Multiuser Detection Problem Research Articles

On Minimum-BER Linear Multiuser Detection for DS-CDMA Channels

The minimum bit-error rate (MBER) linear multiuser detection of direct-sequence code-division multiple-access (DS-CDMA) communications is considered. It is shown that the problem of MBER linear multiuser detection is equivalent to a constrained optimization problem where the constrained space is the surface and interior of a hyperellipsoid. It is further shown that any solution of the constrained optimization problem must be a solution of a set of nonlinear equations. Based on these the MBER linear multiuser detector of the two-user case is obtained. For general cases, we propose a convex subspace of the constrained space and show that the BER cost function is convex on the subspace and therefore has a unique solution. Some sufficient conditions that guarantee the convex subspace always contains the global minimizer are provided, which show that if the signal-to-noise ratio (SNR) is sufficiently large, the convex subspace always contains the global minimizer. A Newton method is developed for the set of nonlinear equations and computer simulation gives some illustrative examples

Multiuser Receiver for DS-CDMA Signals in Multipath Channels: An Enhanced Multisurface Method

This paper deals with the problem of multiuser detection in direct-sequence code-division multiple-access (DS-CDMA) systems in multipath environments. The existing multiuser detectors can be divided into two categories: (1) low-complexity poor-performance linear detectors and (2) high-complexity good-performance nonlinear detectors. In particular, in channels where the orthogonality of the code sequences is destroyed by multipath, detectors with linear complexity perform much worse than the nonlinear detectors. In this paper, we propose an enhanced multisurface method (EMSM) for multiuser detection in multipath channels. EMSM is an intermediate piecewise linear detection scheme with a run-time complexity linear in the number of users. Its bit error rate performance is compared with existing linear detectors, a nonlinear radial basis function detector trained by the new support vector learning algorithm, and Verdu's optimal detector. Simulations in multipath channels, for both synchronous and asynchronous cases, indicate that it always outperforms all other linear detectors, performing nearly as well as nonlinear detectors.

An introduction to convex optimization for communications and signal processing

Convex optimization methods are widely used in the design and analysis of communication systems and signal processing algorithms. This tutorial surveys some of recent progress in this area. The tutorial contains two parts. The first part gives a survey of basic concepts and main techniques in convex optimization. Special emphasis is placed on a class of conic optimization problems, including second-order cone programming and semidefinite programming. The second half of the survey gives several examples of the application of conic programming to communication problems. We give an interpretation of Lagrangian duality in a multiuser multi-antenna communication problem; we illustrate the role of semidefinite relaxation in multiuser detection problems; we review methods to formulate robust optimization problems via second-order cone programming techniques

The Application of Successive Quadratic Programming Algorithm to Multiuser Detection in CDMA

In this paper, based on the semidefinite programming relaxation of the CDMA maximum likelihood (ML) multiuser detection problem, a detection strategy by the successive quadratic programming algorithm is presented. Coupled with the randomized cut generation scheme, we obtain the suboptimal solution of multiuser detection problem. Comparing with the reported interior point methods based on semidefinite programming, simulations demonstrate that the successive quadratic programming algorithm often yields the similar BER performances of the multiuser detection problem. But the average CPU time of this approach is significantly reduced.

Part 3: Brain science, information science and associative memory model

I review recent progress on the associative memory model, which is a kind of neural network model. First, I introduce this model and a mathematical theory called statistical neurodynamics describing its properties. Next, I discuss an associative memory model with hierarchically correlated memory patterns. Initially, in this model, the state approaches a mixed state that is a superposition of memory patterns. After that, it diverges from the mixed state, and finally converges to a memory pattern. I show that this retrieval dynamics can qualitatively replicate the temporal dynamics of face-responsive neurons in the inferior temporal cortex, which is considered to be the final stage of visual perception in the brain. Finally, I show an unexpected link between associative memory and mobile phones (CDMA). The mathematical structure of the CDMA multi-user detection problem resembles that of the associative memory model. It enables us to apply a theoretical framework of the associative memory model to CDMA.

