Capacity regions and optimal power allocation for groupwise multiuser detection

In this letter, optimal power allocation and capacity regions are derived for groupwise successive interference cancellation (GSIC) systems operating in multipath fading channels, under imperfect channel estimation conditions. It is shown that the impact of channel estimation errors on the system capacity is two-fold: It affects the receiver performance within a group of users, as well as the cancellation performance (through cancellation errors). An iterative power allocation algorithm is derived, based on which it can be shown that that the total required received power is minimized when the groups are ordered according to their cancellation errors, and the first detected group has the smallest cancellation error. Performance/complexity tradeoff issues are also discussed by directly comparing the system capacity for different implementations: GSIC with linear minimum-mean-square error (LMMSE) receivers within the detection groups; GSIC with matched filter (MF) receivers; multicode LMMSE systems; and simple all MF receivers systems.     

Achieving near-optimum asymptotic efficiency and fading resistanceover the time-varying Rayleigh-faded CDMA channel

We study multiuser receiver design and analysis for synchronous code-division multiple-access (CDMA) channels with time-varying Rayleigh fading. Starting from an error probability criterion, we first derive a near-optimum receiver for this channel that admits a detector-estimator decomposition, has certain asymptotic optimality properties and a complexity which is independent of the length of the observation interval. The performance of this detector is analytically characterized and contrasted with that of the optimal multiuser detector for the time-invariant (or static) CDMA Rayleigh-fading channel when it is implemented over the time-varying channel. Notable among our conclusions is the fact that, unlike the static channel multiuser detector, the time-varying channel detector is able to withstand not only the estimated interference from the other system users, but also, the residual interference (that cannot be estimated) arising out of imperfect estimation of the interferer fading parameters. Using estimation error covariance information, this detector shows flexibility in accommodating a wide range of interferer fading conditions     

Unified design of iterative receivers using factor graphs

Iterative algorithms are an attractive approach to approximating optimal, but high-complexity, joint channel estimation and decoding receivers for communication systems. We present a unified approach based on factor graphs for deriving iterative message-passing receiver algorithms for channel estimation and decoding. For many common channels, it is easy to find simple graphical models that lead directly to implementable algorithms. Canonical distributions provide a new, general framework for handling continuous variables. Example receiver designs for Rayleigh fading channels with block or Markov memory, and multipath fading channels with fixed unknown coefficients illustrate the effectiveness of our approach     

Antenna selection for spatial multiplexing systems with linearreceivers

Future cellular systems will employ spatial multiplexing with multiple antennas at both the transmitter and receiver to take advantage of large capacity gains. In such systems it will be desirable to select a subset of available transmit antennas for link initialization, maintenance or handoff. We present a criterion for selecting the optimal antenna subset when linear, coherent receivers are used over a slowly varying channel. We propose use of the post-processing SNRs (signal to noise ratios) of the multiplexed streams whereby the antenna subset that induces the largest minimum SNR is chosen. Simulations demonstrate that our selection algorithm also provides diversity advantage thus making linear receivers useful over fading channels     

Multiple differential detection of parallel concatenatedconvolutional (turbo) codes in correlated fast Rayleigh fading

A new technique for iterative decoding of parallel concatenated convolutional (turbo) codes (PCCCs) for the correlated fast Rayleigh fading channel is proposed and evaluated. This technique is based upon the use of a multiple differential detector (MDD) receiver structure which exploits the statistical characteristics of the fading process to overcome the effects of the rapid phase and amplitude variations. Since traditional MDD receivers cannot be used with PCCCs because they do not produce soft output and are not compatible with channel interleaving, a novel MDD receiver structure is derived which overcomes these shortfalls. In addition, with careful use of extrinsic information related to the a posteriori probability distribution function of the transmitted symbols, the receiver is designed in such a fashion as to allow channel estimation to improve with each iteration. Evaluation of the proposed receiver by means of computer simulation has shown dramatic performance improvements in fast Rayleigh fading channels as compared to long constraint-length conventional convolutional codes using both single and traditional MDD receiver structures     

Partial sampling MMSE interference suppression in asynchronousmulticarrier CDMA system

