Multiuser detection for overloaded CDMA systems

Multiuser detection for overloaded code-division multiple-access (CDMA) systems, in which the number of users is larger than the dimension of the signal space, is of particular interest when bandwidth is at a premium. In this paper, certain fundamental questions are answered regarding the asymptotic forms and performance of suboptimum multiuser detectors for cases where the desired and/or interfering signal subspaces are of reduced rank and/or have a nontrivial intersection. In the process, two new suboptimum detectors are proposed that are especially well suited to overloaded systems, namely, the group pseudo-decorrelator and the group minimum mean-squared error (MMSE) detector. The former is seen to be the correct extension of the group decorrelator in the sense that it is the limiting form (in the low-noise regime) of the group MMSE detector. Pseudo-decorrelation is also used as a feedforward filter in a new decision feedback scheme. For the particular case of real-valued modulation, it is shown that the proposals of the so-called "improved" linear (also known as "linear-conjugate" or "widely linear") detectors were more simply derived earlier using the idea of minimal sufficiency, which we also apply to the new detectors of this paper.     

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.     

Near-ML multiuser detection with linear filters and reliability-based processing

The prohibitive - exponential in the number of users - computational complexity of the maximum-likelihood multiuser detector for direct-sequence code-division multiple-access communications has fueled an extensive research effort for the development of low-complexity multiuser detection alternatives. We show that we can efficiently and effectively approach the error rate performance of the optimum multiuser detector as follows. We utilize a multiuser zero-forcing or minimum mean-square error (MMSE) linear filter as a preprocessor and we establish that the output magnitudes, when properly scaled, provide a reliability measure for each user bit decision. Then, we prepare an ordered, reliability-based error search sequence of length linear in the number of users; it returns the most likely user bit vector among all visited options. Numerical and simulation studies for moderately loaded systems that permit exact implementation of the optimum detector indicate that the error rate performance of the optimum and the proposed detector are nearly indistinguishable over the whole predetection. signal-to-noise ratio range of practical interest. Similar studies for higher user loads (that prohibit comparisons with the optimum detector) demonstrate error rate performance gains of orders of magnitude in comparison with straight decorrelating or MMSE multiuser detection.     

Output MAI distributions of linear MMSE multiuser receivers inDS-CDMA systems

Multiple-access interference (MAI) in a code-division multiple-access (CDMA) system plays an important role in performance analysis and characterization of fundamental system limits. We study the behavior of the output MAI of the minimum mean-square error (MMSE) receiver employed in the uplink of a direct-sequence (DS)-CDMA system. We focus on imperfect power-controlled systems with random spreading, and establish that in a synchronous system (1) the output MAI of the MMSE receiver is asymptotically Gaussian, and (2) for almost every realization of the signatures and received powers, the conditional distribution of the output MAI converges weakly to the same Gaussian distribution as in the unconditional case. We also extend our study to asynchronous systems and establish the Gaussian nature of the output interference. These results indicate that in a large system the output interference is approximately Gaussian, and the performance of the MMSE receiver is robust to the randomness of the signatures and received powers. The Gaussianity justifies the use of single-user Gaussian codes for CDMA systems with linear MMSE receivers, and implies that from the viewpoints of detection and channel capacity, signal-to-interference ratio (SIR) is the key parameter that governs the performance of the MMSE receiver in a CDMA system     

Large-system performance analysis of blind and group-blindmultiuser receivers

We present a large-system performance analysis of blind and group-blind multiuser detection methods. In these methods, the receivers are estimated based on the received signal samples. In particular, we assume binary random spreading, and let the spreading gain N, the number of users K, and the number of received signal samples M all go to infinity, while keeping the ratios K/N and M/N fixed. We characterize the asymptotic performance of the direct-matrix inversion (DMI) blind linear minimum mean-square error (MMSE) receiver, the subspace blind linear MMSE receiver, and the group-blind linear hybrid receiver. We first derive the asymptotic average output signal-to-interference-plus-noise ratio (SINR) for each of these receivers. Our results reveal an interesting "saturation" phenomenon: The output SINR of each of these receivers converges to a finite limit as the signal-to-noise ratio (SNR) of the desired user increases, which is in stark contrast to the fact that the output SINR achieved by the exact linear MMSE receiver can get arbitrarily large. This indicates that the capacity of a wireless system with blind or group-blind multiuser receivers is not only interference-limited, but also estimation-error limited. We then show that for both the blind and group-blind receivers, the output residual interference has an asymptotic Gaussian distribution, independent of the realizations of the spreading sequences. The Gaussianity indicates that in a large system, the bit-error rate (BER) is related to the SINR simply through the Q function     

