Performance of a spatio-temporal matched filter receiver forDS/SSMA communications

A spatio-temporal matched filter receiver for direct-sequence spread-spectrum multiple-access (DS/SSMA) communications with aperiodic random quadriphase spreading sequences is derived, and the system performance is analyzed. It is shown with the method of characteristic functions that the cross-correlation coefficients between the desired user's and the interfering users' spreading sequences tend, in distribution, to independently and identically distributed circularly symmetric complex Gaussian random variables as the processing gain goes to infinity. Based on this Gaussian approximation, the structure of the spatio-temporal matched filter receiver is derived and a bit error rate formula is obtained. Using Monte-Carlo simulations, as well as analytical methods, it is shown that the spatio-temporal matched filter receiver achieves a significant performance improvement over the conventional, temporal, and spatial matched filter receivers by effectively suppressing the multiple access interference     

On ML Bit Detection of Binary Signals with Intersymbol Interference in Gaussian Noise

Various forms and properties of the maximum-likelihood (ML) bit detector structure for binary signals with intersymbol interference in the presence of additive stationary Gaussian noise are presented and two receiver implementation forms are considered. A simple analytical approximation which also has a heuristic interpretation as a lower bound on the bit probability of error for this detector is presented. The performance of this detector for typical small and moderate degrees of intersymbol interference is presented and compared to other detectors. Both cases indicate that the analytical approximation is quite tight and thus useful in predicting the performance of this highly nonlinear device.     

An Approximate Statistical Analysis of the Widrow LMS Algorithm with Application to Narrow-Band Interference Rejection

The Widrow LMS algorithm is considered for the implementation of an adaptive prewhitening filter in a direct-sequence (DS) spread-spectrum receiver. Exact expressions for the steady-state tapweight covariance matrix and resulting average excess mean square error are developed for the real LMS algorithm when the input contains a random binary sequence (used to model a pseudonoise spreading sequence). It is shown here that the output samples of the adaptive filter possess approximately Gaussian statistics under the conditions of slow convergence and a large number of filter taps. Using this approximation, expressions for the resulting bit error rate (BER) when the adaptive algorithm is used to suppress a fading gone jammer are developed, and numerical results obtained from these expressions are compared to simulation results for the DS receiver.     

Average bit-error-rate performance of band-limited DS/SSMA communications

Direct-sequence spread-spectrum multiple-access (DS/SSMA) communications, strictly band-limited transmitter chip waveforms with excess bandwidth in the interval between zero and one, pseudo-random spreading sequences, an additive white Gaussian noise channel, and matched filter receivers are considered. First, a new expression for the average bit error rate (BER) is derived for systems with quaternary phase-shift keying (QPSK) spreading, the conventional matched filter receiver, a coherent detector for binary phase-shift keying (BPSK) data symbols, and chip waveforms that result in no interchip interference. The expression consists of a well known BER expression based on the standard Gaussian approximation to multiple-access interference and a few correction terms. It enables accurate BER evaluations without any numerical integration for various choices of system parameters of interest. The accuracy of the expression is guaranteed as long as the conditional Gaussian approximation to the cross-correlation coefficients between the desired user's spreading sequence and the interfering users' spreading sequences is valid. The expression well reflects the effect of filtering on the system performance. Extensions of the expression are discussed for systems with QPSK spreading and different detection schemes, systems with BPSK spreading, and systems with different transmit and receive filters. Monte Carlo simulation results are also provided to verify the accuracy.     

Performance bounds for DS/SSMA communications with complexsignature sequences

A unified performance analysis of direct-sequence spread-spectrum multiple-access (DS/SSMA) communications with deterministic complex signature sequences is presented. The probability density function (PDF) of the multiple-user interference is determined. Using a round-down and round-up procedure on the PDF, arbitrarily tight lower and upper bounds on the probability of bit error (PBE) are obtained. Results based on the Gaussian approximation method are also presented. It is shown that complex sequences can yield better PBE performance than binary sequences. Using complex sequences, the number of signature sequences that have good auto- and cross-correlation properties is greatly enlarged. New users employing complex or binary signature sequences can be added to existing systems with graceful performance degradation     

Performance study of a maximum-likelihood receiver for FFH/BFSKsystems with multitone jamming

