Polynomial Expansion Detector Research Articles

Low Complexity Polynomial Expansion Detector With Deterministic Equivalents of the Moments of Channel Gram Matrix for Massive MIMO Uplink

We consider a low complexity polynomial expansion (PE) detector in a massive multiple-input multiple-output (MIMO) uplink channel. In contrast to most massive MIMO systems in the literature, where single antenna user equipments (UEs) are assumed, multiple antenna UEs are employed in this paper. Moreover, the channel between a base station (BS) and a UE is a jointly correlated Rician fading channel. The PE detector reduces the computational complexity of the minimum mean square error (MMSE) detector by replacing the matrix inversion with an approximate matrix polynomial. The coefficients of the approximate matrix polynomial are computed from the deterministic equivalents of the moments of the channel Gram matrix. We use operator-valued free probability, which is a more general version of free probability, to derive the deterministic equivalents. In particular, we use the operator-valued moment-cumulant formula. The proposed low complexity PE detector is easy to compute. Simulation results show that the proposed detector can achieve performance close to the MMSE detector.

Asynchronous CDMA Systems With Random Spreading—Part II: Design Criteria

Totally asynchronous code-division multiple-access (CDMA) systems are addressed. In Part I, the fundamental limits of asynchronous CDMA systems are analyzed in terms of spectral efficiency and SINR at the output of the optimum linear detector. The focus of Part II is the design of low-complexity implementations of linear multiuser detectors in systems with many users that admit a multistage representation, e.g. reduced rank multistage Wiener filters, polynomial expansion detectors, weighted linear parallel interference cancellers. The effects of excess bandwidth, chip-pulse shaping, and time delay distribution on CDMA with suboptimum linear receiver structures are investigated. Recursive expressions for universal weight design are given. The performance in terms of SINR is derived in the large-system limit and the performance improvement over synchronous systems is quantified. The considerations distinguish between two ways of forming discrete-time statistics: chip-matched filtering and oversampling.

Low‐complexity linear group‐SIC detectors

AbstractIn this paper, we consider a linear group polynomial expansion successive interference cancellation (GPE‐SIC) detector in a synchronous CDMA system. It is a hybrid detector, which combines parallel and successive cancellation techniques in order to extract the advantages of both schemes. We use the fact that even if the cross‐correlation matrix of the system is not diagonal dominant, the sub‐matrices corresponding to different groups can be forced to be diagonal dominant by suitable grouping of users to approximate the decorrelator/MMSE detector by a low‐complexity polynomial expansion detector. The latter is computationally very efficient if the cross‐correlation matrix of users within the same group is diagonal dominant.Simulation results showed that the (GPE‐SIC) detector has the same performance as the linear group decorrelator successive interference cancellation (GDEC‐SIC) detector but with low‐computational complexity. Copyright © 2006 John Wiley & Sons, Ltd.

A Systematic Approach to Multistage Detectors in Multipath Fading Channels

We consider linear multistage detectors with universal (large system) weighting for synchronous code-division multiple access (CDMA) in multipath fading channels with many users. A convenient choice of the basis of the projection subspace allows a joint projection of all users. Taking advantage of this property, the complexity per bit of multistage detectors with universal weights scales linearly with the number of users on the uplink CDMA channel, while other known multistage detectors with universal weights and different bases of the projection subspace keep the same quadratic complexity order per bit as the linear minimum mean-square error (LMMSE) detector. We focus on the design of two kinds of detectors with linear complexity. The detector of Type I is obtained as an asymptotic approximation of the polynomial expansion detector proposed by Moshavi et al. The detector of Type II has the same performance as the multistage Wiener filter (MSWF) in large systems. Additionally, general performance expressions for large systems, applicable to any multistage detector with the same basis of the projection subspace (e.g., linear parallel interference canceling detectors), are derived. As a by-product, the performance analysis disproves the widespread belief that the MSWF and the polynomial expansion detector are equivalent. We show that, in general, the MSWF outperforms the latter one and they are equivalent only asymptotically in the case of equal received powers.

Low Complexity Polynomial Expansion Multiuser Detector for CDMA Systems

The polynomial expansion (PE) multiuser detector can iteratively approximate the linear decorrelating and MMSE multiuser detectors. This is a very promising approach since the complexity of the PE detector is considerably less than that of the decorrelating and MMSE detectors. The concept of the PE multiuser detector is a weighted matrix polynomial for which optimal weighting has been suggested in the literature. Unfortunately, the optimal weights apply only to a specific correlation matrix. As soon as the correlation between the users changes (and hence also the correlation matrix), a new set of optimal weights has to be calculated. The calculation of these weights is computationally very intense. In this paper, an approach is presented where the weights are predefined and apply for all matrices. Furthermore, a normalization factor is needed to ensure convergence. It will be shown how this factor has to be chosen to obtain the optimal convergence speed. For the optimal normalization factor the minimum and maximum eigenvalues are needed. A low complexity and accurate method to estimate these eigenvalues is derived which can be applied to all correlation matrices and therefore to any code division multiple access (CDMA) scenario. Hence, the matrix-dependent optimal normalization factor can easily be calculated and ensures a good bit error rate (BER) performance, even if the correlation between the users changes quickly (e.g., in time-variant channels). Furthermore, it will be shown how to enhance the PE detector such that it has a high near-far resistance. Additionally, for the first time it can be proven that the approximation error of the proposed detector diminishes exponentially with the number of iterations. Finally, simulations verify the fast convergence of the proposed PE detector and its flexible usage in a variety of scenarios.

Rapidly converging polynomial expansion multiuser detector with low complexity for CDMA systems

A polynomial expansion (PE)-based multiuser detector (MUD) with low complexity O(N2) is presented. It approximates the computational intense (O(N3)) matrix inversion necessary for the decorrelating and minimum mean-squared error (MMSE) MUDs. Optimal convergence speed is obtained by normalising the PE detector's matrix with respect to its smallest and largest eigenvalues. An efficient method to accurately estimate these eigenvalues is shown. Simulations in a CDMA-based system demonstrate that the presented PE MUD converges rapidly to the MMSE MUD.

Adaptive implementation of polynomial expansion detector for multi-user detection in DS-CDMA systems

The polynomial expansion (PE) multi-user detector was proposed to eliminate the computational complexity of matrix inversion involved in the decorrelating detector and the MMSE detector. Computation of the polynomial coefficients in a PE detector is, however, a complex task. A fast converging adaptive algorithm based on the Davidon-Fletcher-Powell (DFP) method is proposed for computing polynomial weights for a PE detector.