A Low Complexity Near Optimal Signal Detection for Large Scale MIMO SC-FDMA Uplink System

This article proposes an improved Newton algorithm as a low complexity signal detection scheme for linear receiver in large scale multiple- input multiple- output (LS-MIMO) single carrier frequency division multiple access (SC-FDMA) uplink system, where a large number of antennas are set up at the base station and active users are with a single antenna system. Data detection for uplink SC-FDMA system is one of the specific challenges due to the significant rise in the dimension of antennas and number of subcarriers. Especially for symbol detection process, LS-MIMO SC-FDMA system with linear detector requires to perform a large matrix inverse computation. Even though linear detectors such as zero forcing (ZF) and minimum mean square error (MMSE) can achieve near-optimal detection performance, they still introduce high computational complexity and obliviously involve in the computation of matrix inversion. Therefore, a design of complexity reduction algorithm based near-optimal detector for LS-MIMO SC-FDMA system attains research interest. The improved Newton algorithm is employed to obtain linear detection solution which iteratively performs matrix free-inversion operation. The new algorithm performs matrix–matrix multiplication into matrix–vector multiplication, which substantially reduces receiver detection complexity. The efficacy of the proposed method is investigated at 16-QAM. Both ZF and MMSE criteria are proposed and compared through simulations. Simulation results illustrate that the proposed scheme outperforms the conventional detection schemes and exhibits near-optimal performance with a small number of iterations. Further, bit-error-rate performance is closer to classical linear detector with affordable computational complexity.

     

Performance of blind and group-blind multiuser detectors

In blind (or group-blind) linear multiuser detection, the detector is estimated from the received signals, with the prior knowledge of only the signature waveform of the desired user (or the signature waveforms of some but not all users). The performance of a number of such estimated linear detectors, including the direct-matrix-inversion (DMI) blind linear minimum mean square error (MMSE) detector, the subspace blind linear MMSE detector, and the form-I and form-II group-blind linear hybrid detectors, are analyzed. Asymptotic limit theorems for each of the estimates of these detectors (when the signal sample size is large) are established, based on which approximate expressions for the average output signal-to-interference-plus-noise ratios (SINRs) and bit-error rates (BERs) are given. To gain insights on these analytical results, the performance of these detectors in an equicorrelated code-division multiple-acces (CDMA) system is compared. Examples are provided to demonstrate the excellent match between the theory developed here and the simulation results     

Asymptotic analysis of the MMSE multiuser detector fornonorthogonal multipulse modulation

We develop the minimum mean-squared-error (MMSE) multiuser detector for nonorthogonal multipulse modulation over the noncoherent additive white Gaussian noise channel. We analyze the asymptotic performance of the detector and show that, unlike the case of linear modulation, the MMSE detector does not generally approach the generalized maximum-likelihood (GML) detection rule as the noise power vanishes. It does, however, approach a detector which nulls out the multiaccess interference. This detector is termed the multipulse decorrelating detector due to its similarity to the linear decorrelating detector. The probability of error for this detector is derived and used to find the asymptotic multiuser efficiencies of both the multipulse decorrelating detector and the MMSE detector. It is shown that for noncoherent binary signaling, in which the multipulse modulation is two-dimensional, the multipulse decorrelating detector is superior to the GML detector asymptotically. This result does not generalize to larger dimensionality signal sets     

