A.L. Swindlehurst

A performance analysis of subspace-based methods in the presence of model errors. I. The MUSIC algorithm

Application of subspace-based algorithms to narrowband direction-of-arrival (DOA) estimation requires that both the array response in all directions of interest and the spatial covariance of the noise must be known. In practice, however, neither of these quantities is known precisely. Depending on the degree to which they deviate from their nominal values, serious performance degradation can result. The performance of the MUSIC algorithm is examined for situations in which the noise covariance and array response are perturbed from their assumed values. Theoretical expressions for the error in the MUSIC DOA estimates are derived and compared with simulations performed for several representative cases, and with the appropriate Cramer-Rao bound. An optimally weighted version of MUSIC is proposed for a particular class of array errors. >

Experimental characterization of the MIMO wireless channel: data acquisition and analysis

Detailed performance assessment of space-time coding algorithms in realistic channels is critically dependent upon accurate knowledge of the wireless channel spatial characteristics. This paper presents an experimental measurement platform capable of providing the narrowband channel transfer matrix for wireless communications scenarios. The system is used to directly measure key multiple-input-multiple-output parameters in an indoor environment at 2.45 GHz. Linear antenna arrays of different sizes and construction with up to ten elements at transmit and receive are utilized in the measurement campaign. This data is analyzed to reveal channel properties such as transfer matrix element statistical distributions and temporal and spatial correlation. Additionally, the impact of parameters such as antenna element polarization, directivity, and array size on channel capacity are highlighted. The paper concludes with a discussion of the relationship between multipath richness and path loss, as well as their joint role in determining channel capacity.

Subspace-based signal analysis using singular value decomposition

A unified approach is presented to the related problems of recovering signal parameters from noisy observations and identifying linear system model parameters from observed input/output signals, both using singular value decomposition (SVD) techniques. Both known and new SVD-based identification methods are classified in a subspace-oriented scheme. The SVD of a matrix constructed from the observed signal data provides the key step in a robust discrimination between desired signals and disturbing signals in terms of signal and noise subspaces. The methods that are presented are distinguished by the way in which the subspaces are determined and how the signal or system model parameters are extracted from these subspaces. Typical examples, such as the direction-of-arrival problem and system identification from input/output measurements, are elaborated upon, and some extensions to time-varying systems are given. >

Cooperative Jamming for Secure Communications in MIMO Relay Networks

Secure communications can be impeded by eavesdroppers in conventional relay systems. This paper proposes cooperative jamming strategies for two-hop relay networks where the eavesdropper can wiretap the relay channels in both hops. In these approaches, the normally inactive nodes in the relay network can be used as cooperative jamming sources to confuse the eavesdropper. Linear precoding schemes are investigated for two scenarios where single or multiple data streams are transmitted via a decode-and-forward (DF) relay, under the assumption that global channel state information (CSI) is available. For the case of single data stream transmission, we derive closed-form jamming beamformers and the corresponding optimal power allocation. Generalized singular value decomposition (GSVD)-based secure relaying schemes are proposed for the transmission of multiple data streams. The optimal power allocation is found for the GSVD relaying scheme via geometric programming. Based on this result, a GSVD-based cooperative jamming scheme is proposed that shows significant improvement in terms of secrecy rate compared to the approach without jamming. Furthermore, the case involving an eavesdropper with unknown CSI is also investigated in this paper. Simulation results show that the secrecy rate is dramatically increased when inactive nodes in the relay network participate in cooperative jamming.

Blind and semi-blind equalization for generalized space-time block codes

This paper presents a general framework for space-time codes (STCs) that encompasses a number of previously proposed STC schemes as special cases. The STCs considered are block codes that employ arbitrary redundant linear precoding of a given data sequence together with embedded training symbols, if any. The redundancy introduced by the linear precoding imposes structure on the received data that under certain conditions can be exploited for blind or semi-blind estimation of the transmitted sequence, a linear receiver that recovers the sequence, or both simultaneously. Algorithms based on this observation are developed for the single-user flat-fading case and then extended to handle multiple users, frequency-selective fading, as well as situations where the channel is rank deficient, or there are fewer receive than transmit antennas.

