Maximum Likelihood Multiuser Detection Research Articles

Exact SER and BER Analysis on Jointly Optimal Maximum Likelihood Detection of Two QPSK Signals With Phase Offset

Analysis on the exact error rate of jointly optimal (JO) maximum likelihood (ML) multiuser detection is limited in the existing literature owing to its high computational complexity. In this paper, the JO ML detection of two quadrature phase-shift keying (QPSK) signals with an arbitrary relative phase offset is investigated. Exact, analytical symbol error rate (SER) and bit error rate (BER) formulas are derived for two users with no less than 3 dB power difference between them. Closed-form union bounds on the user SER and BER with an arbitrary phase offset and an arbitrary user power ratio are also given as a simpler approach to acquire the asymptotic error rate performance. Furthermore, insights on the potentials and properties of the JO ML detector regarding its error rate behaviors for each user are revealed through comparisons with the successive interference cancellation receiver. The accuracies of the obtained formulas are demonstrated through simulation. The results show the error rates for the two-user QPSK case no longer follow the classic knowledge on the error rate behaviors in the single signal detection. In addition, the performance and dB penalty employing different modulation types are also compared and discussed.

A Near-Optimal and Low-Complex Joint Multiuser Detection for QCSS-MC-CDMA System

Joint maximum likelihood (ML) multiuser detection for quasi-synchronous multicarrier code division multiple access (MC-CDMA) system has an excessive computational complexity, and it increases exponentially as the number of users and bits in each of the modulation symbols increases. Recently, sphere decoding (SD) has been adopted for multiuser detection whose complexity is polynomial in nature with the number of users, and it does not rely on the number of bits in the modulation. In this article, first we provide a construction of large size quasi-complementary sequence sets (QCSSs), and then a low-complexity optimum SD algorithm is proposed to detect the multiuser communication in QCSS-based MC-CDMA (QCSS-MC-CDMA) system. The complexity analysis has shown that the proposed SD-based QCSS-MC-CDMA receiver for multiuser communication provides lower complexity than that of ML-based QCSS-MC-CDMA receiver. We also show that peak to average power ratio of the proposed system is lesser than that of complete complementary code (CCC) based MC-CDMA (CCC-MC-CDMA) system. The proposed system overcomes the fractional delay problem which is noticed for CCC-MC-CDMA receiver. The bit error rate performance of the proposed SD-based QCSS-MC-CDMA system is compared with maximum ratio combining based MC-CDMA, ML-based MC-CDMA, frequency domain equalization based MC-CDMA, and CCC-MC-CDMA receivers over Rayleigh frequency selective fading channels. The work is validated through Monte Carlo simulation results.

Spatially Modulated Code-Division Multiple-Access for High-Connectivity Multiple Access

In order to take the advantages of spatial modulation (SM) and support the multiple-access (MA) communications requiring high connectivity, we integrate the SM with DS-CDMA to propose a SM/DS-CDMA scheme, which is in favor of attaining both antenna diversity and frequency diversity. Associated with the SM/DS-CDMA scheme, a range of linear and nonlinear multiuser detectors (MUDs) are proposed and studied. Specifically, for linear MUDs, both minimum mean-square-error-aided joint spatial demodulation (MMSE-JSD) and MMSE-aided separate spatial demodulation (MMSE-SSD) are introduced. For nonlinear MUDs, we first present the joint maximum-likelihood MUD (JML-MUD) for demonstrating the potential of the SM-/DS-CDMA systems. Then, the MMSE-relied iterative interference cancellation (MMSE-IIC) is suggested, and the associated two types of low-complexity high-efficiency reliability measurement schemes are proposed. In this paper, we mathematically analyze both the single-user average bit error rate (ABER) of the SM/DS-CDMA systems employing joint spatial demodulation (JSD) and the approximate ABER of the SM/DS-CDMA systems employing the MMSE-JSD. We investigate and compare the ABER performance of the SM/DS-CDMA systems with various detection schemes and also with some legacy schemes. Our studies and performance results show that the SM/DS-CDMA systems in conjunction with appropriate MUD schemes are capable of providing a desirable tradeoff among the number of users supportable, implementation complexity, and the ABER performance.

