Binary orthogonal signaling over the Gaussian channel with unknownphase/fading: new results and interpretations

The problem of binary orthogonal signaling over a Gaussian noise channel with unknown phase/fading is considered. By viewing the problem in a rotated coordinate system, the orthogonal signal structure is considered as the combination of an antipodal signal set and a pilot tone for channel measurement. For data detection the optimum matched-filter envelope-detector is shown to be identical to a novel detector-estimator receiver in which the detector performs partially coherent detection, using an absolute coherent reference generated by the estimator from the channel measurement provided by the pilot-tone component of the orthogonal signal structure. This detector-estimator interpretation shows that it is incorrect to refer to the optimum receiver as a noncoherent receiver. It also leads to the development of new approaches for analyzing the error probability of the receiver. An exponential Chernoff upper bound is obtained for the Rician channel     

Universal receivers with side information from the demodulators: anexample for nonselective Rician fading channels

We consider binary orthogonal signaling over a nonselective Rician-fading channel with additive white Gaussian noise. The received signal over such a channel may have both a specular component and a scatter (Rayleigh-faded) component. If there is only a scatter component, the noncoherent receiver is optimal. If there is only a specular component, the optimal receiver is the coherent receiver. In general, the optimal receiver for a Rician channel depends on the strengths of the two signal components and the noise density, and the set of possible optimal receivers is infinite. We consider a system in which the noncoherent receiver and the coherent receiver are employed in a parallel configuration for a symbol-by-symbol demodulation of the received signal. Each sequence of transmitted symbols produces a sequence at the output of each of the parallel receivers. The task of identifying which of these received sequences is a more reliable reproduction of the transmitted sequence is the data verification problem. In this paper, we show that data verification can be accomplished by combining side information from the demodulators with a suitable error-control coding scheme. The resulting system is a universal receiver that provides good performance over the entire range of channel parameters. In particular, the universal receiver performs better than the traditional noncoherent receiver     

Optimal detection of digital data over the nonselective Rayleighfading channel with diversity reception

Based on the criterion of minimum symbol error probability, an analysis is made of symbol-by-symbol detection of a sequence of digital data transmitted using linear suppressed-carrier modulation over L independent diversity channels with AWGN (additive white Gaussian noise) and slow nonselective Rayleigh fading. The optimal receiver is derived, but is found to be difficult to implement in practice because of its exponential growth in complexity as a function of sequence length. Suboptimal decision-feedback approximations are then suggested which are linear and readily implementable and can be integrated as generalized differentially coherent receivers. The exact bit error probabilities of these suboptimal receivers are obtained. Tight upper bounds on these error probabilities are also obtained which show simply how they behave as a function of signal-to-noise ratio and order of diversity. A main conclusion of this work is that optimal data detection on a fading channel should be performed using MMSE (minimum mean squared error) estimates of the quadrature amplitudes of the channel fading processes as a coherent reference     

On orthogonal signaling over the slow nonselective Rician fadingchannel with unknown specular component

Orthogonal signaling over the slow nonselective Rician fading channel is considered. Previous receiver designs have all assumed the amplitude and phase of the specular component of the received carrier to be known completely, but this assumption is entirely unrealistic. The problem is reformulated with unknown random amplitude and phase of the specular component. The optimum maximum likelihood receiver is obtained for equally likely equal-energy orthogonal signals and is shown to be identical to the quadratic receiver for the purely unknown phase channel and the pure Rayleigh fading channel. The error probability performance is analyzed for a fixed known specular amplitude. When specialized to the binary signaling case this error probability result exhibits a performance that is very close to and asymptotically approaches that of the conventional coherent-specular-component case for high SNR. Thus, knowledge of the specular component phase is not important to the optimum receiver     

Generalized Quadratic Receivers for Unitary Space–Time Modulation Over Rayleigh Fading Channels

We propose the generalized quadratic receivers (GQRs) for unitary space-time modulation over flat Rayleigh fading channels. The GQRs realize the performance improvement potential, known to be approximately 2-4 dB, between the quadratic receiver (QR) and the coherent receiver (CR), by performing channel estimation without the help of additional training signals that consume additional bandwidth. They are designed for various unitary space-time constellations (USTC) in which signal matrices may or may not contain explicit inherent training blocks, and may be orthogonal or nonorthogonal to one another. As the channel memory span exploited for channel estimation increases, the error probability of the GQRs reduces from that of the QR to that of the CR. The GQRs work well for both slow and fast fading channels, and the performance improvement increases as the channel fade rate decreases. For a class of USTC with the orthogonal design structure, the GQR is simplified to a form whose complexity can be less than the complexity of the QR or even that of the simplified form of the QR.     

