P. A. Bello, "Characterization of randomly time-variant linear channels", IEEE Trans. Commun. Syst., vol. CS-11, pp. 360--393, 1963.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... captured for many channels that have been reported from wideband channel measurements [17] 19] and demonstrated in field experiments with wideband CDMA transmissions [20] The model of the channel is a special case of the Gaussian wide sense stationary uncorrelated scattering (WSSUS) channel [21]. The channel process for the th transmitter is represented as a complex valued Gaussian random process , which is characterized by its specular part and the autocovariance function of its diffuse part where and are time variables, and are path delay variables, and is the Dirac delta function. ....

P. A. Bello, "Characterization of randomly time variant linear channels," IEEE Trans. Commun. Syst., vol. CS-11, pp. 360--393, Dec. 1963.

....#1 Mean=0 Var=d o o Butterworth 3rd Order Filter GRV Gaussian Random Variable Generator GRV #2 Mean=0 Var=b o 3rd Order Filter Mean=0 GRV #3 Var=b o 3rd Order SCATTER Figure 2. 5: Shadowed Rician Fading Simulator are generally not sensitive to the number of taps involved [5][37] In this application, a two tap delay line model is used, which leads to the two beam fading channel [27] In fact, a flat fading model is a special case of the delay line model with J = 0, as there is only one term in (2.34) The expression of the received signal y(t) relates to the input ....

Bello P.A., "Characterization of randomly time-variant linear channels", IEEE Trans. Commun. Systems, CS-11, pp. 360-393, 1963.

....algorithm. Finally, simulation results are provided in Section VI. II. LTI Multichannel Representation The input output relation (1) can be rewritten as (cf. 1] N D 1 l=0 l [m] s l [n m] 2) where h l [m] h [m; l] e lm N with the (delay Doppler) spreading function [4] S h [m; l] n=0 [n; m] e Funding by FWF grant P12228 TEC. 1 [n] 1 [m] 0 [n] 1 [n] Fig. 1: LTI multichannel representation of a multiuser LTV channel. l [n] and ND is the maximum Doppler shift. This corresponds to an LTI ....

.... that will be relevant to our method are the active Doppler shifts l k and the length L of the corresponding channel impulse responses h k [m] all h k [m] are assumed to have the same length) For WSSUS channels, these model parameters can be deduced from the scattering function [4, 6] corresponding to the respective user (we assume that the M LTV channels corresponding to a given user possess the same scattering function) Because the scattering function does not change with time, it is much easier to estimate than the channel itself [7, 8] In the following, the active ....

P. A. Bello, \Characterization of randomly time-variant linear channels," IEEE Trans. Comm. Syst., vol. 11, pp. 360-393, 1963.

....Computer simulation of mobile radio channels is of great importance for the development and evaluation of mobile communications systems. A discrete time channel model that is convenient for channel simulation is the time varying tapped delay line (FIR filter) with input output relation [1, 2] y[n] M 1 m=0 hm [n] x[n m] Here, x[n] is the channel input signal, y[n] is the channel output signal, hm [n] is the channel s time varying impulse response (with m the delay index and n the time index) and M 1 is the maximum delay. For wide sense stationary uncorrelated scattering ....

....and M 1 is the maximum delay. For wide sense stationary uncorrelated scattering (WSSUS) channels, each tap weight sequence hm [n] is a stationary random process with autocorrelation function rm [l] E hm [n l] h # m [n] and di#erent tap weight processes hm [n] hm # [n] are uncorrelated [1, 2]. The power spectra of the hm [n] Sm (#) l= # rm [l] e j2##l , m = 0, 1, M 1 , are termed the channel s Doppler spectra or scattering function [1, 2] Here, # is the Doppler frequency normalized by the sampling frequency. For wideband CDMA and OFDM systems, the sampling frequency is ....

[Article contains additional citation context not shown here]

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Comm. Syst., vol. 11, pp. 360-- 393, 1963.

....e , where h l [n] # h[nN, l] 2) and the noise z[n, k] m=0 # [nN m]e . In what follows, the time varying channel will be considered random. Under the wide sense stationary uncorrelated scattering (WSSUS) assumption, E h[m # , l] h # [m # m, l ] r h [m, l] # [l l # ] [9, 10]. The channel s scattering function is then defined as [9, 10] S h (l, #) # m= # r h [m, l] e j2##m , l = 0,1, L 1 , with # the normalized Doppler frequency. In what follows, # max will denote the maximum Doppler frequency of the channel. The channel s path loss is defined as ....

