Optimum Multiuser Asymptotic Efficiency

The degradation in bit error rate due to the presence of multiple-access interference in a white Gaussian channel can be measured by the multiuser asymptotic efficiency, defined as the ratio between the SNR required to achieve the same uncoded bit error rate in the absence of interfering users and the actual SNR. In this paper, the asymptotic efficiency of the optimum multiuser demodulator (a bank of matched filters followed by a Viterbi algorithm) is investigated and compared to that of the conventional single-user matched filter receiver. The computation of the optimum asymptotic efficiency of any given user is equivalent to the minimization of the Euclidean distance between any pair of multiuser signals which differ in at least one of the symbols of that user. It is shown that the optimum multiuser efficiency of asynchronous systems is nonzero with probability 1, and therefore the optimum demodulator does not become multiple-access limited in contrast to the single-user receiver. A class of signal constellations with moderate cross-correlation requirements is shown to achieve unit optimum multiuser efficiencies and, hence, to be equivalent to orthogonal signal sets from the viewpoint of performance of the optimum multiuser detector.     

Soft-Output Demodulation on Frequency-Selective Rayleigh Fading Channels Using AR Channel Models

This paper is a study of high-performance soft-output demodulation for slow or moderate frequency-selective and flat Rayleigh fading using an autoregressive (AR) channel model. For channel taps modeled as AR processes, the discrete-time-equivalent channel model is derived for a matched filter (matched to the transmit pulse) and symbol rate-sampled receiver front end. The optimum symbol-by-symbol demodulator is then derived and shown to consist of a joint data and Kalman filter (KF) channel estimator. Additionally, a symbol-by-symbol demodulator with an extended KF is proposed that jointly identifies and tracks the channel and the unknown parameters in AR channel models. A simulation study shows that the proposed algorithms offer significant advantages in performance or complexity compared to several previously proposed algorithms. The algorithms do not exhibit a significant error floor, provide soft-output metrics needed for interleaved coded modulation, provide high performance with a blind initialization, are capable of blind operation with fast acquisition though compatible with pilot-symbol-assisted modulation, and are robust to parameter mismatch.     

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     

Robust detection in DS-CDMA

Robust single-user detection is employed in a direct sequence code-division multiple-access (DS-CDMA) system in which the noise process contains impulsive components. The breakdown point is computed for a mixture noise model. The bit error probability expressions are derived under a Gaussian mixture. The performance is also evaluated in the presence of power imbalance and asynchronous reception. Noise, rather than interference, is shown to be the primary obstacle in achieving good performance for certain practical signal power and user load levels. It is concluded that DS-CDMA employing a robust correlator receiver performs better than the conventional matched filter in an impulsive noise environment     

Error Probability Evaluation for Systems Employing Differential Detection in a Rician Fast Fading Environment and Gaussian Noise

A method is presented for determining the error probability of a receiver using differential detection in the presence of Gaussian noise and fast Rician fading. Equations for the covariances of the fading component are derived, which include the effect of IF filter distortion. It is shown that these equations may be readily evaluated numerically. A simple formula for the error probability is derived for systems using BPSK and a matched filter receiver. An example of the error probability is given using this receiver. Also given is an example of a system using MSK with a practical IF filter. Different spectral shapes and bandwidths for the fading process are investigated for this example and their effect on the error probability is determined.     

Decision-feedback MAP receiver for time-selective fading CDMAchannels

A decision-feedback maximum a posteriori (MAP) receiver is proposed for code-division multiple-access channels with time-selective fading. The receiver consists of a sequence-matched filter and a MAP demodulator. Output samples (more than one per symbol) from the matched filter are fed into the MAP demodulator. The MAP demodulator exploits the channel memory by delaying the decision and using a sequence of observations. This receiver also rejects multiple-access interference and estimates channel fading coefficients implicitly to give good demodulation decisions. Moreover, computer simulations are performed to evaluate the bit-error rate performance of the receiver under various channel conditions     

Performance of direct-sequence spread-spectrum receiver usingdecision feedback and transversal filters for combatting narrowbandinterference