Linear minimum mean square error (LMMSE) receivers for asynchronous multicarrier code division multiple access (MC-CDMA) system under frequency-selective Rayleigh fading channel is studied. The performance of this LMMSE receiver is evaluated and shown to be superior to that of the other two schemes, equal-gain combining (EQC) and maximum-ratio combining (MRC). However, a perfect timing estimation of the desired user is needed for these receivers, as a misaligned sampling interval of these receivers results in severely self intersymbol interference (ISI) and intercarrier interference (ICI) for the desired signal at the output. In order to remove the timing acquisition requirement of a receiver for an asynchronous MC-CDMA system, we proposed a novel partial sampling MMSE (PS-MMSE) receiver. Numerical result shows that the PS-MMSE receiver without timing knowledge provides significantly stronger interference suppression capability than the LMMSE receiver with known timing. Moreover, a so-called reduced complexity partial sampling MMSE (RPS-MMSE) receiver is proposed to make the number of the receiver's taps independent of the number of subcarriers. Results show that with a proper grouping parameter, a much less complicated RPS-MMSE receiver achieves almost the same performance as the PS-MMSE receiver. Thus, one is able to implement an MMSE receiver without a prior timing requirement to perform multiuser detection for the MC-CDMA system in an asynchronous scenario at the expense of a slight complexity increase     

A robust noncoherent equalizer receiver for fading channels with short memory .I. Basic structure

Traditional equalizers are very sensitive to carrier frequency offsets between the transmitter and receiver. Coherent receivers with frequency estimation algorithms can remove the offset to prevent the equalizer breakdown, but with a penalty in receiver complexity. On the other hand, noncoherent receivers such as differential detectors are inherently robust to the frequency offsets but cannot employ standard equalization techniques due to their nonlinear front-end. We introduce a simple noncoherent equalizer receiver structure for fading channel environments with short memory (up to two-bit intervals). The receiver consists of a whitened matched filter followed by a differential detector and a maximum likelihood sequence estimation (MLSE) equalizer. We examine the performance of this noncoherent equalizer by both analysis and simulation. It is shown that despite the simplicity, this receiver structure is capable of significant performance improvement as compared to an ordinary differential detector while operating with receiver frequency offsets two orders of magnitude greater than a traditional MLSE equalizer. This structure offers an attractive solution for high-bit-rate cordless transmission systems such as Digital Enhanced Cordless Telecommunications (DECT) that use simple noncoherent receivers whose performance can be constrained by channel dispersion. Using DECT as a case study, we show that the equalizer's performance limits are caused by the receiver nonlinearity and can be improved by adaptation of this nonlinearity to channel conditions.     

Multisampling decision-feedback linear prediction receivers for differential space-time modulation over Rayleigh fast-fading channels

Novel decision-feedback (DF) linear prediction (LP) receivers, which process multiple samples per symbol interval in conjunction with optimal sample combining, are proposed for differential space-time modulation (DSTM) over Rayleigh fast-fading channels. Performance analysis demonstrates that multisampling DF-LP receivers outperform their symbol-rate sampling counterpart in fast fading substantially. In addition, an asymptotically tight upper bound on the pairwise error probability is derived. In view of this bound, the design criterion of DSTM for fast fading is the same as that for block-wise static fading. To avoid the estimation of the second-order statistics of the channel, a polynomial-model-based DF-LP receiver is proposed. It can approach the performance of the optimum DF-LP receiver at high signal-to noise ratios, provided fading is moderate.     

Receiver design in multicarrier direct-sequence CDMA communications

Multicarrier direct-sequence code-division multiple access (MC-DS-CDMA) has emerged recently as a promising candidate for the next generation broad-band mobile networks. We consider the design of multiuser receivers for MC-DS-CDMA communications over fading channels. We present a class of spreading codes that enables the simple despreading-combining receiver to achieve the performance of the optimum multiuser linear receiver. These codes are shown to be optimum for independent fading channels under a code design criterion derived. Also derived are analytic solutions of optimum spreading codes for any given channel fading statistics. Simulation results are provided to demonstrate the significant gains in performance and simplicity due to the proposed techniques     

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     

Optimum multiuser noncoherent DPSK detection in generalized diversity Rayleigh-fading channels

The jointly optimum multiuser noncoherent detector for differential phase-shift keying (DPSK) modulation over the generalized diversity Rayleigh-fading (GDRF) channel is derived and analyzed. The GDRF channel includes time/frequency/receiver antenna diversity and allows fading correlations between the various diversity branches of each user. Noncoherent detection here refers to the case where the receiver has neither knowledge of the instantaneous phases nor of the envelopes of the users' channels. Upper and lower bounds on the bit-error probability of the optimum detector are derived for a given user. For fast fading, when the fading coefficients vary from one symbol interval to the next (but are still essentially constant over one symbol interval), the detector asymptotically (for high signal-to-noise ratios (SNRs)) reaches an error floor, which is bounded from below and above for different fast fading scenarios. For slow fading, when the channel is constant for at least two consecutive symbol intervals, the upper bound is shown to converge asymptotically to the lower bound. Thus, the asymptotic efficiency of optimum multiuser DPSK detection can be determined and is found to be positive. In contrast to coherent detection, however, it is smaller than unity in general. Since the asymptotic efficiency is independent of the interfering users' signal strengths, the optimum detector is near-far resistant. While optimum multiuser detection is exponentially complex in the number of users, its performance provides the benchmark for suboptimal detectors. In particular, it is seen that the previously suggested post-decorrelative detectors can be far from satisfactory.     