....m=0 # [nN m]e . In what follows, the time varying channel will be considered random. Under the wide sense stationary uncorrelated scattering (WSSUS) assumption, E h[m # , l] h # [m # m, l ] r h [m, l] # [l l # ] 9, 10] The channel s scattering function is then defined as [9, 10] S h (l, #) # m= # r h [m, l] e j2##m , l = 0,1, L 1 , with # the normalized Doppler frequency. In what follows, # max will denote the maximum Doppler frequency of the channel. The channel s path loss is defined as # h # # S h (l, #)d# . h 0 [n] IDFT x[n,0] x[n,K 1] ....

P. A. Bello, "Characterization of randomly time-variant linear channels, " IEEE Trans. Comm. Syst., vol. 11, pp. 360--393, 1963.

....a l,k (l #Z, # 0, K 1 ) denotes the data symbol at symbol time l and subcarrier k. The symbols a l,k are assumed i.i.d. with zero mean and mean power E a l,k = s a . Channel. Transmitting s(t) over a random time varying channel H with time varying impulse response h(t,t) [9,10] yields the received signal (integrals are from to ) r(t) Hs) t) h(t,t)s(t t)dt . In this paper, we will consider only the noiseless case. The channel H is assumed to satisfy the wide sense stationary uncorrelated scattering (WSSUS) property. Thus, the secondorder statistics of H ....

....= Hs) t) h(t,t)s(t t)dt . In this paper, we will consider only the noiseless case. The channel H is assumed to satisfy the wide sense stationary uncorrelated scattering (WSSUS) property. Thus, the secondorder statistics of H are described by the Doppler spectrum or scattering function [9] CH (t,n) where t denotes time delay and n denotes Doppler frequency. Practical wireless WSSUS channels are underspread [4,10,11] i.e. their scattering function is effectively supported within a rectangular region S # [0, t max ] n max , n max ] of area 2t max n max 1. Demodulator. At ....

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Comm. Syst., vol. 11, pp. 360--393, 1963.

....i 0 ] e ; 4) and the noise w[nN s h m]e Channel statistics. In what follows, we assume that the timevarying channels associated to different transmitters and receive antennas are mutually uncorrelated and satisfy the wide sense stationary uncorrelated scattering (WSSUS) assumption [12, 13], i.e. m m; l] h H 0 [m ; l ] R i [m; l] d [l l ]d [i i ] I : Note that the time delay correlation function R i [m; l] is assumed to be equal for all antennas. We model R i [m; l] as being separable, R [m; l] r [m]P [l] 5) with time correlation ....

....i ] I : Note that the time delay correlation function R i [m; l] is assumed to be equal for all antennas. We model R i [m; l] as being separable, R [m; l] r [m]P [l] 5) with time correlation function r i [m] and delay profile P i [l] The channel s Doppler profile is given by [12, 13] S i (n) m= r i [m]e j2pnm ; 6) where n denotes the normalized Doppler frequency. 3 MMSE Channel Estimation We next consider estimation of the channel coefficients H i [n; k] for a given i corresponding to one of the I transmitters (the respective time offset h i will be set equal ....

P. A. Bello, "Characterization of randomly time-variant linear channels, " IEEE Trans. Comm. Syst., vol. 11, pp. 360--393, 1963.

....is the symbol rate. The additive noise is white Gaussian noise with two sided power spectral density . A frequency nonselective channel is considered in this work; henceforth, the fading is modeled as a complex multiplier . The Gaussian wide sense stationary uncorrelated scattering fading model [18] is assumed, where the independent in phase and quadrature components of are zero mean Gaussian processes with autocorrelation function . Hence, the channel is modeled as a Rayleigh fading channel. It is also assumed that varies slowly enough so that it can be considered as constant over a single ....

P. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst., vol. COM-11, pp. 360--393, Dec. 1963.

....scale path loss, reflections and shadowing effects. We assume the tap means known from a preceding training phase, and concentrate on tracking their time variant part, which has autocorrelation properties corresponding to the widesense stationary and uncorrelated scattering WSSUS model of Bello [13]. If the tap means are zero, the channel is said to introduce Rayleigh fading (worst case) while a non zero mean tap corresponds to Ricean fading. The Kalman channel estimator is aided by previous hard decisions about the transmitted symbols from all users, produced by the MIMO equalizer. ....

