Miguel Angel Lagunas

Joint Tx-Rx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization

This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multiple-input multiple-output (MIMO) channels under a variety of design criteria. Instead of considering each design criterion in a separate way, we generalize the existing results by developing a unified framework based on considering two families of objective functions that embrace most reasonable criteria to design a communication system: Schur-concave and Schur-convex functions. Once the optimal structure of the transmit-receive processing is known, the design problem simplifies and can be formulated within the powerful framework of convex optimization theory, in which a great number of interesting design criteria can be easily accommodated and efficiently solved, even though closed-form expressions may not exist. From this perspective, we analyze a variety of design criteria, and in particular, we derive optimal beamvectors in the sense of having minimum average bit error rate (BER). Additional constraints on the peak-to-average ratio (PAR) or on the signal dynamic range are easily included in the design. We propose two multilevel water-filling practical solutions that perform very close to the optimal in terms of average BER with a low implementation complexity. If cooperation among the processing operating at different carriers is allowed, the performance improves significantly. Interestingly, with carrier cooperation, it turns out that the exact optimal solution in terms of average BER can be obtained in closed form.

A robust maximin approach for MIMO communications with imperfect channel state information based on convex optimization

This paper considers a wireless communication system with multiple transmit and receive antennas, i.e., a multiple-input-multiple-output (MIMO) channel. The objective is to design the transmitter according to an imperfect channel estimate, where the errors are explicitly taken into account to obtain a robust design under the maximin or worst case philosophy. The robust transmission scheme is composed of an orthogonal space-time block code (OSTBC), whose outputs are transmitted through the eigenmodes of the channel estimate with an appropriate power allocation among them. At the receiver, the signal is detected assuming a perfect channel knowledge. The optimization problem corresponding to the design of the power allocation among the estimated eigenmodes, whose goal is the maximization of the signal-to-noise ratio (SNR), is transformed to a simple convex problem that can be easily solved. Different sources of errors are considered in the channel estimate, such as the Gaussian noise from the estimation process and the errors from the quantization of the channel estimate, among others. For the case of Gaussian noise, the robust power allocation admits a closed-form expression. Finally, the benefits of the proposed design are evaluated and compared with the pure OSTBC and nonrobust approaches.

Optimum linear joint transmit-receive processing for MIMO channels with QoS constraints

This paper considers vector communications through multiple-input multiple-output (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmit-receive processing (also termed linear precoder at the transmitter and linear equalizer at the receiver) is designed to satisfy the QoS constraints with minimum transmitted power (the exact conditions under which the problem becomes unfeasible are given). Although the original problem is a complicated nonconvex problem with matrix-valued variables, with the aid of majorization theory, we reformulate it as a simple convex optimization problem with scalar variables. We then propose a practical and efficient multilevel water-filling algorithm to optimally solve the problem for the general case of different QoS requirements. The optimal transmit-receive processing is shown to diagonalize the channel matrix only after a very specific prerotation of the data symbols. For situations in which the resulting transmit power is too large, we give the precise way to relax the QoS constraints in order to reduce the required power based on a perturbation analysis. We also propose a robust design under channel estimation errors that has an important interest for practical systems. Numerical results from simulations are given to support the mathematical development of the problem.

Finite sample size effect on minimum variance beamformers: optimum diagonal loading factor for large arrays

Minimum variance beamformers are usually complemented with diagonal loading techniques in order to provide robustness against several impairments such as imprecise knowledge of the steering vector or finite sample size effects. This paper concentrates on this last application of diagonal loading techniques, i.e., it is assumed that the steering vector is perfectly known and that diagonal loading is used to alleviate the finite sample size impairments. The analysis herein is asymptotic in the sense that it is assumed that both the number of antennas and the number of samples are high but have the same order of magnitude. Borrowing some results of random matrix theory, the authors first derive a deterministic expression that describes the asymptotic signal-to-noise-plus-interference ratio (SINR) at the output of the diagonally loaded beamformer. Then, making use of the statistical theory of large observations (also known as general statistical analysis or G-analysis), the authors derive an estimator of the optimum loading factor that is consistent when both the number of antennas and the sample size increase without bound at the same rate. Because of that, the estimator has an excellent performance even in situations where the quotient between the number of observations is low relative to the number of elements of the array.

Modified Subspace Algorithms for DoA Estimation With Large Arrays

This paper proposes the use of a new generalized asymptotic paradigm in order to analyze the performance of subspace-based direction-of-arrival (DoA) estimation in array signal processing applications. Instead of assuming that the number of samples is high whereas the number of sensors/antennas remains fixed, the asymptotic situation analyzed herein assumes that both quantities tend to infinity at the same rate. This asymptotic situation provides a more accurate description of a potential situation where these two quantities are finite and hence comparable in magnitude. It is first shown that both MUSIC and SSMUSIC are inconsistent when the number of antennas/sensors increases without bound at the same rate as the sample size. This is done by analyzing and deriving closed-form expressions for the two corresponding asymptotic cost functions. By examining these asymptotic cost functions, one can establish the minimum number of samples per antenna needed to resolve closely spaced sources in this asymptotic regime. Next, two alternative estimators are constructed, that are strongly consistent in the new asymptotic situation, i.e., they provide consistent DoA estimates, not only when the number of snapshots goes to infinity, but also when the number of sensors/antennas increases without bound at the same rate. These estimators are inspired by the theory of G-estimation and are therefore referred to as G-MUSIC and G-SSMUSIC, respectively. Simulations show that the proposed algorithms outperform their traditional counterparts in finite sample-size situations, although they still present certain limitations.