Downlink Multiuser Detection in the Virtual Cell-Based Ultra-Low Latency Vehicular Networks

To achieve ultra-low latency mobile networking, recent efforts to integrate virtual cell with open-loop communications and proactive network association suggest the facilitation of new technological paradigm, but the interference from different co-locating virtual cells is hard to handle. Open-loop transmissions make beam-forming/interference alignment infeasible due to the need of channel state information feedback. Multiuser detection (MUD) is therefore employed to address the downlink interference. We note that the bit error rate (BER) of maximum-likelihood MUD (ML-MUD) is sensitive to the modulation of the interference. As the interferer uses low-order modulation, the BER of desired signal can approach the ideal case without interference. But if the interferer adopts high-order modulation, the resultant BER is significantly degraded. Our study shows that, such modulation sensitivity can be eased by the multi-antenna technique. We also propose two methods to reduce the notorious computational complexity of MUD, particularly involving higher order modulations. The first scheme is termed as the reduced-computation ML-MUD (R-ML-MUD) that exploits the characteristic of downlink to shrink the ML solution space, consequently leading to lower detection complexity. The second scheme is a new projection receiver, called generalized linear minimum mean square error equalizer, resulting in notable signal-to-noise ratio gain over the conventional projection method. The simulation results indicate that the proposed schemes and their integration can achieve satisfactory BER performance.

Iterative interference cancellation in multiuser relaying with fast frequency‐hopping modulation

A novel iterative receiver is proposed for relay-assisted multiuser communications in which multiple users transmit to a destination with the help of a relay and using fast frequency-hopping modulation. Each user employs a channel encoder to protect its information and facilitate interference cancellation at the receiver. The signal received at the relay is either amplified, or partially decoded with a simple energy detector, before being forwarded to the destination. The proposed iterative receiver exploits the soft outputs of a channel decoder to successively extract the maximum-likelihood symbols of the users and perform interference cancellation. Under the same spectral efficiency, simulation results demonstrate superior performance of the proposed receiver when compared to the performance of an interference cancellation scheme that was previously proposed for multiuser communications and is extended to multiuser amplify-and-forward relaying considered in this study, as well as performance of the maximum-likelihood multiuser detection for uncoded transmission.

Fixed-Complexity Quantum-Assisted Multi-User Detection for CDMA and SDMA

In a system supporting numerous users the complexity of the optimal Maximum Likelihood Multi-User Detector (ML MUD) becomes excessive. Based on the superimposed constellations of K users, the ML MUD outputs the specific multi-level K-user symbol that minimizes the Euclidean distance with respect to the faded and noise-contaminated received multi-level symbol. Explicitly, the Euclidean distance is considered as the Cost Function (CF). In a system supporting K users employing M-ary modulation, the ML MUD uses M^K CF evaluations (CFE) per time slot. In this contribution we propose an Early Stopping-aided Durr-H\o yer algorithm-based Quantum-assisted MUD (ES-DHA QMUD) based on two techniques for achieving optimal ML detection at a low complexity. Our solution is also capable of flexibly adjusting the QMUD's performance and complexity trade-off, depending on the computing power available at the base station. We conclude by proposing a general design methodology for the ES-DHA QMUD in the context of both CDMA and SDMA systems.