....(t) t) i T : 8) With this setup, the channel is a complex Gaussian vector process c t with dimensions (n T nR ( 1) Theta 1, which has a constant mean vector c. The time variant part of the channel is the vector process fh t g. According to the WSSUS model of Bello [13], all the channel taps are independent, namely all the entries of vector h t vary independently, according to the autocorrelation model of (4) If we let index k enumerate all the taps k = 1; n T nR ( 1) and denote f D = f D the Doppler of the m tap of the channel from input i ....

P. A. Bello, "Characterization of randomly time-variant linear channels," Transactions on Communication Systems, vol. CS, no. 11, pp. 360--393, Dec. 1963.

....procedure amounts to an LTV lter. 4.1.2 Underspread Filters The LTV lters discussed here are supposed to perform a TF weighting; in this context, significant time shifts or frequency shifts are undesired. The TF shifts introduced by an LTV lter H are characterized by the spreading function [28 37] SH (m; 4.2) Here, m and denote time shift (time lag, delay) and frequency shift (frequency lag, Doppler shift) respectively. The input output relation (4.1) can be reformulated as SH (m; x[n m] e d ; 4.3) whereby the lter output signal y[n] is represented as ....

....we consider the explicit design of TF lters. We start with an especially simple design scheme. 4.2.1 Zadeh Function and Zadeh Filter Zadeh Function. For a discrete time LTV lter H, Zadeh s time varying transfer function (brie y called Zadeh function hereafter) is a TF representation de ned as [3, 28 32, 34, 38, 39] ZH (n; The spreading function in (4.2) is the 2 D Fourier transform of the Zadeh function, i.e. SH (m; The impulse response g[n; m] can be reobtained from ZH (n; through the inversion formula g[n; m] If H is underspread as de ned in Subsection 4.1.2, ....

P. A. Bello, \Characterization of randomly time-variant linear channels," IEEE Trans. Comm. Syst., vol. 11, pp. 360-393, 1963.

.... G x (t, f ) 21] evolutionary spectrum G [3] and transitory evolutionary spectrum G ( 1 2) x (t, f ) 21, 22] We finally recall the underspread concept for linear systems (operators) and random processes To this end, consider the following moments of the spreading function S H (t,n) [16, 24] of a linear system (or operator) H: n t , n n n . Since S H (t,n) characterizes the TF shifts of H, t H and n H are global measures of the amount of delay (time shift) and Doppler (frequency shift) respectively, introduced by H. A system H is then called ....

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Comm. Syst., vol. 11, pp. 360--393, 1963.

.... is, fG( R ; T )g is a family of zero mean Gaussian random variables: E[G( R ; T )G T ) M( R ; T )ffi( R Gamma T ) 29) for some M( R ; T ) 0 reflecting the channel power as a function of ( R ; T ) In line with the terminology used for temporal channels (see, e.g. [14]) we call M( R ; T ) the spatial scattering function. Even if we have high resolution measurements of b G( R ; T ) available, actual system performance will be governed by a smoothed version whose resolution is commensurate with the array apertures. It follows from (8) that for the aliased ....

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst., vol. CS-11, pp. 360--393, Nov. 1963.

....signal of duration T seconds, two sided bandwidth B Hz, and average power P . w(t) is additive white Gaussian noise (AWGN) with spectral density # , and Tm denotes the multipath spread of the channel. Due to essentially finite signaling bandwidth, y(t) can be accurately approximated as [1, 6] y(t) where L . #TmB# and h l . h(l B) where h(#) is a smoothed version of h(#) 6] The number of resolvable components and the number of channel degrees of freedom are both L. We consider an uncorrelated scattering, Rayleigh fading channel, for which the delay coe#cients h l are ....

....additive white Gaussian noise (AWGN) with spectral density # , and Tm denotes the multipath spread of the channel. Due to essentially finite signaling bandwidth, y(t) can be accurately approximated as [1, 6] y(t) where L . #TmB# and h l . h(l B) where h(#) is a smoothed version of h(#) [6]. The number of resolvable components and the number of channel degrees of freedom are both L. We consider an uncorrelated scattering, Rayleigh fading channel, for which the delay coe#cients h l are uncorrelated, complex zero mean Gaussian random variables. Average channel power is normalized to ....

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst., vol. CS-11, pp. 360--393, Nov. 1963.