We derive the optimum structure of a maximum-likelihood (ML) receiver for a fast frequency-hopped binary frequency-shift-keying (FFH/BFSK) spread-spectrum (SS) communication system operating in the presence of multitone jamming (MTJ) and additive white Gaussian noise (AWGN). It is shown that the side information of noise variance, signal tone amplitude, and multiple interfering tone amplitude at each hop, as well as the computation of nonlinear modified Bessel function are required to implement the optimum ML receiver. We have also derived and analyzed two suboptimum receivers-namely, the ML-I and ML-II receivers-for large and small signal-to-noise ratio (SNR), respectively. Performance comparisons among various receivers show that the ML receiver gives the best performance, while the ML-I and ML-II receivers also outperform the other existing methods under both high and low SNR conditions     

A GLRT-based spread-spectrum receiver for joint channel estimationand interference suppression

The author considers the problem of demodulating a direct-sequence (DS) spread-spectrum signal in the presence of narrowband interference and multipath. A receiver is considered that is based on the generalized likelihood-ratio test (GLRT), in which the interferer is modeled as an Nth-order circular Gaussian autoregressive (AR) process and the multipath channel is represented by a tapped-delay line. The maximum-likelihood joint estimator for the channel coefficients and interferer AR parameters is then derived. Analytical expressions for bit-error rate are presented for GLRT receiver, under the assumption of perfect estimates of the channel and interferer parameters. The performance of the GLRT receiver is compared to that of a DS receiver using a transversal equalizer. It is shown that the GLRT receiver consistently outperforms the equalizer-based receiver by 2-3 dB. The performance of an adaptive GLRT receiver is evaluated where the recursive least-squares algorithm is used to jointly estimate the interferer and channel parameters     

PN code synchronization effects on narrow-band interferencerejection in a direct-sequence spread-spectrum receiver

The impact of imperfect synchronization on the performance of prediction-error interference rejection filters in noncoherent direct-sequence (DS) spread-spectrum communications is considered. Bit-error-rate analysis (BER) analysis (BER) of binary DPSK (differential phase-shift keying) data modulation used in conjunction with direct-sequence spread-spectrum is used as a performance measure. A first-order noncoherent delay-lock loop is used for the pseudonoise (PN) code tracking. Conditional BER results for the DS/DPSK systems for fixed values of the code tracking error are obtained. The average BER of the system is then evaluated by averaging the conditional BER expressions over the probability density function of the code tracking error. Results include the effects of both a single fading tone and a narrowband Gaussian interferer on the overall system performance. Interferer offset frequency is considered in determining the code tracking loop noise as well as the receiver BER     

Differentially coherent detection of binary partial responsecontinuous phase modulation with index 0.5

The performance of binary partial response continuous phase modulation (with index 0.5) using a differentially coherent receiver depends on the choice of the receiver filter. An optimum MMSE design method for this filter is presented. The receiver filter is equivalent to the cascade of a matched filter and an equalizer in order to reduce inherent intersymbol interference (ISI). It is shown that performance degradation with respect to that of the differential binary phase shift keying (BPSK) system is due to inherent ISI contained in the signal and also to noise enhancement and correlation caused by the receiver filter. The bit error probability on the Gaussian channel is calculated by assuming that ISI is Gaussian. The Gaussian minimum shift keying (MSK) signal is used for illustration     

Bit-to-bit error dependence in slotted DS/SSMA packet systems withrandom signature sequences

A technique is developed to find an accurate approximation to the probability of data bit error and the probability of packet success in a direct-sequence spread-spectrum multiple-access (DS/SSMA) packet radio system with random signature sequences. An improved Gaussian approximation to the probability of data bit error is performed. Packet performance is analyzed by using the theory of moment spaces to gain insight into the effect of bit-to-bit error dependence caused by interfering signal relative delays and phases which are assumed constant over the duration of a desired packet. Numerical results show that if no error control exists in the desired packet or if block error control is used when multiple-access interference is high, the error dependence increases the average probability of packet success beyond that predicted by models which use independent bit errors. However, when block error control is used and the multiple-access interference is low, the bit error dependencies cause a reduction in packet error performance     

Performance of DS/SSMA communications in impulsive channels. II.Hard-limiting correlation receivers