Multicell uplink spectral efficiency of coded DS-CDMA with randomsignatures

A simple multicell uplink communication model is suggested and analyzed for optimally coded randomly spread direct sequence code-division multiple access (DS-CDMA). The model adheres to Wyner's (1994) infinite linear cell-array model, according to which only adjacent-cell interference is present, and characterized by a single parameter 0⩽α⩽1. The discussion is confined to asymptotic analysis where both the number of users and the processing gain go to infinity, while their ratio goes to some finite constant. Single cell-site processing is assumed and four multiuser detection strategies are considered: the matched-filter detector, “optimum” detection with adjacent-cell interference treated as Gaussian noise, the linear minimum mean square error (MMSE) detector and a detector that performs MMSE-based successive interference cancellation for intracell users with linear MMSE processing of adjacent-cell interference. Spectral efficiency is evaluated under three power allocation policies: equal received powers (for all users), equal rates, and a maximal spectral efficiency policy. Comparative results demonstrate how performance is affected by the introduction of intercell interference, and what is the penalty associated with the randomly spread coded DS-CDMA strategy. Finally, the effect of intercell time-sharing protocols as suggested by Shamai and Wyner (1997) is also examined, and a significant system performance enhancement is observed     

Blind adaptive multiuser detection

The decorrelating detector and the linear minimum mean-square error (MMSE) detector are known to be effective strategies to counter the presence of multiuser interference in code-division multiple-access channels; in particular, those multiuser detectors provide optimum near-far resistance. When training data sequences are available, the MMSE multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes. This paper introduces an adaptive multiuser detector which converges (for any initialization) to the MMSE detector without requiring training sequences. This blind multiuser detector requires no more knowledge than does the conventional single-user receiver: the desired user's signature waveform and its timing. The proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest     

Asynchronous block-based minimum mean square error (B-MMSE) CDMA multi-user detection

This paper introduces a novel asynchronous CDMA multi-user detector, the block-based MMSE (B-MMSE) multi-user detector, in which the data stream is segmented into blocks by inserting zero bits and detection takes place block-by-block without compromising the MMSE detection efficiency. The BER performance of the B-MMSE detector is studied and the results are compared with those of the decorrelating detector. It is shown that the B-MMSE detector offers promising detection efficiency at a much lower implementation complexity, which is linear in the product of number of users and block size, than that of the traditional MMSE detector. © 1998 John Wiley & Sons, Ltd.     

MMSE detection in asynchronous CDMA systems: an equivalence result

The analysis of linear minimum mean-square error (MMSE) detection in a band-limited code-division multiple-access (CDMA) system that employs random spreading sequences is considered. The key features of the analysis are that the users are allowed to be completely asynchronous, and that the chip waveform is assumed to be the ideal Nyquist sinc function. It is shown that the asymptotic signal-to-interference ratio (SIR) at the detector output is the same as that in an equivalent chip-synchronous system. It is hence been established that synchronous analyses of linear MMSE detection can provide useful guidelines for the performance in asynchronous band-limited systems.     

On the average near-far resistance for MMSE detection of directsequence CDMA signals with random spreading

The performance of a near-far-resistant, finite-complexity, minimum mean squared error (MMSE) linear detector for demodulating direct sequence (DS) code-division multiple access (CDMA) signals is studied, assuming that the users are assigned random signature sequences. We obtain tight upper and lower bounds on the expected near-far resistance of the MMSE detector, averaged over signature sequences and delays, as a function of the processing gain and the number of users. Since the MMSE detector is optimally near-far-resistant, these bounds apply to any multiuser detector that uses the same observation interval and sampling rate. The lower bound on near-far resistance implies that, even without power control, linear multiuser detection provides near-far-resistant performance for a number of users that grows linearly with the processing gain     

MMSE/PIC multiuser detection for DS/CDMA systems with inter- andintra-cell interference

This paper analyzes combinations of the linear minimum mean square error (MMSE) detector and a nonlinear parallel interference canceller (PIC) for multiuser code-division multiple-access (CDMA) detection. Both the case where all users' codes are known at the receiver and the case where only some codes are known are considered. An upper bound and an approximate formula for the error probability are derived and verified through simulation. It is shown that the combined MMSE/PIC detector can have a considerable performance gain over the MMSE. It is also shown that while the MMSE detector is sensitive to large code cross-correlation values, the combined MMSE/PIC detector is robust to code cross correlations. Finally, use of the MMSE/PIC detector for cellular systems with both inter- and intra-cell interference is considered     

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.     

