Differential modulation for two-way wireless communications: a perspective of differential network coding at the physical layer

This work considers two-way relay channels (TWRC), where two terminals transmit simultaneously to each other with the help of a relay node. For single antenna systems, we propose several new transmission schemes for both amplify-and-forward (AF) protocol and decode-and-forward (DF) protocol where the channel state information is not required. These new schemes are the counterpart of the traditional noncoherent detection or differential detection in point-to-point communications. Differential modulation design for TWRC is challenging because the received signal is a mixture of the signals from both source terminals. We derive maximum likelihood (ML) detectors for both AF and DF protocols, where the latter can be considered as performing differential network coding at the physical layer. As the exact ML detector is prohibitively complex, we propose several suboptimal alternatives including decision feedback detectors and prediction-based detectors. All these strategies work well as evidenced by the simulation results. The proposed protocols are especially useful when the required average data rate is high. In addition, we extend the protocols to the multiple-antenna case and provide the design criterion of the differential unitary space time modulation (DUSTM) for TWRC.     

Performance evaluation of a novel M-detector for coherent receiverantenna diversity in a GSM-type mobile radio system

Powerful adaptive detectors such as the maximum-likelihood (ML) detector based on the Viterbi algorithm (VA) are required at the receivers for GSM type mobile radio systems in order to combat the effect of frequency-selective fading radio channels. The use of diversity techniques like receiver antenna diversity leads to a further improvement of the receiver performance. Hence, ML detectors for coherent receiver antenna diversity (CRAD) have attracted the attention of many authors. However, the complexity of the defector for CRAD can be considerably decreased when the VA is replaced with the M-algorithm, which is a suboptimum tree search algorithm. In the course of this paper, the M-detector is extended to CRAD in the case of maximal-ratio combining (MRC), equal-gain combining (EGC), and selection combining (SC), and its performance in GSM type mobile radio systems is studied by simulations using the radio channel models rural area (RA), typical urban (TU), and bad urban (BU) specified by COST 207. It is demonstrated that this novel M-detector for CRAD can perform similarly to the ML detector for CRAD thus being a favorable alternative     

Lattice-reduction aided equalization for OFDM systems

Orthogonal Frequency Division Multiplexing (OFDM) is an effective technique to deal with frequency-selective channels since it facilitates low complexity equalization and decoding. Many existing OFDM designs successfully exploit the multipath diversity offered by frequency-selective channels. However, most of them require maximum likelihood (ML) or near-ML detection at the receiver, which is of high complexity. On the other hand, empirical results have shown that linear detectors have low complexity but offer inferior performance. In this paper, we analytically quantify the diversity orders of linear equalizers for linear precoded OFDM systems, and prove that they are unable to collect full diversity. To improve the performance of linear equalizers, we further propose to use a lattice reduction (LR) technique to help collect diversity. The LR-aided linear equalizers are shown to achieve maximum diversity order (i.e., the one collected by the ML detector), but with low complexity that is comparable to that of conventional linear equalizers. The theoretical findings are corroborated by simulation results.     

Adaptive joint multiuser detection and channel estimation in multipath fading CDMA channels

The problem of joint multiuser detection and channel estimation in frequency-selective Rayleigh fading CDMA channels is considered. First the optimal multiuser detector for such channels is derived, which is seen to have a computational complexity exponential in the product of the number of users and the length of the transmitted data sequence. Two suboptimal detectors are then developed and analyzed, both of which employ decorrelating filters at the front-ends to eliminate the multiple-access interference and the multipath interference. The symbol-by-symbol detector uses a Kalman filter and decision feedback to track the fading channel for diversity combining. The per-survivor sequence detector is in the form of the Viterbi algorithm with the trellis updates being computed by a bank of Kalman filters in the per-survivor fashion. Both suboptimal detectors require the knowledge of all waveforms of all users in the channel and the channel fading model parameters. Adaptive versions of these suboptimal detectors that require only the knowledge of the waveform of the user of interest are then developed. The adaptive receivers employ recursive-least-squares (RLS) minimum-mean-square-error (MMSE) filters at the front-end to mitigate the interference, and use a bank of linear predictors to track the fading channels. It is shown that the front-end RLS-MMSE filters can be implemented using systolic arrays to exploit massively parallel signal processing computation, and to achieve energy efficiency. Finally, the performance of the suboptimal detectors and their adaptive versions are assessed by simulations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Symbol detection in spatial multiplexing system using particle swarm optimization meta-heuristics

