Linear multiuser receivers: effective interference, effectivebandwidth and user capacity

Multiuser receivers improve the performance of spread-spectrum and antenna-array systems by exploiting the structure of the multiaccess interference when demodulating the signal of a user. Much of the previous work on the performance analysis of multiuser receivers has focused on their ability to reject worst case interference. Their performance in a power-controlled network and the resulting user capacity are less well-understood. We show that in a large system with each user using random spreading sequences, the limiting interference effects under several linear multiuser receivers can be decoupled, such that each interferer can be ascribed a level of effective interference that it provides to the user to be demodulated. Applying these results to the uplink of a single power-controlled cell, we derive an effective bandwidth characterization of the user capacity: the signal-to-interference requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own SIR requirement, and simple expressions are derived for three linear receivers: the conventional matched filter, the decorrelator, and the MMSE receiver. The effective bandwidths under the three receivers serve as a basis for performance comparison     

Effective interference and effective bandwidth of linear multiuserreceivers in asynchronous CDMA systems

The performance of linear multiuser receivers in terms of the signal-to-interference ratio (SIR) achieved by the users has been analyzed in a synchronous CDMA system under random spreading sequences. In this paper, we extend these results to a symbol-asynchronous but chip-synchronous system and characterize the SIR for linear receivers-the matched-filter receiver the minimum mean-square error (MMSE) receiver and the decorrelator. For each of the receivers, we characterize the limiting SIR achieved when the processing gain is large and also derive lower bounds on the SIR using the notion of effective interference. Applying the results to a power controlled system, we derive effective bandwidths of the users for these linear receivers and characterize the user capacity region: a set of users is supportable by a system if the sum of the effective bandwidths is less than the processing gain of the system. We show that while the effective bandwidth of the decorrelator and the MMSE receiver is higher in an asynchronous system than that in a synchronous system, it progressively decreases with the increase in the length of the observation window and is asymptotic to that of the synchronous system, when the observation window extends infinitely on both sides of the symbol of interest. Moreover, the performance gap between the MMSE receiver and the decorrelator is significantly wider in the asynchronous setting as compared to the synchronous case     

CDMA systems in fading channels: admissibility, network capacity,and power control

We study the admissibility and network capacity of imperfect power-controlled code-division multiple access (CDMA) systems with linear receivers in fading environments. In a CDMA system, a set of users is admissible if their simultaneous transmission does not result in violation of any of their quality-of-service (QoS) requirements; the network capacity is the maximum number of admissible users. We consider a single-cell imperfect power-controlled CDMA system, assuming known received power distributions. We identify the network capacities of single-class systems with matched-filter (MF) receivers for both the deterministic and random signature cases. We also characterize the network capacity of single-class systems with linear minimum-mean-square-error (MMSE) receivers for the deterministic signature case. The network capacities can be expressed uniquely in terms of the users' signal-to-interference ratio (SIR) requirements and received power distributions. For multiple-class systems equipped with MF receivers, we find a necessary and sufficient condition on the admissibility for the random signature case, but only a sufficient condition for the deterministic signature case. We also introduce the notions of effective target SIR and effective bandwidth, which are useful in determining the admissibility and hence network capacity of an imperfect power-controlled system     

Group-blind multiuser detection for uplink CDMA

Previously developed blind techniques for multiuser detection in code division multiple access (CDMA) systems lead to several near-far resistant adaptive receivers for demodulating a given user's data with the prior knowledge of only the spreading sequence of that user. In the CDMA uplink, however, typically the base station receiver has the knowledge of the spreading sequences of all the users within the cell, but not that of the users from other cells. In this paper, group-blind techniques are developed for multiuser detection in such scenarios. These new techniques make use of the spreading sequences and the estimated multipath channels of all known users to suppress the intracell interference, while blindly suppressing the intercell interference. Several forms of group-blind linear detectors are developed based on different criteria. Moreover, group-blind multiuser detection in the presence of correlated noise is also considered. In this case, two receiving antennas are needed for channel estimation and signal separation. Simulation results demonstrate that the proposed group-blind linear multiuser detection techniques offer substantial performance gains over the blind linear multiuser detection methods in a CDMA uplink environment     