Multiuser detection in asynchronous CDMA frequency-selective fading channels

Multipath fading severely limits the performances of conventional code division multiple-access (CDMA) systems. Since every signal passes through an independent frequency-selective fading channel, even modest cross-correlations among signature sequences may induce severe near-far effects in a central multiuser receiver. This paper presents a systematic approach to the detection problem in CDMA frequency-selective fading channels and proposes a low complexity linear multiuser receiver, which eliminates fading induced near-far problem.We initially analyze an optimal multiuser detector, consisting of a bank of RAKE filters followed by a dynamic programming algorithm and evaluate its performance through error probability bounds. The concepts of error sequence decomposition and asymptotic multiuser efficiency, used to characterize the optimal receiver performance, are extended to multipath fading channels.The complexity of the optimal detector motivates the work on a near-far resistant, low complexity decorrelating multiuser detector, which exploits multipath diversity by using a multipath decorrelating filter followed by maximal-ratio combining. Analytic expressions for error probability and asymptotic multiuser efficiency of the suboptimal receiver are derived that include the effects of multipath fading, multiple-access interference and signature sequences correlation on the receiver's performance.The results indicate that multiuser detectors not only alleviate the near-far problem but approach single-user RAKE performance, while preserving the multipath diversity gain. In interference-limited scenarios multiuser receivers significantly outperform the RAKE receiver.This paper was presented in part at the Twenty-Sixth Annual Conference on Information Sciences and Systems, Princeton, NJ, March 1992 and MILCOM'92, San Diego, CA, October 1992. This work was performed while author was with the Department of Electrical and Computer Engineering, Northeastern University, Boston, USA.     

A systematic approach to carrier recovery and detection ofdigitally phase modulated signals of fading channels

The problem of optimal carrier recovery and detection of digitally phase modulated signals on fading channels by using a nonstructured approach is presented, i.e. no constraint is placed on the receiver structure. First, the optimal receiver is derived for digitally phase-modulated signals when transmitted over a frequency-nonselective fading channel with memory. The memory results from the fact that usually the coherence time of the channel is larger than the symbol period. Symbols adjacent in time cannot be detected independently and therefore the well-known quadratic receiver is not optimal in this case. A maximum a posteriori (MAP) detector is derived and explicitly utilizes the channel memory for carrier recovery. The derivation shows that the optimal carrier recovery is, under certain conditions, a Kalman filter. Some attractive properties of this carrier recovery unit (including the absence of hang up) are discussed. Then the error rate of several digital modulation schemes is calculated taking the performance of the filter into account. The differences in susceptibility of the modulation schemes to carrier phase jitter are specified     

Secure Communication Over Fading Channels

The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an information-theoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established, which gives the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then applied to study the fading BCC. The ergodic performance is first studied. The ergodic secrecy capacity region and the optimal power allocations that achieve the boundary of this region are derived. The outage performance is then studied, where a long-term power constraint is assumed. The power allocation is derived that minimizes the outage probability where either the target rate of the common message or the target rate of the confidential message is not achieved. The power allocation is also derived that minimizes the outage probability where the target rate of the confidential message is not achieved subject to the constraint that the target rate of the common message must be achieved for all channel states.     

Effects of Nonzero-Centroid and Skewness of Fading Spectrum on Incoherent FSK and DPSK Error Probabilities

The effects of nonzero-centroid and skewness of a fading spectrum are shown to influence the binary error probabilities of incoherent FSK and differentially coherent phase-reversal (DPSK) matched-filter receivers. It is also shown that for incoherent FSK, the skewness or nonzero centroid in the fading spectrum causes different error probabilities for binary signals, resulting in a binary asymmetric channel. The difference in error probabilities for binary signals can be used as a criterion for aligning the transmitter and receiver antennas coupled through a fading channel.     