Low-Complexity Soft-Output Quantum-Assisted Multiuser Detection for Direct-Sequence Spreading and Slow Subcarrier-Hopping Aided SDMA-OFDM Systems

Low-complexity suboptimal multiuser detectors (MUDs) are widely used in multiple access communication systems for separating users, since the computational complexity of the maximum likelihood (ML) detector is potentially excessive for practical implementation. Quantum computing may be invoked in the detection procedure, by exploiting its inherent parallelism for approaching the ML MUDs performance at a substantially reduced number of cost function evaluations. In this contribution, we propose a soft-output (SO) quantum-assisted MUD achieving a near-ML performance and compare it to the corresponding SO ant colony optimization MUD. We investigate rank deficient direct-sequence spreading (DSS) and slow subcarrier-hopping aided (SSCH) spatial division multiple access orthogonal frequency division multiplexing systems, where the number of users to be detected is higher than the number of receive antenna elements used. We show that for a given complexity budget, the proposed SO-Dürr-Høyer algorithm (DHA) QMUD achieves a better performance. We also propose an adaptive hybrid SO-ML/SO-DHA MUD, which adapts itself to the number of users equipped with the same spreading sequence and transmitting on the same subcarrier. Finally, we propose a DSS-based uniform SSCH scheme, which improves the system's performance by 0.5 dB at a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> , despite reducing the complexity required by the MUDs employed.

Multiuser Detection in SDMA–OFDM Wireless Communication System Using Complex Multilayer Perceptron Neural Network

The space division multiple access–orthogonal frequency division multiplexing (SDMA–OFDM) wireless system has become very popular owing high spectral efficiency and high load capability. The optimal maximum likelihood multiuser detection (MUD) technique suffers from high computational complexity. On the other hand the linear minimum mean square error (MMSE) MUD techniques yields poor performance and also fails to detect users in overload scenario, where the number of users are more than that of number of receiving antennas. By contrast, the differential evolution algorithm (DEA) aided minimum symbol error rate (MSER) MUD can sustain in overload scenario as it can directly minimizes probability of error rather than mean square error. However, all these classical techniques are still complex as these do channel estimation and multiuser detection sequentially. In this paper, complex multi layer perceptron (CMLP) neural network model is suggested for MUD in SDMA–OFDM system as it do both channel approximation and MUD simultaneously. Simulation results prove that the CMLP aided MUD performs better than the MMSE and MSER techniques in terms of enhanced bit error rate performance with low computational complexity.

Quantum Search Algorithms, Quantum Wireless, and a Low-Complexity Maximum Likelihood Iterative Quantum Multi-User Detector Design

The high complexity of numerous optimal classic communication schemes, such as the maximum likelihood (ML) multiuser detector (MUD), often prevents their practical implementation. In this paper, we present an extensive review and tutorial on quantum search algorithms (QSA) and their potential applications, and we employ a QSA that finds the minimum of a function in order to perform optimal hard MUD with a quadratic reduction in the computational complexity when compared to that of the ML MUD. Furthermore, we follow a quantum approach to achieve the same performance as the optimal soft-input soft-output classic detectors by replacing them with a quantum algorithm, which estimates the weighted sum of a function's evaluations. We propose a soft-input soft-output quantum-assisted MUD (QMUD) scheme, which is the quantum-domain equivalent of the ML MUD. We then demonstrate its application using the design example of a direct-sequence code division multiple access system employing bit-interleaved coded modulation relying on iterative decoding, and compare it with the optimal ML MUD in terms of its performance and complexity. Both our extrinsic information transfer charts and bit error ratio curves show that the performance of the proposed QMUD and that of the optimal classic MUD are equivalent, but the QMUD's computational complexity is significantly lower.

A Continuous Relaxation Method for Multiuser Detection Problem

Based on the binary quadratic programming model of the code division multiple access maximum likelihood multiuser detection problem, a detection strategy by the continuous relaxation method is presented. The proposed method relaxes the binary quadratic programming as a nonlinear programming, which is a quadratic objective function with simple quadratic constraints. A feasible direction method is used to solve the nonlinear programming. Based on the KKT solution of the nonlinear programming, a near optimal solution is obtained for the multiuser detection problem. Simulation results show that the bit error rate performances of a detection strategy based on the continuous relaxation method is low. Furthermore, average CPU time of continuous relaxation method is much lower than that of the semidefinite programming relaxation method, especially for the large-scale detection problems. This approach provides good approximations to the optimal maximum likelihood performance.