....over the ionospheric propagation channel. Also, spread spectrum cordless telephones typically operate in locations such as homes where multipleaccess interference may be infrequent. II. DOUBLY SELECTIVE FADING CHANNELS The Gaussian wide sense stationary uncorrelated scattering (WSSUS) channel [4] is represented by a time varying impulse response which is a zero mean Gaussian random process h(t, It is characterized by its ensemble autocovariance function where t and x are time variables and and c are path delay variables. Each autocovariance function is the product of a ....

P.A. Bello, "Characterization of randomly time variant linear chaunels," IEEE Trans. Commun. Syst., vol. CS-11, pp 360-393, Dec. 1963.

....complex baseband channel is a linear, timevarying (LTV) system. This LTV system can be characterized by its kernel that relates the input and the output [see Fig. 1(a) as (1) In mobile radio applications, the term impulse response usually refers to the channel s input delay spread function [8] defined as . Alternatively, the output delay spread function [8] can be used. These functions are related by simple coordinate transforms (2) The Fourier transform of with respect to is referred to as time varying frequency response or time varying transfer function [8] 9] It allows to ....

....This LTV system can be characterized by its kernel that relates the input and the output [see Fig. 1(a) as (1) In mobile radio applications, the term impulse response usually refers to the channel s input delay spread function [8] defined as . Alternatively, the output delay spread function [8] can be used. These functions are related by simple coordinate transforms (2) The Fourier transform of with respect to is referred to as time varying frequency response or time varying transfer function [8] 9] It allows to rewrite the input output relation (1) as (3) where denotes the ....

[Article contains additional citation context not shown here]

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst, vol. COM-11, pp. 360--393, 1963.

....and the noise z[n, k] # [nN m]e . In what follows, the time varying channel will be considered random. Under the wide sense stationary uncorrelated scattering (WSSUS) assumption, the autocorrelation function of h[m, l] is h[m m, l] h # [m # , l # ] r h [m, l]# [l l # ] [7, 8], and the channel s Doppler spectra or scattering function is defined as [7, 8] S h (# , l) m= # r h [m, l] e j2##m , l = 0,1, L . 2) Here, # is the normalized Doppler frequency. 3. MMSE CHANNEL PREDICTOR Before considering adaptive predictors, we extend the MMSE channel ....

....channel will be considered random. Under the wide sense stationary uncorrelated scattering (WSSUS) assumption, the autocorrelation function of h[m, l] is h[m m, l] h # [m # , l # ] r h [m, l]# [l l # ] 7, 8] and the channel s Doppler spectra or scattering function is defined as [7, 8] S h (# , l) m= # r h [m, l] e j2##m , l = 0,1, L . 2) Here, # is the normalized Doppler frequency. 3. MMSE CHANNEL PREDICTOR Before considering adaptive predictors, we extend the MMSE channel predictor from [4] to prediction horizon p 1. As was shown in [4] the MMSE ....

P. A. Bello, "Characterization of randomly time-variant linear channels, " IEEE Trans. Comm. Syst., vol. 11, pp. 360--393, 1963.

....simulator. A perfect channel simulator enables the simulation of measured wide band mobile radio channels without any model approximations. II. THE DGUS MODEL In this chapter, we briefly describe the DGUS model. The DGUS model can be interpreted as the deterministic counterpart of Bello s [3] stochastic WSSUS model. Throughout te paper, we describe the model in the equivalent complex baseband, whereby the system functions and characteristic quantities of the DGUS model are marked with a swung dash ( to distinguish them from those of the stochastic WSSUS model. A. System Functions of ....

Bello P.A., 1963, "Characterization of randomly time-variant linear channels", IEEE Trans. Comm. Syst., 4, 360--393.

.... techniques are known to offer valuable counter measures against fading [9] Frequency selective channels offer multipath diversity [15] while time selective channels can provide Doppler diversity [12] Based on a basis expansion model (BEM) we adopt for time selective frequency flat channels [1], 13] 4] 12] 2] we will show that the maximum Doppler diversity order equals the number of bases . Subsequently, we will design linearly precoded transmissions capable of enabling this maximum diversity order. Linearly Manuscript received August 27, 2001; revised September 2003 ....

....is present, one can appeal to the central limit theorem to validate the following assumption: A2) The BEM coefficients M A ,I are zero mean, complex Gaussian random variables. We note that related sampled representations of time and frequency selective channels have also been advocated in [1], 13] 4] 12] 2] III. BLOCK TRANSMISSIONS AND DIVERSITY Figure 1 depicts the discrete time equivalent transmission model when communicating through the doubly selective channel (1) where P S and S P denote parallel to serial and serial to parallel operations, respectively. The ....