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     

Near-far resistance of multiuser detectors in asynchronous channels

Consideration is given to an asynchronous code-division multiple-access environment in which receiver has knowledge of the signature waveforms of all the users. Under the assumption of white Gaussian background noise, the authors compare detectors by their worst case bit error rate in a near-far environment with low background noise, where the received energies of the users are unknown to the receiver and are not necessarily similar. Conventional single-user detection in a multiuser channel is not near-far resistant, and the substantially higher performance of the optimum multiuser detector requires exponential complexity in the number of users. The authors explore suboptimal demodulation schemes which exhibit a low order of complexity while not exhibiting the impairment of the conventional single-user detector. It is shown that there exists a linear detector whose bit-error-rate is independent of the energy of the interfering users. It is also shown that the near-far resistance of optimum multiuser detection can be achieved by a linear detector. The optimum linear detector for worst-case energies is found, along with existence conditions, which are always satisfied in the models of practical interest     

Performance of the MMSE multiuser detector with equicorrelated signatures

In this letter, we analyze the performance of the minimum mean-square error (MMSE) detector for a code-division multiple-access system employing binary phase-shift keying. The performance is measured in terms of the probability distribution and the average number of correctly decoded users. We consider the case of equipower users having equicorrelated signature waveforms. The distribution of the number of correctly decoded users is expressed as an integral over sum of products of Gaussian Q-functions. From it, a closed-form expression for the average number of correctly decoded users is derived.     

Performance analysis of linear multiuser detectors for randomlyspread CDMA using Gaussian approximation

The performance of a linear decorrelating detector (LDD) and a minimum mean square error (MMSE) detector is analyzed for random spreading waveforms. The performance of the LDD and MMSE detectors is expressed in terms of the so-called near-far resistance, defined by a reciprocal of a diagonal component of inverse matrix. For random code division multiple access, which employs random spreading waveforms, the near-far resistance can be regarded as a random variable. Many papers have dealt with the analysis of multiuser detectors for random spreading sequences. In most cases, however, these analyses derived only the expectations or bounds for the near-far resistance. In this paper, we directly derive the approximate probability density function (PDF) of the near-far resistance and corresponding bit error rate expression for random spreading sequences. It is based on Gaussian approximation of the cross correlation between any two randomly generated spreading codes. The resulting PDF turned out to be a reversed-and-scaled version of chi-square distribution. The approximate expressions, both the PDF and the corresponding bit error rate expression, were verified via Monte Carlo simulations. The results showed that the approximation is quite close to the simulation results when the number of users is less than half the processing gain     

Optimal adaptive multiuser detection in unknown multipath channels

An optimal multiuser detector in the weighted least squares (WLS) sense is derived. This detector, which includes the maximum likelihood multiuser detector as a special case, consists of two parts: a bank of linear fractionally chip spaced minimum mean squared error (MMSE) filters, and a nonlinear WLS metric minimizer. It is shown that the symbol spaced samples at the output of the MMSE filter bank provide a set of sufficient statistics for WLS detection. The relationship between the taps of a centralized decision feedback detector and the MMSE filter bank is derived. It is proven that all the necessary parameters for implementing the WLS detector can be realized by adaptively training a centralized decision feedback detector. Therefore, the WLS detector achieves optimal joint synchronization and data detection even in the presence of colored noise, such as narrowband interference, without any a priori knowledge of the users' signatures, multipath channel taps or statistics of the colored noise. Significant features of the WLS detector are that: (1) the WLS detector is a generalization of the maximum likelihood multiuser detector that employs a bank of matched filters; (2) it is implemented adaptively; and (3) it has structural flexibility in terms of implementation complexity