Symbol detection in multi-input multi-output (MIMO) communication systems using different particle swarm optimization (PSO) algorithms is presented. This approach is particularly attractive as particle swarm intelligence is well suited for real-time applications, where low complexity and fast convergence is of absolute importance. While an optimal maximum likelihood (ML) detection using an exhaustive search method is prohibitively complex, PSO-assisted MIMO detection algorithms give near-optimal bit error rate (BER) performance with a significant reduction in ML complexity. The simulation results show that the proposed detectors give an acceptable BER performance and computational complexity trade-off in comparison with ML detection. These detection techniques show promising results for MIMO systems using high-order modulation schemes and more transmitting antennas where conventional ML detector becomes computationally non-practical to use. Hence, the proposed detectors are best suited for high-speed multi-antenna wireless communication systems. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust detection with the gap metric

In a multipath communication channel, the optimal receiver is matched to the maximum likelihood (ML) estimate of the multipath signal. In general, this leads to a computationally intensive multidimensional nonlinear optimization problem that is not feasible in most applications. We develop a detection algorithm that avoids finding the ML estimates of the channel parameters while still achieving good performance. Our approach is based on a geometric interpretation of the multipath detection problem. The ML estimate of the multipath signal is the orthogonal projection of the received signal on a suitable signal subspace S. We design a second subspace G, which is the representation subspace, that is close to S but whose orthogonal projection is easily computed. The closeness is measured by the gap metric. The subspace G is designed by using wavelet analysis tools coupled with a reshaping algorithm in the Zak transform domain. We show examples where our approach significantly outperforms the conventional correlator receiver (CR) and other alternative suboptimal detectors     

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     

A new approach to greedy multiuser detection

We propose a new suboptimum multiuser detector for synchronous and asynchronous multiuser communications. In this approach, a greedy strategy is used to maximize the cost function, the maximum-likelihood (ML) metric. The coefficients of the ML metric are utilized as weights indicating in which order bits can be estimated. The complexity of the algorithm is approximately K/sup 2/ log K per bit, where K is the number of users. We analyze the performance of the greedy multiuser detection in the additive white Gaussian noise channel as well as in the frequency-nonselective Rayleigh fading channel, and compare it with the optimum detector and several suboptimum schemes such as conventional, successive interference cancellation, decorrelator, sequential, and multistage detectors. The proposed greedy approach considerably outperforms these suboptimum schemes, especially for moderate and high loads in low and moderate signal-to-noise ratio regions. The results show that when there is a significant imbalance in the values of the coefficients of the ML metric due to moderate to high noise, fading, and asynchronous transmission, near-optimum performance is achieved by the greedy detection.     

Near optimum tree-search detection schemes for bit-synchronousmultiuser CDMA systems over Gaussian and two-path Rayleigh-fadingchannels

Simple reduced tree-search detection schemes of the breadth-first type are applied to suboptimal joint multiuser detection in bit-synchronous code-division multiple access (CDMA) systems over both Gaussian and two-path Rayleigh-fading channels. It is pointed out that in contrast to the case of the optimal multiuser detector, the choice of the receiver filter severely influences the performance of suboptimal multiuser detectors. Simulation results supported by analysis show that breadth-first tree-search algorithms using a decorrelating noise whitening receiver filter perform better than similar receivers, which solely use a matched filter (MF) for virtually all nonsingular spreading code sets studied. Most of the code sets are randomly generated. The M- and T-algorithm detectors based on decorrelating noise whitening filter (WF) outputs can achieve near optimum performance at a very low complexity compared to the optimal detector, although the proposed detectors are more complex than some known suboptimum detectors. Furthermore, the use of combining techniques is considered for a two-path Rayleigh-fading channel, and a semi-synchronous CDMA structure is proposed. It is shown that if maximum ratio combining (MRC) is employed, the decorrelating noise WF still exists. The corresponding suboptimal combining detector with a decorrelating noise WF outperforms a similar noncombining detector     

A Simplified Maximum Likelihood Detector with the Aid of Reduced-Size Searching Set for MIMO Systems

In this paper, a simplified maximum likelihood (ML) detector is proposed for multi-input multi-output (MIMO) systems over the Rayleigh flat-fading channels. The main idea of the proposed method is to pre-construct a reduced-size searching set for the optimal ML detection to reduce its computational load without significant performance loss. This can be done by a two-stage searching algorithm combined with the ordered successive interference cancellation scheme. Computer simulations show that with an adequate size of searching set, the proposed simplified ML detection can outperform the conventional MIMO detectors and achieve the same performance as that of the optimal ML detection.     