Robust Power Allocation Designs for Multiuser and Multiantenna Downlink Communication Systems through Convex Optimization

In this paper, we study the design of the transmitter in the downlink of a multiuser and multiantenna wireless communications system, considering the realistic scenario where only an imperfect estimate of the actual channel is available at both communication ends. Precisely, the actual channel is assumed to be inside an uncertainty region around the channel estimate, which models the imperfections of the channel knowledge that may arise from, e.g., estimation Gaussian errors, quantization effects, or combinations of both sources of errors. In this context, our objective is to design a robust power allocation among the information symbols that are to be sent to the users such that the total transmitted power is minimized, while maintaining the necessary quality of service to obtain reliable communication links between the base station and the users for any possible realization of the actual channel inside the uncertainty region. This robust power allocation is obtained as the solution to a convex optimization problem, which, in general, can be numerically solved in a very efficient way, and even for a particular case of the uncertainty region, a quasi-closed form solution can be found. Finally, the goodness of the robust proposed transmission scheme is presented through numerical results. Robust designs, imperfect CSI, multiantenna systems, broadcast channel, convex optimization.

On power allocation strategies for maximum signal to noise and interference ratio in an OFDM-MIMO system

Orthogonal frequency division multiplexing (OFDM) has been recently established for several systems such as HiperLAN/2 and Digital video/audio broadcasting, due the easy implementation of the modulator/demodulator and the equalizer. Moreover, also increasing interest is currently being put on multiple-input multiple-output (MIMO) channels, based on the use of antenna arrays at both the transmitter and the receiver. Here, we propose two joint beamforming strategies of low computational load for systems combining OFDM and MIMO. The ultimate objective is the maximization of the signal-to-noise and interference ratio (SNIR) over the carriers subject to a total transmit power constraint. Specifically, the maximization of the harmonic SNIR mean and the minimum SNIR over the subcarriers are proposed. The asymptotic behavior of the proposed methods is analyzed to provide a complete comparative and general view of the most relevant and already known transmit power allocation strategies. Finally, a theoretical analysis of the performance degradation of these techniques is carried out for the case in which the channel state information (CSI) is not perfect. Monte Carlo simulation results for the system bit-error rate and performance degradation with imperfect CSI are provided.

Joint array combining and MLSE for single-user receivers in multipath Gaussian multiuser channels

The well-known structure of an array combiner along with a maximum likelihood sequence estimator (MLSE) receiver is the basis for the derivation of a space-time processor presenting good properties in terms of co-channel and intersymbol interference rejection. The use of spatial diversity at the receiver front-end together with a scalar MLSE implies a joint design of the spatial combiner and the impulse response for the sequence detector. This is faced using the MMSE criterion under the constraint that the desired user signal power is not cancelled, yielding an impulse response for the sequence detector that is matched to the channel and combiner response. The procedure maximizes the signal-to-noise ratio at the input of the detector and exhibits excellent performance in realistic multipath channels.

Correlation Matching Approach for Spectrum Sensing in Open Spectrum Communications

In the new paradigm of open spectrum access, the envisioned radio agility calls for fast and accurate spectrum sensing, this challenges traditional spectral estimation. In this study, we propose three new procedures that are able to sense the known spectrum of the candidate or primary user, fulfilling the requirements of open spectrum scenarios. These procedures are developed by following the framework of correlation matching, changing the traditional single frequency scan to a spectral scan with a particular shape and generalizing filter-bank designs. The proposed techniques are called Candidate methods, because their goal is to react only when the candidates spectral shape is present. First, Candidate-F is proposed as a spectral detection method, where this is based on minimizing the Frobenius distance between correlation matrices, and can be viewed as an extended version of the weighted overlapped spectrum averaging estimate. Next, Candidate-G is presented, which is a new procedure that is based on a geodesic distance, and that presents the lowest complexity. Lastly, a third procedure is studied, Candidate-M, which provides the most compliant performance with the demanding open spectrum scenario by generalizing the Capon-spectral estimator. By means of the analytical results, simulations of receiver operating characteristics, and estimation variance, this study shows the advantages of Candidate-M over the existing filter bank or cyclostationary detector methods.

Capacity results of spatially correlated frequency-selective MIMO channels in UMTS

Multi-input multi-output (MIMO) channels arising from the use of multi-element antenna (MEA) systems both in transmission and reception have been shown to support a considerable amount of bit rate. The information-theoretic capacity of such channels is severely affected by the spatial correlation. In this paper, we evaluate the ergodic and outage capacity of typical MIMO channels appearing in UMTS indoor scenarios. The frequency-selectivity and the spatial correlation of the MIMO channel are taken into account using realistic models obtained from field measurements performed within the IST project METRA (http://www.ist-metra.org). For capacity assessment, we use the transmission schemes considered by the 3GPP for UMTS. In particular, we analyze the cases of having and not having channel state information (CSI) at the transmitter, and also the case in which beamforming is used for transmission.