Robust Secure Transmission in MISO Channels Based on Worst-Case Optimization

This paper studies robust transmission schemes for multiple-input single-output (MISO) wiretap channels. Both the cases of direct transmission and cooperative jamming with a helper are investigated with imperfect channel state information (CSI) for the eavesdropper links. Robust transmit covariance matrices are obtained based on worst-case secrecy rate maximization, under both individual and global power constraints. For the case of an individual power constraint, we show that the nonconvex maximin optimization problem can be transformed into a quasi-convex problem that can be efficiently solved with existing methods. For a global power constraint, the joint optimization of the transmit covariance matrices and power allocation between the source and the helper is studied. We also investigate the robust wiretap transmission problem for the case with a quality-of-service constraint at the legitimate receiver. Numerical results show the advantage of the proposed robust design. In particular, for the global power constraint scenario, although cooperative jamming is not necessary for optimal transmission with perfect eavesdroppers CSI, we show that robust jamming support can increase the worst-case secrecy rate and lower the signal to interference-plus-noise ratio at the eavesdropper in the presence of channel mismatches between the transmitters and the eavesdropper.

Spatial signature estimation for uniform linear arrays with unknown receiver gains and phases

The problem of spatial signature estimation using a uniform linear array (ULA) with unknown receiver gain and phase responses is studied. Sufficient conditions for identifying the spatial signatures are derived, and a closed-form ESPRIT-like estimator is proposed. The performance of the method is investigated by means of simulations and on experimental data collected with an antenna array in a suburban environment. The results show that the absence of receiver calibration is not critical for uplink signal waveform estimation using a plane wave model.

Performance of space-time modulation for a generalized time-varying Rician channel model

We analyze the performance of trained and differential space-time modulation for channels with a constant specular component and time-varying diffuse fading. We examine the case where the channel varies from sample to sample within a space-time symbol matrix according to a first-order time-varying model. We show that the effect of the time-varying diffuse channel can be described by an effective signal-to-noise ratio (SNR) that decreases with time. We derive pairwise probability of error expressions based on these effective SNR values that accurately describe performance for unitary modulation. We quantify the significant advantage that differential modulation provides at high SNR where the effect of the time-varying channel dominates. At low SNR where additive noise dominates, we note that trained modulation with perfect channel state information provides a 3-dB advantage over differential modulation, but decoding based on a maximum likelihood channel estimate yields worse performance than differential modulation at all SNR values. Simulation results are provided to support our analysis.

Effective SNR for space-time modulation over a time-varying Rician channel

Rapid temporal variations in wireless channels pose a significant challenge for space-time modulation and coding algorithms. This letter examines the performance degradation that results when time-varying flat fading is encountered when using trained and unitary space-time modulation. Performance is characterized for a channel having a constant specular component plus a time-varying diffuse component. A first-order autoregressive (AR) model is used to characterize diffuse channel coefficients that vary from symbol to symbol, and is shown to lead to an effective signal-to-noise ratio (SNR) that decreases with time. Differential modulation is shown to have an advantage in effective SNR over trained unitary modulation at high power. Simulation results are provided to support our analysis.

Some experiments with array data collected in actual urban and suburban environments

We compare the performance of several algorithms for signal separation based on actual mobile cellular radio data. The data were collected by base stations in two different environments: using an eight element linear array on a hillside overlooking a suburban area, and using a four element square array at the top of a ten story building in a dense urban area. Calibration data were available for one of the arrays used for the suburban data, allowing for performance comparisons between DOA-based and blind signal separators. Experiments were conducted with three different types of signal waveforms: sinewaves, simple FM waveforms, and /spl pi//4-DQPSK signals, each of which necessitated the use of a different performance metric. We focus on the results obtained for cases where the data were approximately low rank, with little delay spread (although not all data sets from the urban environment were of this type).