Semidefinite programming relaxation approach for multiuser detection of QAM signals

A semidefinite programming (SDP) relaxation approach is proposed to solve multiuser detection problems in systems with M-ary quadrature amplitude modulation (M-QAM). In the proposed approach, the optimal M-ary maximum likelihood (ML) detection is carried out by converting the associated M-ary integer programming problem into a binary integer programming problem. Then a relaxation approach is adopted to convert the binary integer programming problem into an SDP problem. This relaxation process leads to a detector of much reduced complexity. A multistage approach is then proposed to improve the performance of the SDP relaxation based detectors. Computer simulations demonstrate that the symbol-error rate (SER) performance offered by the proposed multistage SDP relaxation based detectors outperforms that of several existing suboptimal detectors.     

On the partial MAP detection with applications to MIMO channels

We investigate a multidimensional detection problem with a partial information of the a posteriori probability, which is referred to as the partial maximum a posteriori probability (MAP) detection problem. We show that the maximum likelihood (ML) detection of a higher dimension can be reduced to the ML detection of a lower dimension with cancellation under a certain condition through the formulation of the partial MAP detection problem. Using this, we can propose a computationally efficient algorithm to apply to the detection problem for multiple input multiple output (MIMO) channels including multiple transmit and multiple receive antenna (MTMR) channels and intersymbol interference (ISI) channels. It is shown that the proposed method has less error propagation effect, and its performance is close to that of the full ML detection with a lower computational complexity.     

Quasi-maximum-likelihood multiuser detection using semi-definiterelaxation with application to synchronous CDMA

The maximum-likelihood (ML) multiuser detector is well known to exhibit better bit-error-rate (BER) performance than many other multiuser detectors. Unfortunately, ML detection (MLD) is a nondeterministic polynomial-time hard (NP-hard) problem, for which there is no known algorithm that can find the optimal solution with polynomial-time complexity (in the number of users). A polynomial-time approximation method called semi-definite (SD) relaxation is applied to the MLD problem with antipodal data transmission. SD relaxation is an accurate approximation method for certain NP-hard problems. The SD relaxation ML (SDR-ML) detector is efficient in that its complexity is of the order of K^3.5, where K is the number of users. We illustrate the potential of the SDR-ML detector by showing that some existing detectors, such as the decorrelator and the linear-minimum-mean-square-error detector, can be interpreted as degenerate forms of the SDR-ML detector. Simulation results indicate that the BER performance of the SDR-ML detector is better than that of these existing detectors and is close to that of the true ML detector, even when the cross-correlations between users are strong or the near-far effect is significant     

Soft-output detection of CPM signals in frequency flat, Rayleighfading channels

Symbol-by-symbol detection algorithms are useful in systems in which soft-decision metrics are important, e.g., systems with interleaved coded modulation. A soft-output algorithm for the detection of continuous phase modulated (CPM) signals transmitted over frequency flat, Rayleigh fading channels is developed. Since the optimum detector is computationally too complex for any practical implementation, some suboptimal detectors which give near optimal performance are proposed. Some theoretical approximations for the performance of the interleaved coded system are given. The performance of the soft-output algorithms is also extensively characterized by means of Monte-Carlo simulations     

Soft quasi-maximum-likelihood detection for multiple-antenna wireless channels

The paper addresses soft maximum-likelihood (ML) detection for multiple-antenna wireless communication channels. We propose a soft quasi-ML detector that maximizes the log-likelihood function by deploying a semi-definite relaxation (SDR). Given perfect channel state information at the receiver, the quasi-ML SDR detector closely approximates the performance of the optimal ML detector in both coded and uncoded multiple-input, multiple-output (MIMO) channels with quadrature phase-shift keying (QPSK) modulation and frequency-flat Rayleigh fading. The complexity of the quasi-ML SDR detector is much less than that of the optimal ML detector, thus offering more favorable performance/complexity characteristics. In contrast to the existing sphere decoder, the new quasi-ML detector enjoys guaranteed polynomial worst-case complexity. The two detectors exhibit quite comparable performance in a variety of ergodic QPSK MIMO channels, but the complexity of the quasi-ML detector scales better with increasing number of transmit and receive antennas, especially in the region of low signal-to-noise ratio (SNR).     

Performance analysis for MIMO systems with lattice-reduction aided linear equalization

Multi-input multi-output (MIMO) systems equipped with multiple antennas have well documented merits in combating fading and enhancing data rates. MIMO V-BLAST transmission is a widely adopted method to achieve high spectral efficiency and low-complexity implementation. When the maximum likelihood (ML) or near-ML detector is employed, receive diversity is collected for MIMO V-BLAST systems to enhance the performance. However, because of its exponential complexity, ML detector may be infeasible for practical systems when the number of antennas and/or the constellation size is large. On the other hand, linear equalizers have much lower complexity but come with inferior performance. In this paper, we analytically quantify the diversity order of linear detectors for MIMO V-BLAST systems. Then, we adopt low-complexity complex lattice-reduction (LR) aided linear equalizers for V-BLAST systems to improve the performance and prove that LR-aided linear equalizers collect the same diversity order as that exploited by the ML detector but with much lower complexity. Relative to the existing real LR-aided equalizers, we illustrate that the complex LR further reduces the complexity while keeping the same performance. Simulation results corroborate our theoretical claims.     