On the design of universal receivers for nonselective Rician-fadingchannels

The purpose of this paper is to illustrate the issues involved in designing the demodulator portion of a universal receiver for unknown or time-varying channels by means of a specific example. We consider the class of nonselective Rician fading channels with additive white Gaussian noise. The optimal receiver for a Rician channel depends on the parameters of the channel, and the collection of optimal receivers for channels in the class of interest forms an infinite receiver class. We find a finite number of receivers in this receiver class with the property that, regardless of the parameters of the channel in effect, at least one of these receivers provides a symbol error probability that is within a specified deviation from the optimal symbol error probability for the channel. These receivers are then used in parallel to perform a symbol-by-symbol demodulation of the received signal. The receiver output that gives the most reliable reproduction of the transmitted sequence is identified by means of a data verification mechanism. The resulting system is a universal receiver. Methods for data verification are developed in other papers. In this paper, we develop an algorithm for finding the required finite set of receivers. Typical issues, such as the tradeoff between the number of parallel receivers and the allowed deviation from optimality, are discussed     

Error Probablity for Optimal and Suboptimal Quadratic Receivers in Rapid Rayleigh Fading Channels

The exact performance of optimal and suboptimal quadratic receivers in a binary hypothesis test between jointly distributed zero mean complex Gaussian variates is derived. The probability of error is given as a function of the characteristic values of a generalized eigenvalue problem set up in terms of the covariance matrix of the received signal-plus-noise and in the matrix of the quadratic form of the receiver. The results include the exact performance of various types of suboptimal receivers including those previously derived for the envelope matched filter for MFSK and the noncoherent DBPSK receiver in rapid Rayleigh fading, nonfrequency-selective channels. Also, the performance of near-optimal stationary process-long observation time [SPLOT] receivers, "energy detectors," and other approximately optimal receivers may be calculated for noncoherent signaling in the same channel.     

Optimal detection of coded differentially encoded QAM and PSKsignals with diversity reception in correlated fast Rician fadingchannels

The optimal sequence estimator for digital signals received over Λ different channels is derived. Each of these channels corrupts the transmitted signal by a mixture of additive white Gaussian noise (AWGN) and frequency-nonselective, correlated, fast Rician fading. By analysis it is shown that for the lth (1⩽l⩽Λ) diversity channel, the basic hardware structure of the optimal receiver consists of a combination of envelope, multiple differential, and coherent detectors. In order to reduce the overall implementation complexity, suboptimal, e.g., having a small number of differential detectors and equal combining diversity structures, versions of the optimal receivers are proposed and evaluated. Two modulation schemes are chosen in order to evaluate the overall performance of the proposed reduced-complexity diversity receivers: the π/4-shift 8-DQAM (differential quadrature amplitude modulation) and the 8-DPSK (differential phase shift keying). Bit-error-rate (BER) performance evaluation results are given. By means of computer simulation, the effect of correlation between the fading processes on the Λ diversity channels is investigated     

Feedback equalization for fading dispersive channels

Data transmission through a slowly fading dispersive channel is considered. A receiver that linearly operates on both the received signal and reconstructed data is postulated. Assuming an absence of decision errors, the receiver is optimized for a minimum-mean-square-error criterion. Transfer functions are determined and superiority over nonfeedback receivers is indicated. The feedback receiver can be realized in a slowly varying unknown environment by means of an adaptive technique that requires neither test signals nor statistical estimation. The receiver will eliminate timing jitter and Doppler shifts. In addition, the receiver provides a time-diversity effect, as the receiver probability of error averaged over the fading statistics is lower in the presence of dispersion than in its absence.     

Iterative receivers for space-time block-coded OFDM systems indispersive fading channels

We consider the design of iterative receivers for space-time block-coded orthogonal frequency-division multiplexing (STBC-OFDM) systems in unknown wireless dispersive fading channels, with or without outer channel coding. First, we propose a maximum-likelihood (ML) receiver for STBC-OFDM systems based on the expectation-maximization (EM) algorithm. By assuming that the fading processes remain constant over the duration of one STBC code word and by exploiting the orthogonality property of the STBC as well as the OFDM modulation, we show that the EM-based receiver has a very low computational complexity and that the initialization of the EM receiver is based on the linear minimum mean square error (MMSE) channel estimate for both the pilot and the data transmission. Since the actual fading processes may vary within one STBC code word, we also analyze the effect of a modeling mismatch on the receiver performance and show both analytically and through simulations that the performance degradation due to such a mismatch is negligible for practical Doppler frequencies. We further propose a turbo receiver based on the maximum a posteriori-EM algorithm for STBC-OFDM systems with outer channel coding. Compared with the previous noniterative receiver employing a decision-directed linear channel estimator, the iterative receivers proposed here significantly improve the receiver performance and can approach the ML performance in typical wireless channels with very fast fading, at a reasonable computational complexity well suited for real-time implementations     

Adaptive Diversity Reception Over a Slow Nonselective Fading Channel

We extend some previous results on adaptive receivers with memory for slow nonselective Rayleigh fading channels to the case of diversity reception. The Bayes receiver in this case is shown to be a generalized maximal ratio combiner. Error probability performance is obtained for antipodal signals such as BPSK. A simple performance upper bound is also derived. Numerical performance results are presented for the particular case of a Markov channel model.     

