Multiuser Efficiency Research Articles

UFMC Waveform and Multiple-Access Techniques for 5G RadCom

In recent years, multiple functions traditionally realized by hardware components have been replaced by digital-signal processing, making radar and wireless communication technologies more similar. A joint radar and communication system, referred to as a RadCom system, was proposed to overcome the drawbacks of the conventional existent radar techniques while using the same system for intervehicular communication. Consequently, this system enhances used spectral resources. Conventional orthogonal frequency division multiplexing (OFDM) was proposed as a RadCom waveform. However, due to OFDM’s multiple shortcomings, we propose universal filtered multicarrier (UFMC), a new 5G waveform candidate, as a RadCom waveform that offers a good trade-off between performance and complexity. In addition to that, we propose multicarrier code division multiple access (MC-CDMA) as a multiple-access (MA) technique that can offer great performance in terms of multiuser detection and power efficiency. Moreover, we study how UFMC filter length and MC-CDMA spreading sequences can impact overall performance on both radar and communication separately under a multipath channel. Analysis of the bit error rate (BER) of the UFMC waveform was performed in order to confirm the experiment results.

Performance Improvement for Multi-User Millimeter-Wave Massive MIMO Systems

In this paper, we study the problem of optimizing the performance of multi-user millimeter-wave (mmWave) communications in three steps. The first one is given by the use of a new pilot mapping to reduce the inter-user interference effect and to perform more accurate channel estimation. In the second step, we designed a hybrid receiver that, based on the accuracy of the channel state information, chooses between the minimum mean square error (MMSE) and the multi-user regularized zero-forcing beamforming (RZFBF) receivers, to combine/precode the massive multiple-input multiple-output (MIMO) signal. In the third step, we propose to improve the beam direction with a slight change in the azimuth angle during the uplink communications to increase the multi-user efficiency and reduce inter-user interference. Numerical results show the performance increase using the proposed solutions in terms of the spectral efficiency by comparing the MMSE, RZFBF, and hybrid receivers.

SINR and Multiuser Efficiency Gap Between MIMO Linear Receivers

Due to their low complexity, Minimum Mean Squared Error (MMSE) and Zero-Forcing (ZF) emerge as two appealing MIMO receivers. Although they provide asymptotically the same achievable rate as the signal-to-noise ratio (SNR) grows large, a non-vanishing gap between the signal to interference and noise ratio (SINR) obtained through the two receivers exists, affecting the error and outage probability, and the multiuser efficiency. Interestingly, both the SINR and the multiuser efficiency gaps can be compactly expressed as quadratic forms of random matrices, with a kernel that depends solely on the statistics of the interfering streams. By leveraging, we derive the closed-form distribution of such indefinite quadratic forms with random kernel matrix, which turns out to be proportional to the determinant of a matrix containing the system parameters. Then, specializing our result to different fading conditions, we obtain the closed-form statistics of both the SINR gap and the multiuser efficiency gap. Although the focus of this work is on the finite-size statistics, for completeness we also provide some results on the doubly-massive MIMO case. We validate all our derivations through extensive Monte Carlo simulations.

Noise-Loop Multiple Access

A fundamental problem for signal processing in wireless communications is the separation of multiple signals/users from their mixture. The problem is simpler if they are nonoverlapping in either the time domain or the frequency domain. Two signals may be overlapping in both time and frequency, but they can still be easily separated if they are uncorrelated (orthogonal), as in code-division multiple-access (CDMA) systems. It may be interesting to know that two signals may be overlapping in both the frequency and time domains and not orthogonal to each other, but they can still be separated if each autocorrelation function at the receiver is separable in the time-lag domain. In this paper, we will show how noise-loop (NL) modulation, which was originally thought to produce security at the physical layer, can be used to effectively separate uncoordinated/nonorthogonal users sharing the same time and frequency interval. To show the potential of the NL multiple-access (NLMA) scheme, the theoretical analysis is carried out and compared with simulations. In particular, together with the error probability, a new figure of merit is derived: the multiuser efficiency index. It can be shown that the NLMA scheme is able to distinguish the bit stream of the users, regardless of their number. In addition, the capacity region of the NLMA scheme is derived and compared with the conventional CDMA scheme. All of the aforementioned features, together with the intrinsic security, make the NL an interesting scheme for wireless technology.