Large system performance of linear multiuser receivers in multipathfading channels

A linear multiuser receiver for a particular user in a code-division multiple-access (CDMA) network gains potential benefits from knowledge of the channels of all users in the system. In fast multipath fading environments we cannot assume that the channel estimates are perfect and the inevitable channel estimation errors will limit this potential gain. We study the impact of channel estimation errors on the performance of linear multiuser receivers, as well as the channel estimation problem itself. Of particular interest are the scalability properties of the channel and data estimation algorithms: what happens to the performance as the system bandwidth and the number of users (and hence channels to estimate) grows? Our main results involve asymptotic expressions for the signal-to-interference ratio of linear multiuser receivers in the limit of large processing gain, with the number of users divided by the processing gain held constant. We employ a random model for the spreading sequences and the limiting signal-to-interference ratio expressions are independent of the actual signature sequences, depending only on the system loading and the channel statistics: background noise power, energy profile of resolvable multipaths, and channel coherence time. The effect of channel uncertainty on the performance of multiuser receivers is succinctly captured by the notion of effective interference     

Performance analysis of linear multisensor multiuser receivers forCDMA in fading channels

Bit-error probability (BEP) analysis for linear multiuser receivers with multiple sensors in frequency selective Rayleigh fading channels is presented. The analysis is applied to evaluate the BEP in antenna diversity reception and in a cellular CDMA system. Diversity and multiuser receivers are compared based on the examples. It is observed that adding new diversity antenna elements improves performance even if the correlation between the antenna elements is relatively large (up to 0.7). However, the large correlation values pose a significant reduction in the diversity gain in comparison to the zero correlation. It is also seen that the macroscopic diversity improves the performance of receivers significantly in cellular CDMA networks. When comparing diversity and multiuser receivers it is concluded that multiuser receivers are necessary to provide low BEPs. It is also highly beneficial to have at least two diversity antennas available, in particular, if there is no multipath diversity provided by the channel. The results also show that the reduction of intercell multiple-access interference yields a significant performance advantage in cellular networks. It is also demonstrated that the combination of spatial diversity and a multiuser receiver provides a significant receiver performance or system capacity gain in comparison to implementing only one of them     

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

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     

Space-time multiplexing for mimo multiuser downlink channels

In this paper, we study the downlink of a multiuser system, in which antenna arrays are employed at both the transmitter (base station) and the receivers (clients). A space-time modulation technique that can be seen as two-dimensional spreading is introduced. It provides full transmit diversity for every user, and accommodates N_t times the number of users as a single-antenna code-division multi-access (CDMA) scheme, where N_t is the number of transmit antennas. Thus multiple access is provided through spatial as well as code dimensions. In addition, the scheme forms groups of users that are orthogonal to each other. This feature translates into simplified detection strategies without loss of performance. The main detector structure of interest is a two-stage interference canceller because of its low complexity compared to other joint detectors. We will demonstrate that in conjunction with an unequal power allocation scheme, this receiver provides full diversity and suffers from only a small performance loss compared to the full-complexity maximum likelihood (ML) receiver. In a single-user multiple antenna system, the same spreading scheme and unequal power allocation yields a new approach to designing full-rate, full-diversity space-time codes having good performance with successive interference cancellers     

Linear receivers for the multiple-input multiple-output multiple-access channel

We consider a multiuser multiple-input multiple-output (MIMO) communication system using code-division multiple access (CDMA) and multiuser detection to discriminate the different users. Our focus is on the CDMA uplink of a frequency-nonselective Rayleigh fading channel. We study two types of receivers: joint receivers, which address simultaneously both spatial and multiple-access interference; and separate receivers, addressing the two types of interference individually. This approach allows assessing the benefits of adding MIMO processing capabilities to existing multiuser single-input single-output systems. For both receiver types, we analyze solutions based on linear (matched filter, decorrelator, minimum mean-square error) and maximum-likelihood receivers. For all the receivers considered, we provide closed-form expressions (as expectations of given functions) of the resulting pairwise error probabilities. Performance results are obtained in terms of frame-error rate versus E/sub b//N/sub 0/, following two different approaches. An analytic approach using large-system asymptotic methods, whereby the system parameters (number of users and antennas, spreading gain) are assumed to grow to infinity with finite limiting ratios. A computer-simulation approach is used to illustrate the differences between asymptotic and simulation results.     