For pt.I see ibid., vol.COM-35, no.11, p.1179-88 (1987). In part I it was demonstrated that impulsive channel noise can be a serious detriment to the performance of direct-sequence spread-spectrum multiple-access (DS/SSMA) communications when conventional linear correlation reception is used. Here, a hard-limiting correlator as an alternative for reception of multiple-access transmission in impulsive channels is considered. For K asynchronous binary PSK DS/SSMA users sharing a linear channel corrupted by impulsive noise that is modeled at the output of the front-end filter of the receiver, techniques are developed for analyzing bit error probabilities of this hard-limiting receiver by exact computation for short spreading sequences, by approximation for longer spreading sequences, and by asymptotic limits for infinitely long spreading sequences. Performance is compared to that of the linear correlator under a variety of conditions, showing that hard-limiting correlation reception can offer substantial improvement over conventional systems in impulsive channels. However, the linear receiver is more effective against multiple-access noise only, and so a tradeoff emerges between rejection of impulsive noise and rejection of multiple-access interference     

Performance of binary and quaternary direct-sequencespread-spectrum multiple-access systems with random signature sequences

The performance of synchronous and asynchronous, binary and quaternary (with and without offset) direct-sequence spread-spectrum multiple-access (DS/SSMA) communication systems using random signature sequences and arbitrary chip waveforms is investigated. The average probability of error at the output of the correlation receiver is evaluated using a characteristic-function approach for these systems. Numerical results are presented that illustrate performance comparisons between systems using random and deterministic signature sequences, synchronous and asynchronous systems, systems with rectangular or sinewave chip waveforms, and binary and quaternary systems with the same data rates and bandwidth. In all cases, the accuracy of the Gaussian approximation is also examined     

Adapted demodulation for spread-spectrum receivers which employtransform-domain interference excision

It has been shown previously that the performance of a direct-sequence spread-spectrum (DS/SS) receiver which incorporates transform-domain excision of narrowband interference is improved by the use of time-weighting when the interference-to-signal power ratio (ISR) is relatively large, but is degraded by its use otherwise. The demodulator employed in this receiver is a filter which is matched to the chip sequence. While the matched filter gives minimum probability of error for additive white Gaussian noise (AWGN) in the absence of time-weighting and excision processing, the matched filter is suboptimal in their presence. Alternative demodulation rules which are adapted to time-weighting and excision processing are developed in the present paper. It is shown that, for the weighting functions considered, the matched filter requires as much as 3 dB more signal power than an adapted demodulator, to obtain a given probability of error. Furthermore, the performance with an adapted demodulator is generally superior to that for a receiver which does not use time-weighting when the ISR is at least moderately large, and is comparable otherwise. The potential benefit that may be derived from the use of an adapted demodulator in a CDMA network overlay is discussed     

Performance analysis of both hybrid and frequency-hoppedphase-coherent spread-spectrum systems. I. A hybrid DS/FH system

The authors present and analyze a model for both hybrid and frequency-hopped spread-spectrum systems in which a fully digital coherent receiver is used to demodulate the data. A receiver for a hybrid DS/FH (direct-sequence/frequency-hopped) system using a digital delay-lock loop is considered. In the absence of frequency uncertainty, it is shown that the tracking error can be modeled as an ergodic Markov chain with a finite-state set, and the probability density function of the steady-state tracking error is evaluated. When there is a frequency uncertainty, the dynamics of the resulting nonstationary phase error can be obtained, and an expression to evaluate the probability distribution of the first time at which the phase error hits predetermined boundary values is derived. Bit error rate performance is determined in the presence of both additive white Gaussian noise and various types of interference, and the performance is compared to that of noncoherent FSK systems     

Error probabilities for DS spread-spectrum systems using an ALE fornarrow-band interference rejection

The effects of the least-mean-squares adaptive line enhancer (ALE) weight misadjustment errors on the bit error rate are investigated for a direct-sequence spread-spectrum binary communication system in the presence of strong narrowband interference. The converged ALE weights are modeled as the parallel connection of a deterministic FIR (finite impulse response) filter and a random FIR filter. The statistics of the random filter are derived, assuming the output of the random filter to be primarily due to the jammer convolved with random filter weights. This output is shown to be nonGaussian and to cause significant error rate degradation in comparison to a Gaussian model. Error probability expressions are derived for the bit error rate, evaluated numerically, and compared to the corresponding error probabilities for a Gaussian model for the random filter output. For some typical system parameter values and error probabilities it is shown that the Gaussian model yields performance results that are too optimistic by several decibels     