A robust adaptive DFE receiver for DS-CDMA systems under multipathfading channels

This paper presents a novel receiver design from signal processing viewpoint for direct-sequence code-division multiple access (DS-CDMA) systems under multipath fading channels. A robust adaptive decision-feedback equalizer (DFE) is developed by using optimal filtering technique via minimizing the mean-square error (MSE). The multipath fading channels are modeled as tapped-delay-line filters, and the tap coefficients are described as Rayleigh distributions in order to imitate the frequency-selective fading channel. Then, a robust Kalman filtering algorithm is used to estimate the channel responses for the adaptation of the proposed DFE receiver under the situation of partially known channel statistics. The feedforward and feedback filters are designed by using not only the estimated channel responses but the uncertainties and error covariance of channel estimation as well. As shown in the computer simulations, the proposed adaptive DFE receiver is robust against the estimation errors and modeling dynamics of the channels. Hence, it is very suitable for receiver design in data transmissions through multipath fading channels encountered in most wireless communication systems     

An adaptive multiuser detector for DS‐CDMA systems in multipath fading channels

In this paper, we investigate the performance of an adaptive multistage detection scheme for direct‐sequence code‐division multiple‐access (DS‐CDMA) systems. The first stage consists of an adaptive multiuser detector which is based on the linear constrained minimum variance (LCMV) criterion. The interference cancellation (IC) occurs in the second stage. The performance of the iterative receiver over both flat and frequency‐selective fading channels is investigated and compared to the single‐user bound. In all cases, and under heavy system loads with near‐far problems, the iterative receiver is shown to offer substantial performance improvement and large gain in user‐capacity relative to the standard LCMV. In flat‐fading channels, our results show that the performance of the iterative detector is very close to the single‐user bound. For the frequency‐selective channel, this performance is noted to be in the order of 1 dB far from the single‐user bound. Copyright © 2007 John Wiley & Sons, Ltd.     

Differential and coherent decorrelating multiuser receivers for space-time-coded CDMA systems

Previously, we proposed a differential space-code modulation (DSCM) scheme that integrates the strength of differential space-time coding and spreading to achieve interference suppression and resistance to time-varying channel fading in single-user environments. In this paper, we consider the problem of multiuser receiver design for code-division multiple-access (CDMA) systems that utilize DSCM for transmission. In particular, we propose two differential receivers for such systems. These differential receivers do not require the channel state information (CSI) for detection and, still, are resistant to multiuser interference (MUI) and time-varying channel fading. We also propose a coherent receiver that requires only the CSI of the desired user for detection. The coherent receiver yields improved performance over the differential receivers when reliable channel estimates are available (e.g., in slowly fading channels). The proposed differential/coherent receivers are decorrelative schemes that decouple the detection of different users. Both long and short spreading codes can be employed in these schemes. Numerical examples are presented to demonstrate the effectiveness of the proposed receivers.     

Multiuser receivers for CDMA systems in Rayleigh fading channels

Multiuser demodulation in relatively fast fading channels is analyzed. The optimal maximum likelihood sequence detection (MLSD) receiver is derived and a general suboptimal receiver to approximate the MLSD is proposed. The performance of the parallel interference cancellation (PIC) and decorrelating receivers is compared. The PIC receiver is demonstrated to achieve better performance in known channels than the decorrelating receiver, but it is observed to be more sensitive to the channel coefficient estimation errors than the decorrelator. At high channel loads the PIC receiver suffers from bit error rate (BER) saturation, whereas the decorrelating receiver does not. The performance of data-aided (DA) and decision-directed (DD) multiuser channel estimation is also compared. DA channel estimation is shown to be more robust than DD channel estimation, which may suffer from BER saturation caused by hangups at high signal-to-noise ratios (SNRs). The impact of channel estimation filter impulse response on the BER is studied by comparing optimal and suboptimal channel estimation filters. The implementation complexity of the decorrelating and PIC receivers is compared in terms of required floating point operations and clock cycles in a practical communication scenario. It is observed that the PIC receiver is only moderately more complex to implement than the conventional matched filter bank receiver, whereas the decorrelating receiver is significantly more complex     

On the duality of Gaussian multiple-access and broadcast channels

We define a duality between Gaussian multiple-access channels (MACs) and Gaussian broadcast channels (BCs). The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of the BC (both constant and fading) can be written in terms of the capacity region of the dual MAC, and vice versa. We can use this result to find the capacity region of the MAC if the capacity region of only the BC is known, and vice versa. For fading channels we show duality under ergodic capacity, but duality also holds for different capacity definitions for fading channels such as outage capacity and minimum-rate capacity. Using duality, many results known for only one of the two channels can be extended to the dual channel as well.