Wiener Receiver Research Articles

Central limit theorem for signal-to-interference ratio of reduced rank linear receiver

Let $\mathbf{s}_{k}=\frac{1}{\sqrt{N}}(v_{1k},\ldots,v_{Nk})^{T}$, with {vik, i, k=1, …} independent and identically distributed complex random variables. Write Sk=(s1, …, sk−1, sk+1, …, sK), Pk=diag(p1, …, pk−1, pk+1, …, pK), Rk=(SkPkSk*+σ2I) and Akm=[sk, Rksk, …, Rkm−1sk]. Define βkm=pksk*Akm(Akm*×RkAkm)−1Akm*sk, referred to as the signal-to-interference ratio (SIR) of user k under the multistage Wiener (MSW) receiver in a wireless communication system. It is proved that the output SIR under the MSW and the mutual information statistic under the matched filter (MF) are both asymptotic Gaussian when N/K→c>0. Moreover, we provide a central limit theorem for linear spectral statistics of eigenvalues and eigenvectors of sample covariance matrices, which is a supplement of Theorem 2 in Bai, Miao and Pan [Ann. Probab. 35 (2007) 1532–1572]. And we also improve Theorem 1.1 in Bai and Silverstein [Ann. Probab. 32 (2004) 553–605].

Asymptotic Analysis of Reduced-Rank Chip-Level MMSE Equalizers in the Downlink of CDMA Systems

In this paper, we address the performance of downlink CDMA receivers that consist in a reduced rank Wiener chip-rate equalizer followed by a despreading operation. In particular, we tackle the question of whether a performance close to the optimum can be achieved for small values of the rank. To answer this question, it is standard to consider the output signal-to-interference plus noise ratio (SINR), and to study its convergence speed versus the rank of the receiver. Unfortunately, this task is difficult due to the fact that the SINR expressions depend on the spreading codes allocated to the various users in a rather complicated way. To be able to obtain positive results, we assume that the spreading factor and the number of users tend to infinity while their ratio remains finite. As in the third-generation UMTS system, the spreading codes we consider coincide with orthogonal Walsh-Hadamard codes scrambled by an independent identically distributed sequence. In this context, we show that the SINR of each reduced-rank receiver converges toward a deterministic limit which depends only of the rank of the receiver, and not of the spreading codes given to the various users. Using some previous results, we prove that the asymptotic SINRs converge exponentially to the SINR of the plain Wiener receiver when the rank of the receiver increases. We obtain the corresponding convergence rate, and exhibit the parameters that influence the convergence speed. We finally compare our asymptotic performance expressions with the results of numerical simulations. We observe a good agreement for spreading factors as low as 16

Linearly precoded analytical constant modulus algorithm for non-constant modulus space-time codes

The analytical constant modulus algorithm (ACMA) is an algebraic method for blind separation of co-channel users. Assuming constant modulus (CM) sources, we propose the linearly precoded ACMA (LPACMA) for blind separation of systems employing space-time codes (STCs) that do not preserve the CM property (non-CM STCs). The proposed algorithm requires fewer snapshots than STC-ACMA and resolves the permutation ambiguity inherent to blind algorithms whilst retaining the asymptotic convergence to the Wiener receiver.

Statistical performance analysis of the algebraic constant modulus algorithm

This paper presents a large sample analysis of the covariance of the beamformers computed by the analytical constant modulus algorithm (ACMA) method for blindly separating constant modulus sources. This can be used to predict the signal-to-interference plus noise ratio (SINR) performance of these beamformers, as well as their deviation from the (nonblind) Wiener receivers to which they asymptotically converge. The analysis is based on viewing ACMA as a subspace fitting optimization, where the subspace is spanned by the eigenvectors of a fourth-order covariance matrix. The theoretical performance is illustrated by numerical simulations and shows a good match.

Geometrical characterizations of constant modulus receivers

Convergence properties of the constant modulus (CM) and the Shalvi-Weinstein (SW) algorithms in the presence of noise remain largely unknown. A new geometrical approach to the analysis of constant modulus and Shalvi-Weinstein receivers is proposed by considering a special constrained optimization involving norms of the combined channel-receiver response. This approach provides a unified framework within which various blind and (nonblind) Wiener receivers can all be analyzed by circumscribing an ellipsoid by norm balls of different types, A necessary and sufficient condition for the equivalence among constant modulus. Shalvi-Weinstein, zero forcing, and Wiener receivers are obtained. Answers to open questions with regard to CM and SW receivers, including their locations and their relationship with Wiener receivers, are provided for the special orthogonal channel and the general two-dimensional (2-D) channel-receiver impulse response. It is also shown that in two dimensions, each CM or SW receiver is associated with one and only one Wiener receiver.

An analysis of constant modulus receivers

This paper investigates connections between (non-blind) Wiener receivers and blind receivers designed by minimizing the constant modulus (CM) cost. Applicable to both T-spaced and fractionally spaced FIR equalization, the main results include (1) a test for the existence of CM local minima near Wiener receivers; (2) an analytical description of CM receivers in the neighborhood of Wiener receivers; (3) mean square error (MSE) bounds for CM receivers. When the channel matrix is invertible, we also show that the CM receiver is approximately colinear with the Wiener receiver and provide a quantitative measure of the size of neighborhoods that contain the CM receivers and the accuracy of the MSE bounds.

An analysis of constant modulus algorithm for array signal processing

The constant modulus (CM) cost function is analyzed for array signal processing. The analysis includes arbitrary source types. It is shown that CM receivers have the signal space property except in two special cases. Local minima of CM cost function are completely characterized for the noiseless case. In the presence of measurement noise, the existence of CM local minima in the neighborhood of Wiener receivers is established, and their mean squared error (MSE) performance, output power, estimation bias and residual interference are evaluated. Numerical examples are presented to demonstrate the effects of signal statistics on the locations of CM local minima.

Relationships between the constant modulus and Wiener receivers

The Godard (1980) or the constant modulus algorithm (CMA) is an effective technique for blind receiver design in communications. However, due to the complexity of the constant modulus (CM) cost function, the performance of the CM receivers has primarily been evaluated using simulations. Theoretical analysis is typically based on either the noiseless case or approximations of the cost function. The following question, while resolvable numerically for a specific example, remains unanswered in a generic manner. In the presence of channel noise, where are the CM local minima and what are their mean-squared errors (MSE)? In this paper, a geometrical approach is presented that relates the CM to Wiener (or minimum MSE) receivers. Given the MSE and the intersymbol/user interference of a Wiener receiver, a sufficient condition is given for the existence of a CM local minimum in the neighborhood of the Wiener receiver. The MSE bounds on CM receiver performance are derived and shown to be tight in simulations. The analysis shows that, while in some cases the CM receiver performs almost as well as the (nonblind) Wiener receiver, it is also possible that, due to its blind nature, the CM receiver may perform considerably worse than a (nonblind) Wiener receiver.