On Optimum Asymptotic Multiuser Efficiency of Randomly Spread CDMA

We extend the result by Tse and Verdu on the optimum asymptotic multiuser efficiency of randomly spread code division multiple access (CDMA) with binary phase shift keying input. Random Gaussian and random binary antipodal spreading are considered. We obtain the optimum asymptotic multiuser efficiency of a $K$ -user system with spreading gain $N$ when $K$ and $N\rightarrow \infty $ and the loading factor, $({K}/{N})$ , grows logarithmically with $K$ under some conditions. It is shown that the optimum detector in a Gaussian randomly spread CDMA system has a performance close to the single user system at high signal-to-noise ratio when $K$ and $N\rightarrow \infty $ and the loading factor, $({K}/{N})$ , is kept less than $({\log _{3}K}/{2})$ . Random binary antipodal matrices are also studied and a lower bound for the optimum asymptotic multiuser efficiency is obtained. Furthermore, we investigate the connection between detecting matrices in the coin weighing problem and optimum asymptotic multiuser efficiency. We obtain a condition such that for any binary input, an $N \times K$ random matrix, whose entries are chosen randomly from a finite set, is a detecting matrix as $K$ and $N\rightarrow \infty $ .

Linear suppression of intercarrier interference in time-varying OFDM systems: From the viewpoint of multiuser detection

Intercarrier interference (ICI) in orthogonal frequency division multiplexing (OFDM) systems, which causes substantial performance degradation in time-varying fading channels, is analyzed. An equivalent spreading code formulation is derived based on the analogy of OFDM and code division multiple access (CDMA) systems. Techniques as linear multiuser detection in CDMA systems are applied to suppress the ICI in OFDM systems. The performance of linear detection, measured using multiuser efficiency and asymptotic multiuser efficiency, is analyzed given the assumption of perfect channel state information (CSI), which serves as an upper bound for the performance of practical systems. For systems without CSI, time domain and frequency domain channel estimation based linear detectors are proposed. The performance gains and robustness of a linear minimum mean square error (LMMSE) filter over a traditional filter (TF) and matched filter (MF) in the high signal-to-noise ratio (SNR) regime are demonstrated with numerical simulation results.

A Novel Method for Improving Fairness over Multiaccess Channels

It is known that the orthogonal multiple access (OMA) guarantees for homogeneous networks, where all users have almost the same received power, a higher degree of fairness (in rate) than that provided by successive interference cancellation (SIC). The situation changes in heterogeneous networks, where the received powers are very disparate, and SIC becomes superior to OMA. In this paper, we propose to partition the network into (almost) homogeneous subnetworks such that the users within each subnetwork employ OMA, and SIC is utilized across subnetworks. The newly proposed scheme is equivalent to partition the users into ordered groups. The main contribution is a practical algorithm for finding the ordered partition that maximizes the minimum rate. We also give a geometrical interpretation for the rate-vector yield by our algorithm. Experimental results show that the proposed strategy leads to a good tradeoff between fairness and the asymptotic multiuser efficiency.

Large-System Analysis of Multiuser Detection With an Unknown Number of Users: A High-SNR Approach

We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. In this environment, users' activity must be estimated along with any other parameters such as data, power, and location. Our main goal is to determine the performance loss caused by the need for estimating the identities of active users, which are not known a priori. To prevent a loss of optimality, we assume that identities and data are estimated jointly, rather than in two separate steps. We examine the performance of multiuser detectors when the number of potential users is large. Statistical-physics methodologies are used to determine the macroscopic performance of the detector in terms of its multiuser efficiency. Special attention is paid to the fixed-point equation whose solution yields the multiuser efficiency of the optimal (maximum a posteriori) detector in the large signal-to-noise ratio regime. Our analysis yields closed-form approximate bounds to the minimum mean-squared error in this regime. These illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. Next, we study the maximum load that the detector can support for a given quality of service specified by error probability.

