microphone)

[620] to produce the combined input signal {F_j(ω)} This combined signal is fed to a bank of input subband filters [630] to produce the combined subband signals S_μ{F_j} as Step A These combined subband signals are then subjected to Step B using a bank of frequency shifting mechanisms [640] per the copendmg application, to get the shifted subband signals 11(CiI₁₁)S₁₁[F_j), in which the contributions from the individual sources are already separated in frequency as shown in the preceding figures In order to select the desired source s, and suppress the contributions from the remaining sources, these shifted subband signals H(a_μ)S_μ{F_j} are then fed to the band-pass selection filter bank [650], as Step C, to obtain the shifted subbands G_τH(ot_μ)S_μ{F_j} as

H(a_μ)G_ιS_μ{F_J} a; H(a_μ)S_μF_ι of the desired signal F₁, per equations (6) and (7) These shifted subbands are then down-shifted by a bank of reverse shifting mechanisms [660] (Step D), yielding H(—a_μ)H(a_μ)S_μF_ι sa S_μF_{ι t} the subbands of the desired signal, and recombmed by a summing device [670], which can be as simple as an operational amplifier (op-amp), to obtain ∑_μ S_μF_τ — F₁, the desired signal

Fig 8 is a simpler version of the receiver of Fig 7, in which the summing device is applied before down¬ shifting, which is only possible when the same value ol o is used in each of the frequency shifting mechanisms [640] In this case, the outputs of the band-pass selection filter bank [650] are immediately recombined by the summing device [670] to produce the desired signal, except that it is still expanded and shifted in frequency as ∑ H(a)S_μF_ι = H(a)F_v, and requires down-shifting by a single reverse shifting mechanisms [662] to yield the desned signal as //(— α) ∑_μ H{a)S_μF_τ = F₁

Fig 9 shows an even simpler receiver that treats the entire signal bandwidth W as one subband, and thus skips both Steps A and E Such a receiver would be adequate, as already explained, when the sources are well separated from one another and the signal bandwidth W does not include d c It would be generally sufficient for broadcast radio and also mobile (cellular) telephones, since the base stations would be typically spread far apart The more complex receiver of Fig 7 would be generally needed at the cellular base stations, however, as the mobile (cellular) phones could even be situated side by side

The related inventive method for detecting interference and estimating the source distribution, given by Steps C and D' m the Summary, is explained in Fig 10 using the same combined input signal [100] as in the preceding figures After Step B, both the original combined incoming signal spectrum [100], and its shifted spectrum, comprising the shifted components [320] and [330] both would be available to the receiver using any applicable means of spectral analysis, including digital signal processing, as typically used for radio or acoustic signals, and refraction or diffraction, e g for optical, microwave or sonar signals In the latter case, it is common practice in related arts like modern astronomy to convert the resulting spectrum to digital form for further processing, storage and viewing It is straightforward, therefore, to also apply smoothenmg and interpolation, to compute autocorrelation of the spectral distributions, and to average over several successive frames, as necessary to obtain good estimates of the spectral distributions

Step C then consists of seeking, from the low frequency end of the measured domain, the first crossings of the obtained distributions above a suitably chosen threshold α_(/, [700], as indicated by the arrows [710] and [720], thereby obtaining the values £[{F, }] and £[7-/(α){F_j }] as the respective abscissae An estimate of the distance r_mm to the nearest source is then computed from the relation

which is the specialisation of equation (17) to a single subband encompassing the full signal bandwidth W Step D' correspondingly consists of seeking, from the high frequency end of the measured domain, the first crossings of the obtained distributions above the same threshold a_th [700], as indicated by the aπows [730] and [740], to obtain the values Η[{-F,}] and Tt[H[Q)[F₃ ]) as the respective abscissae The distance r_max to the farthest source is then estimated using the relation

_ _Q-i (HlHJa)[F₃)] _ \

which similarly specializes equation (19) to a single subband encompassing the full nominal signal bandwidth W As remarked in the Summary, these two steps could be performed in the reverse order i e Step D' before Step C, since the crossing detections are independent, and for the same leason, it would be trivial to perform these steps simultaneously or in random order m a receiver, for example as independent threads of execution m a software implementation

It would be trivial to extend this procedure for measuring r_mln and r_max identically to each oi the subbands S_μ[F(ω)} ≡ [F_μ(ω)} of the combined received signal to compute the corresponding values r^_n and CJ_x for each subband, and to thereby arrive at the minimum and maximum spread estimates defined in equation (21), or other suitable statistics from these measurements

