Abstract—The performance of reduced-rank linear filtering is studied for the suppression of multiple-access interference. A reduced-rank filter resides in a lower dimensional space, relative to the full-rank filter, which enables faster convergence and tracking. We evaluate the large system output signal-to-interference plus noise ratio (SINR) as a function of filter rank for the multistage Wiener filter (MSWF) presented by Goldstein and Reed. The large system limit is defined by letting the number of users and the number of dimensions tend to infinity with fixed. For the case where all users are received with the same power, the reduced-rank SINR converges to the full-rank SINR as a continued fraction. An important conclusion from this analysis is that the rank needed to achieve a desired output SINR does not scale with system size. Numerical results show that a V is sufficient to achieve near-full-rank performance even under heavy loads @ aIA. We also evaluate the large system output SINR for other reduced-rank methods, namely, Principal Components and Cross-Spectral, which are based on an eigendecomposition of the input covariance matrix, and Partial Despreading (PD). For those methods, the large system limit lets with fixed. Our results show that for large systems, the MSWF allows a dramatic reduction in rank relative to the other techniques considered. Index Terms—Interference suppression, large system analysis, multiuser detection, reduced-rank filters. I.

Abstract—Reduced-rank minimum mean-squared error (MMSE) multiuser detectors using asymptotic weights have been shown to reduce receiver complexity while maintaining good performance in long-sequence code-division multiple-access (CDMA) systems. In this paper, we consider the design of reduced-rank MMSE receivers in a general framework which includes fading, single and multiantenna receivers, as well as direct-sequence CDMA (DS-CDMA) and multicarrier CDMA (both uplink and downlink). In all these cases, random matrix results are used to obtain explicit expressions for the asymptotic eigenvalue moments of the interference autocorrelation matrix and for the asymptotic weights used in the reduced-rank receiver. Index Terms—Code-division multiple access (CDMA), fading channels, minimum mean-squared error (MMSE) receivers, multiantenna systems, multicarrier CDMA, multiuser detection, random matrix theory. I.

Abstract—In the traditional transmitting beamforming radar system, the transmitting antennas send coherent waveforms which form a highly focused beam. In the multiple-input multiple-output (MIMO) radar system, the transmitter sends noncoherent (possibly orthogonal) broad (possibly omnidirectional) waveforms. These waveforms can be extracted at the receiver by a matched filterbank. The extracted signals can be used to obtain more diversity or to improve the spatial resolution for clutter. This paper focuses on space–time adaptive processing (STAP) for MIMO radar systems which improves the spatial resolution for clutter. With a slight modification, STAP methods developed originally for the single-input multiple-output (SIMO) radar (conventional radar) can also be used in MIMO radar. However, in the MIMO radar, the rank of the jammer-and-clutter subspace becomes very large, especially the jammer subspace. It affects both the complexity and the convergence of the STAP algorithm. In this paper, the clutter space and its rank in the MIMO radar are explored. By using the geometry of the problem rather than data, the clutter subspace can be represented using prolate spheroidal wave functions (PSWF). A new STAP algorithm is also proposed. It computes the clutter space using the PSWF and utilizes the block-diagonal property of the jammer covariance matrix. Because of fully utilizing the geometry and the structure of the covariance matrix, the method has very good SINR performance and low computational complexity. Index Terms—Clutter subspaces, multiple-input multiple-output (MIMO) radar, prolate spheroidal wave function, space–time adaptive processing (STAP). I.

Abstract—A class of adaptive reduced-rank interference suppression algorithms is presented based on the multi-stage Wiener filter (MSWF). The performance is examined in the context of direct-sequence (DS) code division multiple access (CDMA). Unlike the Principal Components method for reduced-rank filtering, the algorithms presented can achieve near full-rank performance with a filter rank much less than the dimension of the signal subspace. We present batch and recursive algorithms for estimating the filter parameters, which do not require an eigen-decomposition. Algorithm performance in a heavily loaded DS-CDMA system is characterized via computer simulation. Results show that the reduced-rank algorithms require significantly fewer training samples than other reduced- and full-rank algorithms. Index Terms—Adaptive filters, code-division multiple access (CDMA), interference suppression. I.

This paper investigates the performance of reduced rank spacetime processors in the context of anti-jam mitigation for an MCode based GPS receiver utilizing a circular array. Several adaptive processing algorithms are discussed utilizing power minimization techniques. It is assumed an INS (Inertial Navigation System) or direction finding algorithm is incorporated into the receiver for satellite look direction based algorithms. Reduced rank space-time processing is accomplished via the innovative Multistage Wiener filter (MSWF). It is demonstrated that the MSWF does not require matrix inversion, thereby reducing computational complexity. The processing algorithms are compared in terms of available degrees of freedom and distortion of the GPS cross correlation function (CCF).