Multi-rate group-orthogonal OFDMA-CDMA for broadband mobile transmission

In this work, the problem of multi-rate Multi-Carrier (MC) Code Division Multiple Access (CDMA) wireless transmission is addressed. In particular, we investigated the possibility of exploiting subcarrier grouping, already considered in literature for constant bit-rate MC-CDMA, in order to reduce mutual interference among different rate users and to allow the use of theoretically-optimum Maximum-Likelihood Multi-User Detection (ML-MUD) with affordable computational burden. We propose a multi-code Group Orthogonal (GO) OFDMA-CDMA system where the available subcarriers are subdivided into fixed-cardinality orthogonal subcarrier groups. The user's data stream is selectively multiplexed into a variable number of substreams, which depends on the data-rate. Then, these substreams are transmitted over an orthogonal subcarrier group, univocally assigned to a user rate class. Experimental results obtained by adopting linear multi-user detection show that the proposed GO-OFDMA-CDMA outperforms state-of-the-art Variable Spreading Length (VSL) and multi-code MC-CDMA as far as higher data rate users are concerned. On the other hand, BER performance of lowest-rate users is slightly worse. Orthogonal subcarrier grouping allows to greatly increasing BER performance when using ML-MUD operated over small subcarrier groups. In such a case, the tradeoff to be managed is between achievable performance and computational complexity.

A New Rank-two Semidefinite Programming Relaxation Method for Multiuser Detection Problem

Based on the semidefinite programming relaxation model of the code division multiple access maximum likelihood multiuser detection problem, a detection strategy by the rank-two method is presented. The proposed method restricts the matrix variable in the semidefinite programming relaxation to be rank-two, and yields a quadratic objective function with simple quadratic constraints. A feasible direction method is used to solve the nonlinear programming. Coupled with randomized method, a suboptimal solution is obtained for the multiuser detection problem. Simulation results show that the bit error rate performances of a detection strategy based on the new rank-two method are almost similar to that of the detection strategy based on the semidefinite programming relaxation. Furthermore, average CPU time of the new rank-two method is at least 10 times lower than that of the semidefinite programming relaxation method, With the increasing of the users number, the average CPU time increasing rate of the new rank-two method is lower than that of the semidefinite programming relaxation method, especially for the large-scale detection problems. This approach provides good approximations to the optimal maximum likelihood performance.

A Second-Order Cone Programming Method for Multiuser Detection Problem

Based on the binary quadratic programming model of the CDMA maximum likelihood multiuser detection problem, a detection strategy by the second-order cone programming method is presented. The proposed method relaxes the binary quadratic programming model as a second-order cone programming model. Coupled with the sign function, a suboptimal solution is obtained for the multiuser detection problem. Comparing with the reported semidefinite programming method, simulations demonstrate that the second-order cone programming method often yields the similar bit error rate (BER) performances for the multiuser detection problem, but the average CPU time of this method is significantly reduced.

Joint Modulation Classification and Detection Using Sphere Decoding

In this letter, we propose a simple yet effective modulation classification method for maximum likelihood multiuser detection. Our method is a modification of generalized likelihood ratio test (GLRT) that approximates the optimal classifier in the Bayesian sense. We show that the proposed method can be implemented by modifying the sphere decoding algorithm to support multimodulation. Simulation results in multiuser detection in high-speed downlink packet access (HSDPA) system show that the proposed method offers considerable performance gain over conventional RAKE and MMSE algorithms.