A family of likelihood ascent search multiuser detectors: approaching optimum performance via random multicodes with linear complexity

Tse and Verdu proved that the global maximum likelihood (GML) detector achieves unit asymptotic multiuser efficiency (AME) in the limit of large random spreading CDMA. In this paper, we show that the wide-sense sequential likelihood ascent search (WSLAS) detectors achieve unit AME with channel load < 1/2 - 1/(4 ln 2) bits/s/Hz. In simulations for random multicode equal-power systems, the WSLAS with a linear per-bit complexity approaches the GML BER in all SNR with channel load as high as 1.05 bits/s/Hz.

A new chip‐level linear SOR‐SIC multiuser detector for long‐code systems

AbstractIn this work, we introduce a new chip‐level linear modified‐SIC multi‐user structure that is asymptotically equivalent to successive over‐relaxation (SOR) iteration, which is known to outperform the conventional Gauss–Seidel iteration by an order of magnitude in terms of convergence speed. The main advantage of this scheme is that it uses directly the spreading codes and not the cross‐correlation coefficients and thus reduces significantly the overall computational complexity. This is critical for the design of low‐complexity multiuser detectors for long‐code CDMA systems such as IS95 and UMTS. We use a matrix algebraic approach to show the equivalence of the proposed scheme to linear matrix filtering. This allows obtaining an analytical expression for both the bit‐error rate (BER) and the asymptotic multiuser efficiency (AME). Moreover, we study the convergence behavior of the proposed scheme and prove that it converges if the relaxation factor is within the interval ]0, 2[. Simulation results are in excellent agreement with theory. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Multiuser Detection of Sparsely Spread CDMA

Code-division multiple access (CDMA) is the basis of a family of advanced air interfaces in current and future generation networks. The benefits promised by CDMA have not been fully realized partly due to the prohibitive complexity of optimal detection and decoding of many users communicating simultaneously using the same frequency band. From both theoretical and practical perspectives, this paper advocates a new paradigm of CDMA with sparse spreading sequences, which enables near-optimal multiuser detection using belief propagation (BP) with low-complexity. The scheme is in part inspired by capacity-approaching low-density parity-check (LDPC) codes and the success of iterative decoding techniques. Specifically, it is shown that BP-based detection is optimal in the large-system limit under many practical circumstances, which is a unique advantage of sparsely spread CDMA systems. Moreover, it is shown that, from the viewpoint of an individual user, the CDMA channel is asymptotically equivalent to a scalar Gaussian channel with some degradation in the signal-to-noise ratio (SNR). The degradation factor, known as the multiuser efficiency, can be determined from a fixed-point equation. The results in this paper apply to a broad class of sparse, semi-regular CDMA systems with arbitrary input and power distribution. Numerical results support the theoretical findings for systems of moderate size, which further demonstrate the appeal of sparse spreading in practical applications.

A Unified Approach to Power control in Large Energy-Constrained CDMS Systems

A unified approach to power control is proposed for maximizing utility in terms of energy efficiency in code-division multiple access (CDMA) networks. The approach is applicable to a large family of multiuser receivers including the matched filter, the decorrelator, the linear minimum mean-square error (MMSE) receiver, and the (nonlinear) optimal detectors. It exploits the linear relationship between the transmit power and the output signal-to-interference-plus-noise ratio (SIR) for each user in the large-system limit. Suppose that each user seeks to selfishly maximize its own energy efficiency, a unique Nash equilibrium is shown to exist and be SIR-balanced, thus extending a previous result on linear receivers. A unified power control algorithm for reaching the Nash equilibrium is proposed, which adjusts transmit powers iteratively by computing the large-system multiuser efficiency, which is independent of instantaneous spreading sequences. The convergence of the algorithm is proved for linear receivers, and is demonstrated via simulation for the multiuser maximum likelihood detector. Moreover, the performance of the algorithm in finite-size systems is studied and compared with that of a conventional power control scheme, in which user powers depend on the instantaneous spreading sequences.