Optimal sequences, power control, and user capacity of synchronousCDMA systems with linear MMSE multiuser receivers

There has been intense effort in the past decade to develop multiuser receiver structures which mitigate interference between users in spread-spectrum systems. While much of this research is performed at the physical layer, the appropriate power control and choice of signature sequences in conjunction with multiuser receivers and the resulting network user capacity is not well understood. In this paper we will focus on a single cell and consider both the uplink and downlink scenarios and assume a synchronous CDMA (S-CDMA) system. We characterize the user capacity of a single cell with the optimal linear receiver (MMSE receiver). The user capacity of the system is the maximum number of users per unit processing gain admissible in the system such that each user has its quality-of-service (QoS) requirement (expressed in terms of its desired signal-to-interference ratio) met. This characterization allows one to describe the user capacity through a simple effective bandwidth characterization: users are allowed in the system if and only if the sum of their effective bandwidths is less than the processing gain of the system. The effective bandwidth of each user is a simple monotonic function of its QoS requirement. We identify the optimal signature sequences and power control strategies so that the users meet their QoS requirement. The optimality is in the sense of minimizing the sum of allocated powers. It turns out that with this optimal allocation of signature sequences and powers, the linear MMSE receiver is just the corresponding matched filter for each user. We also characterize the effect of transmit power constraints on the user capacity     

多天线无线数据通信系统中多用户分集的研究

研究当接收天线不少于发送天线时多输入多输出(MIMO)系统的多用户分集能力。首先从理论上分析了发送天线个数等于1和2时最大似然接收和迫零接收系统的平均吞吐量和调度增益,以及仿真分析了发送天线个数大于2时系统性能。理论分析和仿真表明：在多用户的MIMO系统中,接收的平均信噪比、用户个数、收发天线个数、接收机的结构等对于多用户分集有很大的影响。当发送天线个数为1时,接收天线较少(1,2,3)和平均信噪比为．10dB时调度增益很大,但调度增益随着天线个数和发送功率增大急剧下降。和最大似然接收相比,迫零接收具有更大的多用户分集增益,因此迫零接收机的吞吐量可以很容易超过最大似然接收机。     

Performance analysis for the improved linear multiuser detectors in BPSK-modulated DS-CDMA systems

Recently, a new class of linear multiuser receivers for direct-sequence code-division multiple-access (CDMA) systems employing binary phase-shift keying modulation has been introduced. Unlike classical decorrelating and minimum mean-square error linear multiuser detectors, the new receivers exploit the information contained in the pseudo-autocorrelation of the observables, and are, thus, capable of achieving much better performance. We present new results on the performance analysis of this class of new receivers. In particular, with reference to a CDMA system with deterministic spreading codes, we show that the new receivers outperform the classical ones in terms of both error probability and near-far resistance. With regard, instead, to CDMA systems with random spreading, we compute the average system near-far resistance, showing that the new receivers can accommodate twice the number of users accommodated by the classical linear multiuser receivers.     

Linear multiuser detectors for incompletely known symmetric signals in CDMA systems

In this paper, we consider a synchronous code-division multiple-access (CDMA) system with a multiuser receiver. All users are assumed to have symmetric signature sequences, but the presence of a subset of the users is unknown to the receiver. We first calculate the signal-to-interference ratio (SIR) in this environment for the matched-filter receiver, the decorrelating receiver, and the linear minimum mean-square error (MMSE) detector. We then identify the user capacity for a single-class system, and the effective bandwidth for a multiple-class system. The result is compared to the case of random sequences and of optimum sequences. For symmetric sequences, the effective bandwidth cannot be expressed by a scalar as in , because two constraints have to be satisfied simultaneously to satisfy the SIR requirement. We introduce a two-dimensional (2-D) vector notion of effective bandwidth with and without unknown users. For both the decorrelator and the MMSE detector, the user capacity is 1 when all users are known to the receivers and is reduced to (1-N/L) when N users are unknown (with L the processing gain). The performance of these three linear detectors, with and without unknown users, is compared.     