Multipass Channel Estimation and Joint Multiuser Detection and Equalization for MIMO Long-Code DS/CDMA Systems

The problem of joint channel estimation, equalization, and multiuser detection for a multiantenna DS/CDMA system operating over a frequency-selective fading channel and adopting long aperiodic spreading codes is considered in this paper. First of all, we present several channel estimation and multiuser data detection schemes suited for multiantenna long-code DS/CDMA systems. Then, a multipass strategy, wherein the data detection and the channel estimation procedures exchange information in a recursive fashion, is introduced and analyzed for the proposed scenario. Remarkably, this strategy provides, at the price of some attendant computational complexity increase, excellent performance even when very short training sequences are transmitted, and thus couples together the conflicting advantages of both trained and blind systems, that is, good performance and no wasted bandwidth, respectively. Space-time coded systems are also considered, and it is shown that the multipass strategy provides excellent results for such systems also. Likewise, it is also shown that excellent performance is achieved also when each user adopts the same spreading code for all of its transmit antennas. The validity of the proposed procedure is corroborated by both simulation results and analytical findings. In particular, it is shown that adopting the multipass strategy results in a remarkable reduction of the channel estimation mean-square error and of the optimal length of the training sequence.

Application of computational geometry to multiuser detection in CDMA

The maximum-likelihood multiuser detection problem in code-division multiple-access is known to be an optimization problem with an objective function that is required to be optimized over a combinatorial decision region. Conventional suboptimal detectors relax the combinatorial decision region by a convex region, without altering the objective function to be optimized. We take an approach wherein the objective function is reduced to a form appropriate for the application of a polynomial complexity algorithm in computational geometry, while keeping the decision region combinatorial. The resulting detector allows a tradeoff between performance and computational complexity. The bit-error rate performance of the detector has been found to be better than the decorrelator and the linear minimum mean-square error detectors, for the same level of complexity.

An Energy-Efficient Approach to Power Control and Receiver Design in Wireless Data Networks

In this paper, the cross-layer design problem of joint multiuser detection and power control is studied, using a game-theoretic approach that focuses on energy efficiency. The uplink of a direct-sequence code-division multiple-access data network is considered, and a noncooperative game is proposed in which users in the network are allowed to choose their uplink receivers as well as their transmit powers to maximize their own utilities. The utility function measures the number of reliable bits transmitted by the user per joule of energy consumed. Focusing on linear receivers, the Nash equilibrium for the proposed game is derived. It is shown that the equilibrium is one where the powers are signal-to-interference-plus-noise ratio-balanced with the minimum mean-square error (MMSE) detector as the receiver. In addition, this framework is used to study power-control games for the matched filter, the decorrelator, and the MMSE detector; and the receivers' performance is compared in terms of the utilities achieved at equilibrium (in bits/joule). The optimal cooperative solution is also discussed and compared with the noncooperative approach. Extensions of the results to the case of multiple receive antennas are also presented. In addition, an admission-control scheme based on maximizing the total utility in the network is proposed.

Optimal power control for Rayleigh-faded multiuser systems with outage constraints

How can we achieve the conflicting goals of reduced transmission power and increased capacity in a wireless network, without attempting to follow the instantaneous state of a fading channel? In this paper, we address this problem by jointly considering power control and multiuser detection (MUD) with outage-probability constraints in a Rayleigh fast-fading environment. The resulting power-control algorithms (PCAs) utilize the statistics of the channel and operate on a much slower timescale than traditional schemes. We propose an optimal iterative solution that is conceptually simple and finds the minimum sum power of all users while meeting their outage targets. Using a derived bound on outage probability, we introduce a mapping from outage to average signal-to-interference ratio (SIR) constraints. This allows us to propose a suboptimal iterative scheme that is a variation of an existing solution to a joint power control and MUD problem involving SIR constraints. We further use a recent result that transforms complex SIR expressions into a compact and decoupled form, to develop a noniterative and computationally inexpensive PCA for large systems of users. Simulation results are presented showing the closeness of the optimal and mapped schemes, speed of convergence, and performance comparisons.

Algoritimos Heurísticos Aplicados à detecção Multiusuário DS/CDMA

The characteristics of nine heuristic algorithms based on genetic evolution theory and local search, applied to a DS/CDMA (Direct Sequence/Code Division Multiple Access) multi-user detection problem in Flat Rayleigh fading channel are introduced. The algorithms comparisons through the performance versus computational complexity tradeoff are carried out. The computational complexity is determined in terms of the number of operations to reach the Maximum Likelihood (ML) performance. The effects on the performance of the errors in the estimates of the channel coefficients are also considered, as well as the performance degradation due to overload. There are three contributions in this work: a) a compared analysis of the evolutionary, evolutionary with cloning and local search algorithms applied to MuD detector in Flat Rayleigh channels; b) a systematic comparison of these algorithms in terms of the same simulation scenario and performance analysis base; c) a more fair and precise complexity analysis for the MuD detector in terms of the number of the computational operations.