A family of likelihood ascent search multiuser detectors: an upper bound of bit error rate and a lower bound of asymptotic multiuser efficiency

In this paper, the bit error performance of a family of likelihood ascent search (LAS) multiuser detectors is analyzed. An upper bound on the BER of any LAS detector is obtained by bounding the fixed point region with the worst initial detector. The concept of indecomposable errors developed by Verdu is applied to tighten the upper bound. In a special instance, the upper bound is reduced to that for all the local maximum likelihood detectors. The upper bound is comparable with that of the optimum detector obtained by Verdu. A lower bound on the asymptotic multiuser efficiency (AME) is then obtained. It is shown that there are nontrivial CDMA channels such that a LAS detector can achieve unit AME regardless of user number. The AME lower bound provides a means for further seeking a good set of spreading sequences and power distribution for spectral and power efficient CDMA.

Successive Interference Cancellation Using Constellation Structure

An approach to successive interference cancellation is presented that exploits the structure of the combined signal constellation in a multiuser system. The asymptotic conditional efficiency of a successive detector is defined, based on the conditional probability of error at high signal-to-noise ratio (SNR), as a quantitative measure for evaluating detector performance at each stage of successive detection. The joint successive interference canceller (JSIC) that jointly detects consecutive users in an ordered set is proposed as an improvement over the conventional successive interference canceller (SIC). The maximal asymptotic conditional efficiency successive interference canceller (MACE-SIC) and its JSIC equivalent (MACE-JSIC) are also derived as the multiuser detectors that achieve the highest asymptotic conditional multiuser efficiency at each stage of successive detection among all possible SIC and JSIC detectors, respectively, given any particular ordering of user signals. The ordering of users achieving the highest asymptotic conditional efficiency at each stage of successive detection is derived. Performance bounds based on the signal constellation structure are derived to quantify the gain of the MACE-JSIC detector compared to the MACE-SIC detector.

Diversity reception in short-code CDMA

Short spreading sequences facilitate efficient multiuser detectors and have hence been incorporated into practical code division multiple access systems such as 3rd Generation Partnership Project UTRA-TDD. However, as the number of users approaches the spreading code length, the asymptotic performance and the numerical stability of linear multiuser detection algorithms degrade. Given some simplifications such as synchronous users, it is shown that receive diversity effectively mitigates these degradations and allows the system to be operated with a high load. A lower bound on the mean asymptotic multiuser efficiency is presented and the numerical stability of linear multiuser detection algorithms for systems with receive diversity is analysed. It is further shown that the performance variability is significantly reduced by receive diversity.

CDMA Systems With Correlated Spatial Diversity: A Generalized Resource Pooling Result

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This correspondence analyzes the behavior of code-division multiple-access (CDMA) systems with correlated spatial diversity. The users transmit to one or more antenna arrays. The centralized receiver employs a linear multiuser detector. We derive the performance of a large system with random spreading sequences and weak assumptions on the flat-fading channel gains—the fading may be correlated and contain line-of-sight components. We show that, as the number of users and the spreading factor grow large with fixed ratio, the performance of the system is fully characterized by a square matrix with size equal to the number of receiving antennas and multiuser efficiencies are not identical for all users. Our general result includes the analysis of CDMA systems with spatial diversity discussed by Hanly and Tse ('01) for independent channel gains in case of both micro-diversity and macro-diversity and provides a rigorous proof for the macro-diversity case missing in their work. We also show that to any scenario with correlated Rayleigh fading, there exists a macro-diversity scenario with independent Rayleigh fading which is characterized by the same signal-to-interference-and-noise ratio (SINR). Furthermore, sufficient conditions are given which force the multiuser efficiencies of all users to become identical also in case of statistically dependent channel gains. </para>