Diversity order gain for narrow-band multiuser communications withpre-combining group detection

In narrow-band multiuser communication systems with fading diversity, it is shown that pre-combining group detection can bridge the diversity-order gap in performance between the optimum and linear detectors. For a system with M diversity channels, the group detector diversity order is M-|G|, where |G| is the interfering group size, a design parameter. Group detection thus provides a more substantial improvement in performance in narrow-band channels over linear detection than in wide-band channels in which the diversity orders of the optimal and linear detectors are equal. Here, the complexity of the receiver is a new parameter which, in addition to the number of antennas, can be used to control the diversity order. Exact formulas for the pairwise-error probabilities and bounds for the bit-error rate are obtained, and numerical results are shown     

Multiuser detectors for synchronous DS-CDMA systems based on a recursive p-norm convex relaxation approach

Multiuser detectors for direct-sequence code-division multiple-access (DS-CDMA) systems based on a recursive convex programming (RCP) relaxation approach are proposed. In these detectors, maximum likelihood (ML) detection is carried out in two steps: first, the combinatorial problem associated with ML detection is relaxed into a convex programming problem and then a recursive approach is applied to get an approximate solution for ML detection. Computer simulations demonstrate that the bit-error rate performance offered by the new detectors is near-optimal and superior to that offered by many existing suboptimal detectors including some recently proposed semidefinite-programming relaxation (SDPR) detectors. In addition, the amount of computation required by the RCP detectors is much less than that required by SDPR detectors.     

Group detection for synchronous Gaussian code-divisionmultiple-access channels

The concept of group detection Is introduced to address the design of suboptimum multiuser detectors for code-division multiple-access (CDMA) channels. A group detection scheme consists of a bank of P group detectors, one each for detecting the information symbols of users in each group of a P group partition of the K simultaneously transmitting users. In a parallel group detection scheme, these group detectors operate independently, whereas in a sequential scheme, each group detector. Uses the decisions of the previous group detectors to successively cancel the interference from those users. Group detectors based on the generalized likelihood ratio test (GLRT) are obtained for the synchronous Gaussian CDMA channel. The complexity of these detectors is exponential in the group size, whereas that of the optimum detector is exponential in K. Since the partition of users is a design parameter, group sizes can be chosen to satisfy a wide range of complexity constraints. A key performance result is that the GLRT group detectors are optimally group near-far resistant. Furthermore, upper and lower bounds on the asymptotic efficiency of the sequential group detectors are derived. These bounds reveal that the sequential group detectors can, under certain conditions, perform as well as GLRT group detectors of much larger group sizes. Group detection provides a unifying approach to multiuser detection. When the users are partitioned into K single-user groups, the GLRT, a modified form of GLRT, and the sequential group detectors reduce to previously proposed suboptimal detectors; namely, the decorrelator, the two-stage detector, and the decorrelating decision-feedback detector, respectively. For the other nontrivial partitions, the group detectors are new and have a performance that is commensurate with their complexity     

Multiuser Detection Based on Adaptive LMS and Modified Genetic Algorithm in DS-CDMA Communication Systems

In this paper, we present an efficient evolutionary algorithm for the multi-user detection (MUD) problem in direct sequence-code division multiple access (DS-CDMA) communication systems. The optimum detector for MUD is the maximum likelihood (ML) detector, but its complexity is very high and involves an exhaustive search to reach the best fitness of transmitted and received data. Thus, there has been considerable interest in suboptimal multiuser detectors with less complexity and reasonable performance. The proposed algorithm is a combination of adaptive LMS Algorithm and modified genetic algorithm (GA). Indeed the LMS algorithm provides a good initial response for GA, and GA will be applied for this response to reach the best answer. The proposed GA reduces the dimension of the search space and provides a suitable framework for future extension to other optimization algorithms. Our algorithm is compared to ML detector, Matched Filter (MF) detector, conventional detector with GA; and Adaptive LMS detector which have been used for MUD in DS-CDMA. Simulation results show that the performance of this algorithm is close to the optimal detector with very low complexity, and it works better in comparison to other algorithms.