ECM and GLR based multiuser detection with I-CSI

This paper deals with the problem of multiuser detection over a direct-sequence code-division multiple access (DS-CDMA) channel with incomplete channel state informations (I-CSI). We devise and assess two novel recursive detectors based on the expectation conditional maximization (ECM) algorithm and the generalized likelihood ratio (GLR) principle, respectively. Both receivers entail an affordable computational complexity. Moreover, the performance assessment, conducted via Monte Carlo techniques, shows that they achieve satisfactory performance levels and outperform linear detectors.

Reduced complexity receivers for layered space-time CPM

Layered space-time (LST) transmissions employing continuous phase modulations (CPM) are well motivated for both bandwidth- and power-limited multiantenna communications. However, one of the major challenges for LST-CPM is the high complexity it incurs with maximum likelihood (ML) detection. In this paper, we develop reduced complexity LST-CPM receivers. First, we consider single antenna systems. Specifically, we study a reduced complexity Viterbi receiver for binary CPM. Based on this design, we introduce differential encoding for a class of CPM signals and analyze its performance gain both theoretically and with simulations. Second, we focus on multiantenna LST systems with minimum shift-keying (MSK)-type modulations. With group nulling-canceling (NC) and low-complexity linear equalization, we convert a coded multiuser detection problem into an uncoded one with small equalization loss. We also find that the combination of sphere decoding with hard-decision iterative processing is effective in boosting performance with a controllable complexity increase. Both analytical and simulated performance confirm that the novel LST-MSK receiver exhibits markedly improved performance relative to conventional NC detectors with moderate complexity increase.

Statistical Physics of Information Processing in Mobile Communications

Recent studies have revealed that statistical mechanics provides powerful concepts and tools for analyzing the user detection problem of the code-division multiple-access (CDMA) communication, which is increasingly used in the third-generation mobile communication systems. The basic and some recent results on performance analysis of CDMA multiuser detection problem using the replica method are reviewed, which yield theoretical bounds on the performance of the optimum multiuser detector under various conditions. The statistical-neurodynamical theory of CDMA parallel interference cancellers (PICs) are also reviewed, which enables us to predict detection dynamics of conventional PICs and to derive novel PIC algorithms with better properties.

Parallel Interference Cancellation for Uplink Multirate Overlay CDMA Channels

To provide new and/or higher rate wireless services with limited spectrum resources, frequency overlay has been naturally proposed to accommodate the new and legacy systems in a common band. We address the multiuser detection problem for overlaid code-division multiple-access (CDMA) scenarios. However, in contrast to the well-studied conventional single-rate CDMA, miscellaneous systems overlay almost always indicates the presence of multirate traffic that introduces an additional degree of freedom in receiver design-i.e., differences in the symbol rates. We concentrate on receiver design for multirate traffic, while assuming a lack of information exchange between the constituent (new and legacy) systems, as is commonplace in practice. We propose a receiver architecture based on linear parallel interference cancellation where the out-of-rate intersystem interference is estimated and subtracted by means of its characteristic subspace, thereby avoiding the need for the exact knowledge of signature waveforms of the interfering system. Simulation results validate our solution and show that the proposed receiver has better performance in various aspects than several other solutions for the same purpose.

Robust Blind Multiuser Detection for Synchronous CDMA Systems Using Worst-Case Performance Optimization

The performance of blind multiuser detection methods is known to degrade severely in the presence of even small mismatches between the actual and the presumed desired user signatures. Such mismatches may occur in practical situations due to an imperfect knowledge of the channel impulse response. We propose a new robust approach to blind multiuser detection in the presence of unknown arbitrary-type mismatches of the desired user signature. Two different formulations of a robust multiuser receiver are considered. The proposed formulations are based on the explicit modeling of uncertainties in the covariance matrix of the desired user signature and/or data covariance matrix and optimization of the worst-case performance. Simple closed-form solutions to the considered robust multiuser detection problems are derived. The proposed methods have a computational complexity comparable to that of the traditional blind multiuser detection algorithms, and, at the same time, offer an improved robustness and faster convergence rates.