Asymptotic normality of linear multiuser receiver outputs

This paper proves large-system asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers. This family of receivers encompasses the single-user matched filter, the decorrelator, the minimum mean square error (MMSE) receiver, the parallel interference cancelers, and many other linear receivers of interest. Both with and without the assumption of perfect power control, we show that the output decision statistic for each user converges to a Gaussian random variable in distribution as the number of users and the spreading factor both tend to infinity with their ratio fixed. Analysis reveals that the distribution conditioned on almost all spreading sequences converges to the same distribution, which is also the unconditional distribution. This normality principle allows the system performance, e.g., the multiuser efficiency, to be completely determined by the output signal-to-interference ratio (SIR) for large linear systems.     

Linear multiuser receivers in random environments

We study the signal-to-interference (SIR) performance of linear multiuser receivers in random environments, where signals from the users arrive in “random directions.” Such a random environment may arise in a DS-CDMA system with random signature sequences, or in a system with antenna diversity where the randomness is due to channel fading. Assuming that such random directions can be tracked by the receiver, the resulting SIR performance is a function of the directions and therefore also random. We study the asymptotic distribution of this random performance in the regime where both the number of users K and the number of degrees of freedom N in the system are large, but keeping their ratio fixed. Our results show that for both the decorrelator and the minimum mean-square error (MMSE) receiver, the variance of the SIR distribution decreases like 1/N, and the SIR distribution is asymptotically Gaussian. We compute closed-form expressions for the asymptotic means and variances for both receivers. Simulation results are presented to verify the accuracy of the asymptotic results for finite-sized systems     

Antenna and User Subset Selection in Downlink Multiuser Orthogonal Space-Division Multiplexing

Block diagonalization (BD) and successive optimization (SO) are two suboptimal but more practical (compared to dirty paper coding (DPC)) orthogonal linear precoding techniques for the downlink of multiuser MIMO systems. Since the numbers of users supported by BD or SO for a given number of transmit antennas are limited, BD or SO should be combined with scheduling so that a subset of users is selected at a given time slot while meeting the dimensionality requirements of these techniques. On the other hand, receive antenna selection (RAS) is a promising hardware complexity reduction technique. In this paper, we consider user scheduling in conjunction with receive antenna selection. Since exhaustive search is computationally prohibitive, we propose simplified and suboptimal user scheduling algorithms for both BD and SO. For BD, we propose capacity and Frobenius-norm based suboptimal algorithms with the objective of sum rate maximization. Starting from an empty set, each step of proposed algorithms adds the best user from the set of users not selected yet until the desired number of users have been selected. Proposed receive antenna selection works in conjunction with user scheduling to further enhance the sum rate of BD. For SO, a Frobenius-norm based low complexity algorithm is proposed, which maximizes the ratio of the squared Frobenius norm of the equivalent channel (projected to the joint null space of the previously selected users) to the sum of the squared Frobenius norms of the previously selected users’ preprocessed channels. Simulation results demonstrate that the proposed algorithms achieve sum rates close to exhaustive search algorithms with much reduced complexity. We also show that in addition to reduced hardware complexity at the receiver, antenna selection enhances multiuser diversity gain that is achieved with user scheduling.     