EMP Effects on the Performance of a Direct Sequence Spread-Spectrum Communication System

This paper presents an analysis of the performance of a direct sequence spread-spectrum communication (processor) system operating in a nuclear EMP environment. EMP-induced interference (conducted EMP) at the receiver is modeled by a damped sinusoid and the analysis of the system uses a frequency domain approach instead of the conventional time domain approach. However, the interference suppression factor derived using the frequency domain approach reduces to that obtained using a time domain approach for the tone jammer case, in which the damping factor in the conducted EMP interference model approaches unity. Using a Gaussian approximation to the interference, numerical results are presented to illustrate the significant EMP-induced interference effects on the system performance and its hardening design parameters.     

Noncoherent maximum-likelihood block detection of orthogonalNFSK-LDPSK signals

This paper investigates the noncoherent block detection of orthogonal N frequency-shift keying (FSK)-L differential phase shift keying (DPSK) signals transmitted over the additive white Gaussian noise channel, based on the principle of maximum-likelihood (ML) sequence estimation. By virtue of a union bound argument, asymptotic upper bounds for the bit error probability of the developed ML block receiver are derived and verified by simulation. It is analytically shown that the noncoherent NFSK-LDPSK ML block receiver performs comparably with the ideal coherent NFSK-L phase shift keying (PSK) receiver for L = 2 and 4, as the observation block length is large enough. Furthermore, substantial performance improvement can be achieved by the ML block detection of the NFSK-LDPSK signal with L > 2 by increasing the observation block length     

Chip waveform design for DS/SSMA systems with aperiodic randomspreading sequences

The dependence of the error performance and spectral efficiency of direct-sequence spread-spectrum multiple-access (DS/SSMA) systems with matched filter receivers on the chip waveform is examined. The actual shape of the chip waveform, as well as its energy, is found to influence the statistical properties of the multiple-access interference (MAI). An approach to design waveforms that may result in interchip interference (ICI) is proposed and a criterion for design based on the conditional Gaussian approximation of the MAI for systems with aperiodic random spreading sequences is derived. For a simplified system, a closed-form solution for optimal band-limited waveforms is obtained for excess bandwidth less than or equal to one by using a performance metric that includes the effect of ICI. Numerical results, based on an analytical method, as well as Monte Carlo simulations, are provided to evaluate the performance of the proposed waveforms in general systems with conventional matched filter receivers     

An asymptotic analysis of DS/SSMA communication systems with randompolyphase signature sequences

Direct-sequence spread-spectrum multiple-access (DS/SSMA) communication systems with random m-phase sequences, for even m, are considered. By examining the asymptotic behavior of the normalized multiple-access interference (MAI), the authors find that a system with random m-phase sequences, for m>4, should have the same performance as one with random quadriphase sequences asymptotically. However, a system, with random m-phase sequences, for m⩾4, may perform better than one with random binary sequences when the number of simultaneous users is relatively small. A new Gaussian approximation is proposed to estimate the probabilities of error in these systems. In two cases, the new approximation reduces to established results which have been shown to provide close estimates to the probabilities of error     

An efficient technique for evaluating direct-sequencespread-spectrum multiple-access communications

A technique is presented for obtaining bounds on the average probability of error for direct-sequence spread-spectrum multiple-access (DS/SSMA) communications. The technique is of interest because it yields arbitrarily right bounds, involves a small amount of computation, avoids numerical integrations, and applies to many types of detection. As an illustration, the technique is applied to binary DS/SSMA communications, an additive white Gaussian noise channel, and a coherent correlation receiver. It is assumed that all the signature sequences are deterministic. Each transmitter is assumed to have the same power, although the approach can accommodate the case of transmitters with unequal powers. Expressions are given for the density functions of the random variables that model the multiple-access interference. These expressions are used to obtain arbitrarily tight upper and lower bounds on the average probability of error without making a Gaussian approximation or performing numerical integrations to incorporate the effects of multiple-access interference