Probability-of-error bounds for binary transmission on the slowly fading Rician channel

Chernoff bounds and tilted distribution arguments are applied to obtain error probability bounds for binary signaling on the slowly-fading Rician channel with L diversity. For the maximum likelihood receiver, the CB-optimum [optimum in the sense of minimizing the Chernoff (upper) bound on error probability] signal correlation is determined and plotted; it is found that antipodal signals should be used ifa > b^{2}(1 + b), where a is the signal-to-noise ratio of the specular components andbis that of the fading components. The CB-optimum number of diversity paths is then obtained. Ifa/b > 0.2, antipodal signaling with unlimited diversity is CB-optimum; whereas, ifa/b < 0.2, orthogonal signaling with properly chosen diversity is very nearly CB-optimum. If restricted to orthogonal signaling, unlimited diversity is CB-optimum whenevera/b > 1.0. Similar results are obtained for the generally nonoptimum square-law-combining receiver. In this case, orthogonal signaling with finite diversity is always CB-optimum.     

Time-frequency packing for linear modulations: spectral efficiency and practical detection schemes

We investigate the spectral efficiency, achievable by a low-complexity symbol-by-symbol receiver, when linear modulations based on the superposition of uniformly time- and frequency-shifted replicas of a base pulse are employed. Although orthogonal signaling with Gaussian inputs achieves capacity on the additive white Gaussian noise channel, we show that, when finite-order constellations are employed, by giving up the orthogonality condition (thus accepting interference among adjacent signals) we can considerably improve the performance, even when a symbol-by-symbol receiver is used. We also optimize the spacing between adjacent signals to maximize the achievable spectral efficiency. Moreover, we propose a more involved transmission scheme, consisting of the superposition of two independent signals with suitable power allocation and a two-stage receiver, showing that it allows a further increase of the spectral efficiency. Finally, we show that a more involved equalization algorithm, based on soft interference cancellation, allows to achieve an excellent bit-error-rate performance, even when error-correcting codes designed for the Gaussian-noise limited channel are employed, and thus does not require a complete redesign of the coding scheme.     

Pilot-based estimation of time-varying multipath channels forcoherent CDMA receivers

Reliable coherent wireless communication requires accurate estimation of the time-varying multipath channel. This paper addresses two issues in the context of direct-sequence code-division multiple access (CDMA) systems: (i) linear minimum-mean-squared-error (MMSE) channel estimation based on a pilot transmission and (ii) impact of channel estimation errors on coherent receiver performance. A simple characterization of the MMSE estimator in terms of a bank of filters is derived. A key channel characteristic controlling system performance is the normalized coherence time, which is approximately the number of symbols over which the channel remains strongly correlated. It is shown that the estimator performance is characterized by an effective signal-to-noise ratio (SNR)-the product of the pilot SNR and the normalized coherence time. A simple uniform averaging estimator is also proposed that is easy to implement and delivers near-optimal performance if properly designed. The receivers analyzed in this paper are based on a time-frequency RAKE structure that exploits joint multipath-Doppler diversity. It is shown that the overall receiver performance is controlled by two competing effects: shorter coherence times lead to degraded channel estimation but improved inherent receiver performance due to Doppler diversity, with opposite effects for longer coherence times. Our results demonstrate that exploiting Doppler diversity can significantly mitigate the error probability floors that plague conventional CDMA receivers under fast fading due to errors in channel estimation     

Iterative Receiver Design with Joint Carrier-Frequency Offset and Channel Estimation for LDPC-Coded MIMO-OFDM Systems

In this paper, we study the design of expectation-maximization (EM)-based iterative receivers for low-density parity check -coded multiple-input multiple-output orthogonal frequency-division multiplexing systems with the presence of carrier-frequency offset (CFO). First, starting from the maximum-likelihood principle, we devise a novel EM-based pilot-aided scheme for joint estimation of CFO and channel coefficients. Then, this estimator is incorporated into the initialization step of the iterative receiver. Simulation results show the effectiveness of our receiver design in combating CFO over unknown frequency selective fading channels.     