P. A. Bello, "Characterization of Randomly Time-Variant Linear Channels, " IEEE Trans. on Communicaiton Systems, vol. CS-11, no.4, pp. 360--393, Dec. 1963.

....is based on the computation of the mean square error. A) Average Doppler Shift and Doppler Spread The mean Doppler shift B and the Doppler spread B are characteristic quantities of a given Doppler power spectral density function S (f) and therefore they are of great importance [13], 14] The mean Doppler shift B is the first central moment (mean) of S (f) and is therefore defined as fS (f)df ; 47) whereas the Doppler spread B is the square root of the second central moment (variance) of S (f) and is consequently defined by u u u u u u f ....

P.A. Bello, "Characterization of Randomly Time-Variant Linear Channels,"IEEE Trans. Commun. Syst., vol. CS-11, no. 4, pp. 360-393, Dec. 1963.

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P. A. Bello, "Characterization of randomly time-variant linear channels", IEEE Trans. Commun. Syst., vol. CS-11, pp. 360--393, 1963.

No context found.

P. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Comm., vol. 11, pp. 360--393, 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Comm. Sys., vol. 11, pp. 360--393, 1963.

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P.A. Bello, "Characterization of randomly time-variant linear channels," IEEE Transactions on Communication Systems, vol. COM-11, pp. 360--393, Dec. 1963.

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P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst., vol. CS-11, pp. 360--393, Dec. 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst., vol. CS-11, pp. 360--393, Dec. 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun., vol. 11, pp. 360--393, Dec. 1963.

No context found.

P. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst., vol. COM-11, pp. 360--393, Dec. 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Systems, vol. 11, pp. 360--393, 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst., vol. COM-11, pp. 360--393, Dec. 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Transactions on Communication Systems, vol. CS-11, pp. 360--393, Dec. 1963.

No context found.

P.A. Bello, "Characterization of Randomly Time-Variant Linear Channels," IEEE Trans. Comm. Syst., vol. CS-11, pp. 360--393, 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Transactions on Communication Systems, vol. CS-11, pp. 360-- 393, Dec. 1963.

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Bello, P.: 1963, `Characterization of randomly time-variant linear channels'. IEEE Trans. Comm. Syst. CS-11, 360-393.

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P. A. Bello, "Characterization of randomly time-variant linear channnels," IEEE Transactions on Communication Systems, vol. CS11, pp. 360 - 393, Dec. 1963.

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P. A. Bello, "Characterization of Randomly Time-Variant Linear Channels, " IEEE Transactions on Communication Systems, vol. CS-11, pp. 360--393, Dec. 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channnels," IEEE Transactions on Communication Systems, vol. CS11, pp. 360 - 393, Dec. 1963.

No context found.

P. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Comm., vol. 11, pp. 360--393, 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Transactions on Communication Systems, vol. CS-11, pp. 360-- 393, Dec. 1963.

No context found.

P.A. Bello, "Characterization of randomly time-variant linear channels," IEEE Transactions on Communication Systems, vol. COM-11, pp. 360--393, Dec. 1963.

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Bello P. A., 1963, "Characterization of Randomly Time-Variant Linear Channels", IEEE Trans on Communication Systems, Vol. CS-11, No. 1, 360-393

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Bello, P. A., "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst., vol. CS-11, pp. 360-393, Dec. 1963.

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P.A. Bello, "Characterization of randomly time-variant linear channels", IEEE Trans. on Circuits and Systems, vol. CS-11, No. 4, pp. 360--393, Dec. 1963.

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P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst., vol. CS-11, pp. 360--393, Dec. 1963.

No context found.

P. A. Bello. Characterization of randomly time-variant linear channels. IEEE Transactions on Communications Systems, CS-11:360393, December 1963.

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P.A. Bello, "Characterization of Randomly Time-Variant Linear Channels," IEEE Transactions on Communications Systems, Vol. COM-11, pp. 360-393, December 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels, " IEEE Trans. Comm. Syst., vol. 11, pp. 360--393, 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Comm. Syst., vol. 11, pp. 360--393, 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Transactions on Communication Systems, vol. CS-11, pp. 360--393, Dec. 1963.

No context found.

P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst., vol. CS-11, pp. 360--393, Dec. 1963.

No context found.

Bello P. A., 1963, "Characterization of Randomly Time-Variant Linear Channels", IEEE Trans on Communication Systems, Vol. CS-11, No. 1, 360-393

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