Scanning with a single, narrow subband filter would be superior for detecting interfering signal or noise sources withm the signal band W, per the modified inventive procedure, Steps A* through C* given in the Summary This is illustrated in Fig 11, in which a single subband filter [450] with a very narrow passband δW -C W is used to scan the received signal spectrum F(ω) [100], to obtain the filtered signal (5 o F)(ω) [150] at each instantaneous position of the filter [450] (Step A*) In Step B*, this filtered signal is subjected to the frequency shifting mechanism of the copending application to yield the shifted spectral distribution H{a)(S o F) (ω) = ∑_r F(ω[l + ar}) a ∑_r F[D[I + ar}) [350] As Step C*, the threshold frequency bound detectors are again applied, as shown by the arrows [710] and [730] to determine the low and high frequency bounds of the shifted distribution, respectively, for computing the source distribution functions δr_mm[δW) and δr_max[δW) per equation (24)

Fig 12 is a block diagram of a receiver incorporating the scanning procedure of Fig 11 In this, the received signal (or combination of signals) from the antenna [620] is first subjected to narrow band filtering, in accordance with Step A*, by a subband filter [450], whose centre frequency is made to periodically sweep over the input band of frequencies by a sweep controller [634] The resulting filtered signal is then input to the frequency shift mechanism [642], per Step B*, and its frequency bounds are measured, per Step C*, by the high [732] and the low [712], respectively The bound values obtained are used to compute ι_mm and Λii_ax, applying equation (24), or other related statistics, by the source distribution computer [680] Related to the scanning procedure is the "scatter plot" method mentioned m the Summary, illustrated in Fig 13 for the case of bistatic (stereophonic) antenna (microphone) feeds [622] and [624] that respectively provide two input signals Fι(ω) [102] and F_R(ω) [104] These signals are first scanned simultaneously by the identical narrow subband filters [452] and [454], per Step Λ*, and then shifted by identical frequency shifting mechanisms to yield the shifted distributions H(a)(SoF_L)(ω) = ∑_r F_L{ω[l +ar}) « ∑_r F_L(ω[l + ar]) [352] and H{ά){SoF_R)(ω) = ∑_r F_R{ω[l + ar}) ~ ∑_τ F_R{Q[l +ar]) [354], per Step B* Next, instead of measuring the frequency bounds according to Step C*, one draws on a separate graph circles [552] and [554] representing the loci of possible source locations, with centres corresponding to the two feeds and radii proportional to the shifts The resulting concentrations ol sparse and dense regions resemble well known two-slit interference patterns of diffraction theory, since each concentration of (signal or noise) sources produces multiple dense regions like [562] and [564] Fig 13 also showb that the "scatter plot" is really a technique for combining the source distance distribution data from multiple antenna feeds, as the distribution information from each individual feed is already revealed by the shifted spectral distributions [352] and [354]

The difference between the "scatter plot" and a diffractive interference pattern is that the plot represents the actvial spatial distribution of sources, albeit with multiple aliases whereas diffractive interlerence is only representative of their spectral distribution This is because the plot starts with the spectral distribution, whereas in diffraction theory, one starts with a spatial distribution of sources or slits The method is in this sense an inverse of diffractive interference

The invention has been described with reference to the preierred embodiment, but it will be appreciated by those of ordinary skill in the arts of general physics, electronics and communication technologies that numerous modifications and variations are possible in the light of the above disclosure For example, the invention can be applied to sound and underwater communication, and to transmission lines or optical fibres Indeed, as the filtering, recombinmg, down-shifting and the key operation of shifting spectra in proportion to the contributing source distances can be conceivably applied to signals over any kind of propagating waves, provided only that they obey the wave equation, as particularly described in the copendmg application for the shifting operation, the invention could be applied even to matter or gravitational wave signals As stated in the Summary, Step D could be replaced by a down-converter, optionally with a modulation- demodulation stage to scale back the bandwidth by the factor (1 + QΓ) The scaling down may be obviated by moving the modulation-demodulation stage before Steps A or B, so that the bandwidth is already scaled down by an estimate of the (1+αr) factor for the desired source This would also require narrower subbanding filters 5_μ and source selection filters G₁, which may be useful from the perspective of ensuring constant or linear phase over the filter spectra, since phase distortions can affect the spectral phase gradient and the linearity of separation assumed in Figs 1, 3, 4 and 5

Likewise, the problem of spectral shadow and the inventive use of subbanding to overcome it have been illustrated using just two subbands, but it would be clear to those skilled in the related arts that more than two subbands may often be necessary and that the lowest subband, especially if including 0 frequency (d c ), may need to be abandoned altogether, as stated in the Summary