Analysis of Rake reception with multiple symbol weight estimation for antipodal signaling

Consider a Rake receiver for coherent binary antipodal signaling with: 1) a delayed received signal configuration; 2) weight estimation by matched filtering using the reference signal along with the decisions of the previous M symbol intervals; and 3) predetection maximal-ratio combining (MRC). The weight estimation errors here are not independent of the additive noise, and do not fit into the Gaussian weighting error model for MRC. Here we analyze the error performance of the receiver by obtaining the conditional symbol error probability, conditioned on past decisions, from the characteristic function of the decision variable, and getting the unconditional error probability (UEP) for a block of M consecutive symbols using a Markov model of the decision process. The channel is Rayleigh fading with independent and identically distributed branch gains. Results show that the error performance of the Gaussian distributed weighting error model is a bound for that of multiple symbol weight estimation by matched filtering, and the steady state UEP decreases with increase of M, but the amount of decrease reduces as M increases.     

Orthogonally multiplexed orthogonal amplitude modulation family

A family of coherent orthogonally multiplexed orthogonally amplitude-modulated (OMOAM) signals is presented. The OMOAM signal is constituted by orthogonally multiplexing AI component signals, each constructed by a data-chosen group of L orthogonal pulse-amplitude-modulated basis signals. A generalized signal format is proposed to model the OMOAM signal in a unified way that the family contains not only classical orthogonally multiplexed modulations as special embodiments, but also a multitude of new modulations. A generalized optimum receiver for coherently demodulating OMOAM signals is developed and analyzed in terms of the bit error probability for the additive white Gaussian noise channel. The spectral characteristics of the OMOAM signals constructed from various time-limited and band-limited basis sets are studied in terms or the fractional out-of-band power containment. Several general trends of error and spectral performance characteristics are exploited     

Receiver structures for time-varying frequency-selective fadingchannels

Several receiver structures for linearly modulated signals are proposed for time-varying frequency-selective channels. Their channel estimators explicitly model the time variation of the channel taps via polynomials. These structures are constructed from the following building blocks: (i) sliding or fixed block channel estimators; (ii) maximum likelihood sequence detectors (MLSDs) or decision feedback equalizers (DFEs); and (iii) single or multiple passes. A sliding window channel estimator uses a window of received samples to estimate the channel taps within or at the end of the window. Every symbol period, the window of samples is slid along another symbol period, and a new estimate is calculated. A fixed block channel estimator uses all received samples to estimate the channel taps throughout the packet, all at once. A single pass receiver estimates the channel and detects data once only. A multipass receiver performs channel estimation and data detection repetitively. The effect of the training symbol positions on the performance of the block multipass approach is studied. The bit error rate (BER) performance of the MLSD structures is characterized through simulation and analysis. The proposed receivers offer a range of performance/complexity tradeoffs, but all are well suited to time-varying channels. In fast fading channels, as the signal-to-noise ratio (SNR) increases, they begin to significantly outperform the per-survivor processing-based MLSD receivers which employ the least mean-squares (LMS) algorithm for channel estimation     

An adaptive coherent receiver for MPSK/MDPSK over the nonselective Rayleigh fading channel with unknown characteristics

A coherent symbol-by-symbol (SBS) diversity receiver for m-ary phase-shift keying (MPSK) and differentially encoded MPSK (MDPSK) signals transmitted over a nonselective Rayleigh fading channel is presented. It incorporates a new adaptive filter for channel estimation that does not require any prior knowledge of the fading process model. It estimates the fading gains through decision-feedback and recursive least squares adaptation of the filter coefficients. A novel forgetting-factor adaptation algorithm that enables the filter to react quickly to randomly changing fading statistics caused by shadowing and acceleration/deceleration is introduced. Simulations show that the receiver performs better than that of Adachi's ( IEEE Trans. Veh. Technol. vol. 47 p. 909, 1998), either without shadowing or under slow lognormal shadowing.     

Sequence estimation over the slow nonselective Rayleigh fadingchannel with diversity reception and its application to Viterbi decoding

The authors consider minimum error probability detection of a data sequence transmitted using linear-suppressed carrier modulations, specifically phase-shift keying (PSK), over the Gaussian channel with slow nonselective Rayleigh fading. Complete channel interleaving/deinterleaving and diversity reception are assumed. The problem is considered with application to Viterbi decoding in particular. It is first shown that the two presently available receivers, namely, the conventional maximum likelihood (ML) receiver and the simultaneous estimation receiver, do not perform adequately for this problem. A two-stage receiver is proposed in which the unknown channel fading gains are estimated in the first stage prior to data sequence estimation in the second stage. This receiver is shown to perform adequately, and leads to an efficient receiver/decoder for Viterbi decoding of convolutionally trellis-coded sequences. The issue of optimum estimation of channel fading gains is clarified. The bit error probability of the receiver/decoder is analyzed, and numerical performance results are presented