A direct-sequence spread-spectrum (DSSS) receiver using both decision feedback (DFB) and two-sided transversal filters for combatting narrowband interference (NBI) is proposed. The receiver is made up of two branches. In the first branch, the conventional demodulator is followed by a DFB filter, while in the second, auxiliary branch, a demodulator with the carrier in quadrature is followed by a two-sided adaptive transversal (AT) filter. Performance of this receiver was analyzed on the basis of the calculated mean-square error and the probability of error at the output of the receiver. Special attention was paid to the effects caused by the propagation of errors in the DFB filter. The results obtained show that NBI rejection is fairly high and practically does not depend upon the difference of frequencies of the desired and interfering carriers or upon the interfering carrier level     

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     

Matched filter bound for OFDM on Rayleigh fading channels

A matched filter bound (MFB) analysis is presented, in which the normalised Doppler rate is unrestricted, and thus applicable to OFDM signalling. In contrast to the static channel case, the optimal matched filter receiver is shown to be time varying and the probability of error is shown to depend on the transmitted pulse shape     

Analysis and optimization of DS-CDMA systems with time-limited partial response chip waveforms

Conventional direct sequence code division multiple access systems (DS-CDMA) using offset quadrature phase shift key (OQPSK) usually employ a strictly bandlimited partial response square-root raised cosine pulse as the chip waveform. They have the disadvantage of large envelope fluctuation that will incur performance degradation due to the intermodulation and bandwidth enlargement caused by post nonlinear processing. To improve the performance of DS-CDMA systems, the chip waveform and receiver should be properly selected. This paper presents a systematic performance analysis of a matched filter receiver and zero-forcing filter (ZF) receiver for DS-CDMA using a time-limited partial response chip waveform. Nevertheless the systematic performance analysis is applicable to bandlimited chip pulse as well. For the zero-forcing filters, we propose to select the frequency responses that satisfy the first Nyquist criterion. With this class of filters, we can choose the roll-off factor to minimize the total power of multiple access interference and noise power. The zero-forcing filter with proper choice of roll-off factor, referred to as optimum ZF, yields a performance better than the matched filter counterpart. The bit error rate (BER) performance of the optimum ZF with superposed quadrature amplitude modulation signal as the time pulse waveform is evaluated. It is shown that the optimum ZF provides better BER performance than conventional OQPSK and minimum shift keying, and its envelope uniformity is much better than that of OQPSK.     

An asymptotically optimal random modem and detector for robustcommunication

Coherent communication over a waveform channel corrupted by thermal noise and by an unknown and arbitrary interfering signal of bounded power is considered. For a fixed encoder, a random modulator/demodulator (modem) and detector are derived. They asymptotically minimize the worst-case error probability as the blocklength of the encoder becomes large. This optimal modem is independent of the encoder, and the optimal detector is the standard correlation receiver. A simple upper bound to the performance of any encoder when used with the optimal modem and detector is presented. These results provide a benchmark with which the performance of spread-spectrum modems and robust detection rules can be compared     

Performance analysis of instantaneous frequency-based interferenceexcision techniques in spread spectrum communications

Jammers characterized by their instantaneous frequencies can be effectively mitigated in direct sequence spread spectrum communications by using open-loop adaptive excision filters. The primary requirement for these filters is that they must possess a notch in tune with the jammer instantaneous frequency (IF) to annihilate the interference power at every time sample. The interference time-varying frequency can be obtained using existing IF estimators, including quadratic time-frequency distribution methods. Without focusing on any specific estimator, we develop expressions for the receiver performance using a general class of multiple-zero FIR excision filters and show the dependence of the bit error rate (BER) on the filter order and its group delay. The effect of inaccuracies in the jammer instantaneous frequency information on the receiver performance is considered and evaluated as a function of the filter notch bandwidth. The latter is defined by the filter zero multiplicity, which is shown to be an important factor in the analysis of the correlator signal-to-noise ratio (SNR)     

Bit error probability of a matched filter in a Rayleigh fadingmultipath channel in the presence of interpath and intersymbolinterference