As stated in the Background and in the Summary, the present invention may be enhanced with direction- sensitive antenna technology to also provide separation of signals from sources at almost the same distance from the receiver, but differing in their directions The inventive method may be conversely employed as an alternative to directional antennae in order to separate sources that are too close in direction The present invention may likewise be combined with content-based separation methods including, but not limited to, amplitude, frequency, phase and spread-spectrum modulations, or TDM, and autocorrelative methods All such modifications, generalizations and variations are intended within the scope and spirit of the invention as defined in the claims appended hereto

Claims

Claims

I claim

1 A method for separating at a receiver a desired signal from a combination of signals received from a multitude of sources,

• each of the sources being located at a different distance from the receiver,

• the desired signal being contributed by a desired source at a distance,

• and each of the signals and their combination occupying an original band of frequencies,

the method comprising the steps of

• splitting the received combination of signals into one or more spectral subbands,

• expanding each of the spectral subbands into a corresponding plurality of component subband spectra, each plurality corresponding to one of the multitude of sources and bemg shifted in frequency in proportion to the distance from the receiver of the corresponding one of the multitude of sources,

• selecting in each plurality of component subband spectra a shifted component subband spectrum corresponding to the desired source,

• down transforming each selected shifted component subband spectrum back to the original band of frequencies,

• and recombinmg the selected shifted component subband spectra to recover the desired signal

2 The method of claim I₁ wherein the number of spectral subbands is exactly one, so that the first and last steps are vacuous

3 The method of claim 1, wherein the down-transforming step is performed after the recombinmg step

4 The method of claim 1 , wherein the step of selecting the shifted component subband spectra is performed using one or more band-pass filters

5 The method of claim 1 , wherein the step of down-transforming each selected shifted component subband spectrum is accomplished by scanning its phase distribution 6 The method of claim 1, whercm the step oi down- transforming each selected shifted component subband spectrum is accomplished by multiplying the selected shifted component subband spectrum with an intermediate frequency carrier signal

7 The method of claim 1, wherein the signals are propagated by acoustic waves

8 Tho method of claim 1, wherein the signals are propagated by matter or gravitational waves

Q The method of claim 1 , wherein the step of expanding each spectral subband is accomplished by scanning the phase distribution of the spectral subband

0 The method of claim 9 wherein the scanning step is performed by digital signal processing

1 The method of claim 9 wherein the scanning step comprises varying the grating intervals of a diffraction grating or a dimension of a resonant cavity

2 Λ method for obtaining, from a combination of signals received at a receiver from a multitude of sources, the distribution of distances to the multitude of sources, each of the signals and their combination occupying an original band of frequencies, the method comprising the steps ol

• splitting the received combination of signals into one or more spectral subbands each having known or measured upper and lower frequency bounds,

• expanding each of the spectral subbands into a corresponding plurality of component subband spectra, each plurality corresponding to one of the multitude of sources and being shifted in frequency in proportion to the distance from the receiver of the corresponding one of the multitude of sources,

• and computing the distance distribution to the multitude of sources from the expanded pluralities of component subband spectra

3 The method of claim 12 wherein the number of spectral subbands is exactly one

4 The method of claim 13 wherein the spectral subband is fixed with upper and lower frequency bounds corresponding to the original band of frequencies

5 The method of claim 13 wherein the spectral subband has a variable centre frequency and the centre frequency is varied within the original band of frequencies The method of claim 12 wherein the step of computing the distance distribution comprises the steps of

• measuring upper and lower frequency bounds of each plurality of the component subband spectra,

• and computing the minimum and the maximum distances to the multitude of signal sources from the ratios of the measured upper and lower frequency bounds of the pluralities of the component subband spectra to the corresponding known or measured upper and lower frequency bounds of the spectral subbands, respectively The method of claim 12 wherein the step of computing the distance distribution comprises plotting an expanded plurality of component subband spectra on a graph A device for separating an electromagnetic or other wave-propagated signal emitted by a desired source from a combination of signals emitted by a multitude of such sources each located at a different distance from the device, each of the signals and their combination occupying an original band of frequencies, the device comprising

• one or more spectral expansion means for expanding the combination of signals or subbands of the combination of signals to form a plurality of component spectra or component subband spectra, respectively, each plurality corresponding to one of the multitude of sources and shifted in frequency in proportion to the distance from the device of the corresponding one of the multitude of sources,

• one or more band-pass filter means for selecting an expanded component spectrum or component subband spectra corresponding to the desired source, and

• one or more down-transformation means for shifting the selected expanded component spectrum or component subband spectra back to the original band of frequencies to form the desired signal or subbands of the desired signal, respectively The device of claαm 18, additionally comprising a subband filtering means for dividing the combination of signals into one or more subbands, and a summing means for recombming the subband spectra of the desired signal back into the desired signal The device of claim 19, comprising a single down-transformation means following the summing means