Adaptive space-time feedforward/feedback detection for high datarate CDMA in frequency-selective fading

We investigate linear and nonlinear space-time minimum mean-square-error (MMSE) multiuser detectors for high data rate wireless code-division multiple-access (CDMA) networks. The centralized reverse-link detectors comprise a space-time feedforward filter and a multiuser feedback filter which processes the previously detected symbols of all in-sector users. The feedforward filter processes chip-rate samples from a bank of chip-matched filters which operate on the baseband outputs from an array of antennas. We present an adaptive multiuser recursive least squares (RLS) algorithm which determines the MMSE adjusted filter coefficients with less complexity than individual adaptation for each user. We calculate the outage probabilities and isolate the effects of antenna, diversity, and interference suppression gains for linear and nonlinear filtering and for CDMA systems with varying levels of system control (e.g., timing control, code assignment, cell layout). For eight users transmitting uncoded 2-Mb/s quadrature phase-shift keying with a spreading gain of eight chips per symbol over a fading channel with a multipath delay spread of 1.25 μs, the performance of a three-antenna feedforward/feedback detector was within 1 dB (in signal-to-noise ratio per antenna) of ideal detection in the absence of interference. By training for 10% of a 5-ms frame, RLS adaptation enabled the same detector to suffer less than a 0.5-dB penalty due to the combined effects of imperfect coefficients and error propagation. The advantage of nonlinear feedforward/feedback detection over linear feedforward detection was shown to be significantly larger for a CDMA system with enhanced system control     

Optimum receivers and low-dimensional spreaded modulation for multiuser space-time communications

The jointly optimum receiver is obtained for multi- user communications in a frequency nonselective Rayleigh-fading channel with N/sub T/ transmit antennas per user and N/sub R/ receive antennas. Based on a general analysis of quadratic receivers in zero-mean complex Gaussian vectors, asymptotically tight expressions (for high signal-to-noise ratio (SNR)) for the pairwise error probabilities are derived. Subsequently, it is shown that N/sub T/-dimensional single-user signaling suffices to provide full diversity order N=N/sub T/N/sub R/ for all the users. In other words, the presence of other users does not increase the minimum dimension required beyond what is needed for the single-user space-time channel. For the special case of low-rank "code-division multiple-access (CDMA)" signaling with N/sub T/=1 and provided the signatures of any two users are linearly independent, it is shown that the error probability of a K-user system asymptotically approaches single-user-like performance for every user. Remarkably, therefore, an increase in the number of users, and hence an increase in the aggregate spectral efficiency, does not require the users to transmit with more power to achieve single-user-like performance asymptotically. A signal design algorithm is proposed to illustrate this point and examples are given. These results are then generalized to the multiple transmit antenna case. A new (N/sub T/+1)-dimensional signaling strategy is proposed for the multiuser channel that leverages existing single-user space-time signal designs while ensuring full diversity order and single-user-like performance asymptotically for every user.     

频谱有效的差分空时编码CDMA系统

该文针对码分多址(Code-Division Multiple-Access,CDMA)系统提出了频谱有效的差分空时传输方案。考虑包含M个同步共道用户的多用户环境,每一用户配备双发射天线。若接收端配备N2个接收天线,该方案将采用解相关检测器和接收天线分集分离M个用户。基于平坦Rayleigh衰落信道,给出了非相干译码器,它可为每一共道用户提供2(N-1)的最小分集增益。与已有的差分空时编码CDMA系统相比,该方案具有两大优势:第一,仅需增加单个接收天线,该方案可在频谱效率提高1/3的条件下显著地改善系统性能;第二,译码仅具有线性复杂度。     

Performance of antenna diversity multiuser receivers in CDMA channels with imperfect fading estimation

The performance of antenna diversity coherent and differentially coherent linear multiuser receivers is analyzed in frequency-nonselective Rayleigh fading CDMA channels with memory. The estimates of the complex fading processes are utilized for maximal-ratio combining and carrier recovery of the coherent multiuser receiver. To analyze the impact of channel estimation errors on the receiver performance, error probability is assessed directly in terms of the fading rate and the number of active users, showing the penalty imposed by imperfect channel estimation as well as the fading-induced error probability floor. The impact of fading dynamics on the differentially coherent decorrelating receiver with equal-gain combining is quantified. While performance of multiuser receivers at lower SNR is determined by both the fading dynamics and the number of active CDMA users, performance at higher SNR is given by an error probability floor which is due to fading only and has the same value as in a single-user case. The comparison of the two receiver structures indicates that the coherent decorrelating receiver with diversity reception may be preferable to the differentially coherent one in nonselective fading CDMA channels with memory.