The exact bit error probability of a matched filter receiver in a known discrete Rayleigh fading multipath channel is determined for a binary antipodal system. The matched filter receiver or the RAKE is one form of a diversity receiver. Traditionally, both the interpath interference (IPI) and the intersymbol interference (ISI) caused by the non-ideal autocorrelation function of the bit waveform are neglected in the analysis of the RAKE. Previously, the exact matched filter bounds; which include IPI, were derived. This bound gives the performance of the matched filter if only one symbol is transmitted. In our analysis, a symbol sequence is transmitted instead of only one symbol. Thus, our analysis includes both IPI and ISI as well as the correlation between the paths, The analysis permits direct comparisons between different kinds of bit waveforms     

Trellis-coded constant-envelope modulations with linear receivers

We present two multilevel constant-envelope continuous-phase modulation (CPM) schemes with four-dimensional (4-D) trellis coding. The receiver is composed of a simple quadrature demodulator, followed by a symbol-rate sampler and a Viterbi decoder matched to the code trellis. The first modulation is a quaternary CPM scheme whose phase transitions over a symbol interval are those of π/4-shift quaternary phase-shift keying (QPSK). The demodulator filter is optimized so as to minimize the combined effect of intersymbol interference (ISI) and noise at the decision instants. We use Wei's (1987) 16-state 4-D trellis code, and redefine the set partitioning tree so as to maintain the same minimum distance between parallel transitions as in quadrature amplitude modulation (QAM) signal sets. The resulting modulation outperforms minimum-shift keying (MSK) by as much as 3.5 dB, in addition to reducing the 30-dB signal bandwidth by 20%. Next, we introduce an octonary (8-level) CPM scheme whose phase transitions are those of π/8-shift 8PSK. The same trellis code and receive filter optimization are also applied to this modulation which is shown to achieve better error rate performance than MSK, while saving some 60% of the transmitted signal bandwidth     

A differentially coherent receiver for minimum shift keying signal

The author extends to the case of minimum-shift-keying (MSK) modulation the differentially coherent reception theory established for phase-shift-keying modulation. A novel differentially coherent detector for MSK is thus derived. The receiver filter is equivalent to the cascade of a matched filter and an equalizer in order to suppress inherent intersymbol interference. It is shown that performance can be improved when the delay between signals, multiplied by the differential detector, is increased from one to M bit time intervals. This decreases the effect of noise correlation and, thus, the bit error probability. The bit error probability of the proposed receiver is calculated. It is found that almost all potential improvement due to the delay M is obtained with M=3     

The Effect of Bandlimiting Filters on Probability of Error of MSK

Minimum Shift Keying (MSK) is a method of modulation which can be viewed as a special case of Frequency Shift Keying or a special form of Offset Quadrature Phase Shift Keying; therefore, it can be detected either by a discriminator or with a pair of matched filters. In the latter case, the system is optimal, provided there are no bandlimiting filters in the transmitter and receiver. These filters introduce intersymbol interference and hence degrade the performance of the system. In this paper we investigate analytically the effect of a bandlimiting filter in the receiver on the error probability of the system, presenting numerical results when that filter is of the Butterworth type. It is shown that a very simple suboptimal detector outperforms the matched filter detector so long as2W/R_{b} < 1.3, where Rbis the bit rate andWis the single sided 3 dB bandwidth of the bandlimiting filter.     

MMSE interference suppression for direct-sequence spread-spectrumCDMA

We consider interference suppression for direct-sequence spread-spectrum code-division multiple-access (CDMA) systems using the minimum mean squared error (MMSE) performance criterion. The conventional matched filter receiver suffers from the near-far problem, and requires strict power control (typically involving feedback from receiver to transmitter) for acceptable performance. Multiuser detection schemes previously proposed mitigate the near-far problem, but are complex and require explicit knowledge or estimates of the interference parameters. In this paper, we present and analyze several new MMSE interference suppression schemes, which have the advantage of being near-far resistant (to varying degrees, depending on their complexity), and can be implemented adaptively when interference parameters are unknown and/or time-varying, Numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver. We conclude that MMSE detectors can alleviate the need for stringent power control. In CDMA systems, and may be a practical alternative to the matched filter receiver     