Feasibility of applying genetic algorithms in space-time block coded multiuser detection systems

A genetic algorithm (GA) for sub-optimal detection applied in space-time block coded (STBC) multiuser detection (MUD) systems in a Rayleigh flat-fading channel is reported for the first time. The technique yields a computational complexity which is two orders lower than that of conventional maximal likelihood (ML) detection. The simulation results confirmed the feasibility of applying GA to solve STBC MUD problems. The bit error rate (BER) performance of the proposed receiver can approach that of the ML detection after sufficient generations.

Blind Multiantenna Receivers for Dispersive DS/CDMA Channels With No Channel-State Information

The problem of blind multiuser detection for a direct sequence code division multiple access (DS/CDMA) system employing multiple transmit and receive antennae over a fading dispersive channel is considered. Relying upon a well-known signal representation, the strategy of two-stage multiuser detection is extended to the multiantenna case. Several design criteria are considered for both interference suppression and integration of the signals available at each antenna. In all cases, substantial immunity to multiple access interference (MAI) and intersymbol interference (ISI) is achieved, with no prior information as to the channel state and as to the number and the signatures of the interfering users. Interestingly, the newly proposed strategy, while being practically equivalent to existing competitors for low users' number, proves much more effective as the network load increases. Additionally, a closed-form formula for the bit-error-rate and a lower bound to the near-far resistance are derived for uncoded systems and subsequently extended to space-time coded systems, showing that these analytical results apply not only to the system under consideration but also to any linear receiver performing differential detection.

A Multiuser Detection Receiver Using Blind Antenna Array and Adaptive Parallel Interference Cancellation

In this paper, the problem of multiuser detection for synchronous code division multiple access systems in both additive white Gaussian noise and multipath channels is addressed. A new multiuser detection receiver that uses an adaptive blind array along with an adaptive parallel interference canceler is proposed. The replacement of a conventional antenna array with a two-dimensional RAKE receiver is also considered for frequency selective Rayleigh fading channels. By using a constrained optimization criterion along with the gradient-projection algorithm, a blind algorithm for the adaptation of the array response vector is proposed. The new algorithm is superior to a few typical blind algorithms in the literature in terms of both performance and computational complexity. The proposed receiver has the ability to cancel very strong multiple access interference coming from the same direction as the desired signal. Simulation results are presented to show the excellent performance of the proposed combination scheme in comparison to that of using either a multiuser detection or adaptive antenna arrays in a severe near-far situation.

Multiuser Detection in CDMA—A Comparison of Relaxations, Exact, and Heuristic Search Methods

In this paper, we compare several optimization methods for solving the optimal multiuser detection problem exactly or approximately. The purpose of using these algorithms is to provide complexity constraint alternatives to solving this nondeterministic polynomial-time (NP)-hard problem. An approximate solution is found either by relaxation or by heuristic search methods, while the branch and bound algorithm is used to provide an exact solution. Simulations show that these approaches can have bit-error rate (BER) performance which is indistinguishable from the maximum likelihood performance. A tabu search method is shown to be an effective (in terms of BER performance) and efficient (in terms of computational complexity) heuristic when compared to other heuristics like local search and iterative local search algorithms. When the number of users increases, the tabu search method is more effective and efficient than the semidefinite relaxation approach.

A Block Alternating Likelihood Maximization Approach to Multiuser Detection

In this paper, we address the maximum-likelihood (ML) multiuser detection problem for asynchronous code-division multiple access (CDMA) systems with multiple receiver antennas in frequency-selective fading environments. Multiuser ML detection (MLD) in this case provides attractive symbol error performance, but it requires the solution of a large-scale combinatorial optimization problem. To deal with the computational complexity of this problem, we propose an efficient approximation method based on a block alternating likelihood maximization (BALM) principle. The idea behind BALM is to decompose the large-scale MLD problem into smaller subproblems. Assuming binary or quaternary phase shift keying (BPSK or QPSK) (which are often employed in CDMA), the combinatorial subproblems are then accurately and efficiently approximated by the semidefinite relaxation (SDR) algorithm-an algorithm that has been recently shown to lead to quasi-ML performance in synchronous CDMA scenarios. Simulation results indicate that this BALM detector provides close-to-optimal bit error rate (BER) performance. The BALM principle is quite flexible, and we demonstrate this flexibility by extending BALM to multicarrier (MC) multiuser systems. By exploiting the special signal correlation structure of MC systems, we develop a variation of BALM in which dynamic programming (DP) is used to solve the subproblems. It is shown using simulations that the BER performance of this DP-based BALM detector is as promising as that of the SDR-based BALM detector.