Abstract—Adaptive iterative receivers which combine multiuser decision-feedback detection with maximum a posteriori (MAP) decoding and soft feedback are presented for synchronous coded direct sequence-code-division multiple access. Both successive and parallel demodulation of users are considered. Optimal filters are derived using both minimum mean squared error and least squares (LS) criteria. The latter assumes short (repeated) spreading codes and that the users to be demodulated simultaneously transmit training sequences. The LS criterion does not require prior knowledge or estimates of spreading codes and channels. Simulation results show that the adaptive receiver can perform significantly better than the standard (soft) interference canceller, since the adaptive algorithm attempts to measure and exploit the second-order statistics between the input and output of the MAP decoder. With limited training, successive feedback and decoding performs significantly better than parallel feedback. The effect of code rate on performance is examined, and reduced-rank versions of the adaptive LS algorithms, which can reduce training overhead, are also presented. Index Terms—Adaptive filters, code division multiaccess (CDMA), interference cancellation, interference suppression, iterative methods, MIMO systems, multiuser detection. I.

Abstract—The performance of adaptive least squares (LS) filtering is analyzed for the suppression of multiple-access interference. Both full-rank LS filters and reduced-rank LS filters, which reside in a lower dimensional Krylov space, are considered with training, and without training but with known signature for the desired user. We compute the large system limit of output signal-to-interference-plus-noise ratio (SINR) as a function of normalized observations, load, and noise level. Specifically, the number of users, the degrees of freedom, and the number of training symbols or observations all tend to infinity with fixed ratios and. Our results account for an arbitrary power distribution over the users, data windowing (e.g., recursive LS (RLS) with exponential windowing), and initial diagonal loading of the covariance matrix to prevent ill-conditioning. Numerical results show that the large system analysis accurately predicts the simulated convergence performance of the algorithms considered with moderate degrees of freedom (typically aQP). Given a fixed, short training length, the relative performance of full- and reduced-rank filters depends on the selected rank and diagonal loading. With an optimized diagonal loading factor, the performance of full- and reduced-rank filters are similar. However, full-rank performance is generally much more sensitive to the choice of diagonal loading factor than reduced-rank performance. Index Terms—Adaptive filter, large system analysis, least squares (LS), reduced-rank filters. I.

Abstract—An adaptive iterative (turbo) decision-feedback equalizer (DFE) for channels with intersymbol interference (ISI) is presented. The filters are computed directly from the soft decisions and received data to minimize a least-squares (LS) cost function. Numerical results show that this method gives a substantial improvement in performance relative to a turbo DFE computed from an exact channel estimate, assuming perfect feedback. Adaptive reduced-rank estimation methods are also presented, based on the multistage Wiener filter (MSWF). The adaptive reduced-rank turbo DFE for single-input/single-output channels is extended to multiple-input/multiple-output (MIMO) channels with ISI and multiple receive antennas. Numerical results show that for MIMO channels with limited training, the reduced-rank turbo DFE can perform significantly better than the full-rank turbo DFE. Index Terms—Adaptive filters, multiple-input/multiple-output (MIMO) channels, space–time processing, turbo equalization.

When wideband and narrowband interferences in a GPS system are stationary, a large number of data samples may be obtained to get a good estimate of the interference. However, the jamming environment may be one in which the narrowband jammers have the ability to change frequencies dynamically or the rapid dynamics of the aircraft during maneuvering causes arrival angles of wideband jammers to change. In either type of jamming environment, an interference suppression algorithm will only be effective if it can rapidly converge with a small sample size. We investigate the performance of reduced-rank interference suppression algorithms under conditions of low sample support. It is demonstrated that the Multi-Stage Nested Wiener Filter (MSNWF) outperforms other reduced-rank techniques in terms of suppressing both wideband and narrowband jammers under conditions of low sample support due to the optimal choice of the reduced-rank subspace effected by the MSNWF. 1

An order recursive algorithm for minimum mean square error (MMSE) estimation of signals under a Bayesian model defined on the steering vector is introduced. The MMSE estimate can be viewed as a mixture of conditional MMSE estimates weighted by the posterior probability density function (PDF) of the random steering vector given the observed data. This paper derives an adaptive closed form Kalman-filter implementation that updates the weight vector by successive incorporations of data collected from additional array elements in the steering vector. The performance of the Bayesian beamformer is compared against several robust beamformers in terms of mean square error (MSE) and output signal-to-interference-plus-noise ratio (SINR). 1. BACKGROUND The received data vector of an N-element sensor array at sample time k has the form x(k) =a s ∗ (k)+i(k)+n(k), (1) where s(k) is the desired signal with known power σ 2 s, a ∈ C N is the steering vector, i(k) is the interence and n(k) is the noise. Let Ri+n � E[(i(k) +n(k))(i(k) +n(k)) H] be the interference-plus-noise covariance. Let (·) ∗ , (·) T and (·) H be the complex conjugate, transpose and Hermitian transpose, respectively. Assume that s(k), i(k) and n(k) are zero mean, temporally white, complex Gaussian processes that are mutually independent to each other. In practice, the true steering vector often deviates from its presumed value for various reasons such as improper array modeling, asynchronous sampling, pointing error, miscalibration, or source motion. It is often reasonable to model these