Ant-Colony-Based Multiuser Detection for Multifunctional-Antenna-Array-Assisted MC DS-CDMA Systems

A novel ant colony optimization (ACO)-based multiuser detector (MUD) is designed for the synchronous multifunctional antenna array (MFAA)-assisted multicarrier direct-sequence code-division multiple-access (MC DS-CDMA) uplink, which supports both receiver diversity and receiver beamforming. The ACO-based MUD aims to achieve a bit-error-rate performance approaching that of the optimum maximum-likelihood (ML) MUD, without carrying out an exhaustive search of the entire MC DS-CDMA search space constituted by all possible combinations of the received multiuser vectors. We will demonstrate that regardless of the number of the subcarriers or of the MFAA configuration, the system employing the proposed ACO-based MUD is capable of supporting 32 users with the aid of 31-chip Gold codes used as the T-domain spreading sequence without any significant performance degradation when compared to the single-user system. As a further benefit, the number of floating-point operations per second imposed by the proposed ACO-based MUD is a factor of lower than that of the ML MUD. We will also show that at a given increase of the complexity, the MFAA will allow the ACO-based MUD to achieve a higher signal-to-noise ratio gain than the single-input-single-output MC DS-CDMA system.

Design of spreading codes with high diversity gain for multicarrier CDMA systems

AbstractThe paper proposes a designing guideline for the spreading codes of the multicarrier code division multiple access (MC‐CDMA) systems based on the evaluation of the performance of the maximum‐likelihood multi‐user detection (ML‐MUD) in the frequency selective fading channels. Two parameters of the spreading codes, the minimum Hamming distance and the minimum product distance, are found to bound the performance of the system. According to this, a new kind of spreading codes, which are constructed by offsetting the phase of conventional orthogonal codes, is proposed to maximize the diversity gain. Simulation results show that full diversity order can be obtained even for full loaded systems. The proposed spreading codes can also improve the performance of single‐user detectors. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Successive quadratic programming multiuser detector

Abstract Based on the semidefinite programming relaxation of the CDMA maximum likelihood multiuser detection problem, a detection strategy by the successive quadratic programming algorithm is presented. Coupled with the randomized cut generation scheme, the suboptimal solution of the multiuser detection problem in obtained. Compared to the interior point methods previously reported 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.

Performance Analysis of Maximum-Likelihood Multiuser Detection in Space–Time-Coded CDMA With Imperfect Channel Estimation

In this paper, the performance of maximum-likelihood multiuser detection in space-time-coded code-division multiple-access (CDMA) systems with imperfect channel estimation is analyzed. A K-user synchronous CDMA system that employs orthogonal space-time block codes with M transmit antennas and N receive antennas is considered. A least-squares estimate of the channel matrix is obtained by sending a sequence of pilot bits from each user. The channel matrix is perturbed by an error matrix that depends on the thermal noise and the correlation between the signature waveforms of different users. Because of the linearity of the channel estimation technique, the characteristic function of the decision variable is used to obtain an exact expression for the pairwise error probability, and by using it, an upper bound on the bit error rate (BER) is obtained. The analytical BER bounds are compared with the BER obtained through simulations. The BER bounds are shown to be increasingly tight for large SNR values. It is shown that the degradation in BER performance due to imperfect channel estimation can be compensated by using a larger number of transmit/receive antennas

A Co-channel Interference Cancellation Method Using Low Dimensional Sphere Decoding for MIMO Communication Systems

This paper proposes a co-channel interference cancellation method for multiple-input multiple-output (MIMO) wireless communication systems. Maximum-likelihood multi-user detection (ML-MUD), which is one of the co-channel interference cancellation methods at a receiver side, has excellent bit error rate (BER) performance. However, computational complexity of the ML-MUD is prohibitive, because the ML-MUD must search for the most probable symbol vector from all candidates of the transmitted signals. We apply sphere decoding (SD) to the ML-MUD in order to reduce the computational complexity of the ML-MUD, and moreover we propose a modified version of the SD suitable for the ML-MUD. The proposed method extracts desired signal components from a received signal vector and a channel matrix decomposed the upper triangular form, and then performs the SD to the low dimensional model in order to detect the transmitted signals of the desired user. Computer simulation confirms that the proposed method can suppress the undesired signals and detect the desired signals, offering significant reduction of the computational complexity of the conventional method.

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.