An optimal whitening approach to linear multiuser detection

We propose a new linear multiuser receiver for synchronous code-division multiple-access (CDMA) systems, referred to as the orthogonal multiuser (OMU) receiver. Unlike the linear minimum mean-squared error (MMSE) receiver, the OMU receiver depends only on the signature vectors and does not require knowledge of the received amplitudes or the channel signal-to-noise ratio (SNR). Several equivalent representations of the receiver are developed with different implications in terms of implementation. In the first, the receiver consists of a decorrelator demodulator followed by an optimal whitening transformation on a space formed by the signatures. In the second, the receiver consists of a bank of correlators with correlating vectors that are projections of a set of orthogonal vectors, and are closest in a least squares sense to the decorrelator vectors and also closest in a least squares sense to the signature vectors. In the third, the receiver consists of a single-user matched filter (MF) followed by an optimal whitening transformation on a space formed by the signatures. We derive exact and approximate expressions for the probability of bit error, as well as the asymptotic signal-to-interference+noise ratio (SINR) in the large system limit. The analysis suggests that over a wide range of channel parameters the OMU receiver can outperform both the decorrelator and the single-user MF and perform similarly to the linear MMSE receiver, despite not knowing the channel parameters.     

Performance of Narrow-Band Manchester Coded FSK with Discriminator Detection

Due to the large discrepancies m the published results, the bit error rate (BER) performance of narrow-band Manchestercoded frequency-shift-keyed systems (MCFSK) with discriminator detection is reviewed and new results are presented which agree closely with measurements. It is found that a minimum BER is obtained for a peak-to-peak frequency deviation of about 1.35 times the bit rate and a receiver bandwidth of about 1.8 times the bit rate. The published results are shown to be rather optimistic. A coherent MCFSK demodulator is then shown to perform 3 dB better than discriminator detection. It is further shown that in the range of receiver bandwidths larger than the bit rate, it is sufficient to consider the intersymbol interference effects to have come only from the two bits adjacent to the bit being detected. Finally, if the phase noise components are assumed to be Gaussian distributed, the error probability formulas obtained do not predict the correct error performance.     

Alternatives for on-board digital multicarrier demodulation

In this paper alternatives for digital multicarrier demodulators (MCD) suitable for advanced digital satellite communications systems are presented. The MCD permits the direct on-board interfacing of FDMA and TDM communication links by digital signal processing techniques. Two main functions are implemented by a MCD: demultiplexing (DEMUX) and demodulation (DEMOD). We focus here only on a digital implementation of the MCD, looking at its advantages, flexibility, better performance and VLSI integrability. The DEMUX may be implemented in a number of ways: the analytic signal method, fast Fourier transform with polyphase network technique, or multistage methods. For all the implementation methods considered it is shown that a certain degree of integration of DEMUX and DEMOD functions is possible. To this end, in the proposed MCD schemes the receiver pulse-shaping filter has been integrated in the DEMUX structure, reducing the overall implementation complexity. It is shown that, for the per-channel structure based on the analytic signal method, a highly modular and flexible implementation can also be achieved. Coherent demodulation is used to reduce the signal-to-noise ratio required to achieve a specified bit error rate. The coherent demodulation is carried out by using the maximum likelihood (ML) estimation method. Two different approaches to receiver synchronization have been studied. For the first, the carrier phase and symbol timing estimates are independently derived by suitable techniques. The second approach makes use of the maximum a posteriori probability method to estimate both the carrier phase and symbol timing of the receivied signal. In particular, for this technique it is shown that, by a suitable choice of the architecture of the digital coherent receiver, the ML demodulator can be integrated in the joint carrier and clock recovery circuit, with no increase in the overall system complexity. The digital architecture of the proposed MCD can be adapted to different digital modulation techniques. However, here we consider only the application for QPSK signals, as this modulation scheme is the most promising for digital satellite communications. A theoretical analysis and computer simulation have been used to evaluate the performance degradation of the proposed MCD, including finite-arithmetic implementation effects.