Performance of multicarrier CDMA in frequency-selective fading via statistical physics

This correspondence extends previous work on direct-sequence code-division multiple access (DS-CDMA) to give a single-user characterization of multicarrier (MC) CDMA systems. Results on the error performance and information rate of a family of multiuser detectors for MC-CDMA are obtained using the replica method, which was originally developed in statistical physics. The central result is the "decoupling principle", namely, an MC-CDMA channel with frequency-selective fading followed by a generic multiuser detection front end can be decoupled into a bank of single-user fading channels in the large-system limit. Thus, conditioned on one's fading coefficients, each user essentially experiences an equivalent single-user Gaussian channel with a degradation in the signal-to-noise ratio (SNR) in lieu of multiaccess interference. A set of joint equations is identified, which determines the degradation for each user, known as the multiuser efficiency. The spectral efficiencies under both optimal joint decoding and separate single-user decoding following multiuser detection are obtained analytically. The result applies to arbitrary input distribution and SNRs, and to optimal multiuser detection as well as various suboptimal schemes.

Decision Aided Hybrid MMSE/SIC Multiuser Detection: Structure and AME Performance Analysis

This paper presents a simple, yet effective hybrid of the minimum mean square error (MMSE) multi-user detection (MUD) and successive interference cancellation (SIC) for direct-sequence code division multiple access (DS-CDMA) systems. The proposed hybrid MUD first divides the users into groups, with each group consisting of users with a close power level. The SIC is then used to distinguish users among different groups, while the MMSE MUD is used to detect signals within each group. To further improve the performance impaired by the propagation errors, an information reuse scheme is also addressed, which can be used in conjunction with the hybrid MMSE/SIC MUD to adequately cancel the multiple access interferences (MAIs) so as to attain more accurate detections. Furthermore, the asymptotic multiuser efficiency (AME), a measure to characterize the near-far resistance capability, is also conducted to provide further insights into the new detectors. Furnished simulations, in both additive white Gaussian noise (AWGN) channels and slow flat Rayleigh fading channels, show that the performances of the proposed hybrid MMSE/SIC detectors, with or without the decision aided scheme, are superior to that of the SIC and, especially, the one with decision aided is close to that of the MMSE MUD but with substantially lower computational complexity.

Multiuser Detection for Square-Law Receiver Under Gaussian Channel Noise With Applications to Fiber-Optic Communications

In fiber-optic wavelength-division multiplexing (WDM) communications systems, the nonlinearity of the channel and the limitations of optical filters result in received channel signals that are correlated. Furthermore, the square-law nature of the detector converts the additive fiber amplifier noise to a data-dependent asymmetric and non-Gaussian noise. The optimal multiuser detector for a Gaussian approximation is compared to the actual statistics and found to give a close performance estimate. Through bounds on the error probability and the asymptotic multiuser efficiency, the optimal multiuser detector based on a Gaussian approximation is found to improve significantly performance in highly correlated data cases. This result is applied to a practical optical WDM system.

Randomly Spread CDMA: Asymptotics Via Statistical Physics

This paper studies randomly spread code-division multiple access (CDMA) and multiuser detection in the large-system limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the posterior mean estimator is applied before single-user decoding. The generic detector can be particularized to the matched filter, decorrelator, linear minimum mean-square error (MMSE) detector, the jointly or the individually optimal detector, and others. It is found that the detection output for each user, although in general asymptotically non-Gaussian conditioned on the transmitted symbol, converges as the number of users go to infinity to a deterministic function of a hidden Gaussian statistic independent of the interferers. Thus, the multiuser channel can be decoupled: Each user experiences an equivalent single-user Gaussian channel, whose signal-to-noise ratio (SNR) suffers a degradation due to the multiple-access interference (MAI). The uncoded error performance (e.g., symbol error rate) and the mutual information can then be fully characterized using the degradation factor, also known as the multiuser efficiency, which can be obtained by solving a pair of coupled fixed-point equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to multiple-input multiple-output (MIMO) channels such as in multiantenna systems.