Vasanthan Raghavan

Maximizing MIMO Capacity in Sparse Multipath With Reconfigurable Antenna Arrays

Emerging advances in reconfigurable radio-frequency (RF) front-ends and antenna arrays are enabling new physical modes for accessing the radio spectrum that extend and complement the notion of waveform diversity in wireless communication systems. However, theory and methods for exploiting the potential of reconfigurable RF front-ends are not fully developed. In this paper, we study the impact of reconfigurable antenna arrays on maximizing the capacity of multiple input multiple output (MIMO) wireless communication links in sparse multipath environments. There is growing experimental evidence that physical wireless channels exhibit a sparse multipath structure, even at relatively low antenna dimensions. We propose a model for sparse multipath channels and show that sparse channels afford a new dimension over which capacity can be optimized: the distribution or configuration of the sparse statistically independent degrees of freedom (DoF) in the available spatial signal space dimensions. Our results show that the configuration of the sparse DoF has a profound impact on capacity and also characterize the optimal capacity-maximizing channel configuration at any operating SNR. We then develop a framework for realizing the optimal channel configuration at any SNR by systematically adapting the antenna spacings at the transmitter and the receiver to the level of sparsity in the physical multipath environment. Surprisingly, three canonical array configurations are sufficient for near-optimum performance over the entire SNR range. In a sparse scattering environment with randomly distributed paths, the capacity gain due to the optimal configuration is directly proportional to the number of antennas. Numerical results based on a realistic physical model are presented to illustrate the implications of our framework

Capacity scaling and spectral efficiency in wide-band correlated MIMO channels

The dramatic linear increase in ergodic capacity with the number of antennas promised by multiple-input multiple-output (MIMO) wireless communication systems is based on idealized channel models representing a rich scattering environment. Is such scaling sustainable in realistic scattering scenarios? Existing physical models, although realistic, are intractable for addressing this problem analytically due to their complicated nonlinear dependence on propagation path parameters, such as the angles of arrival and delays. In this paper, we leverage a recently introduced virtual representation of physical models that is essentially a Fourier series representation of wide-band MIMO channels in terms of fixed virtual angles and delays. Motivated by physical considerations, we propose a D-connected model for correlated channels defined by a virtual spatial channel matrix consisting of D nonvanishing diagonals with independent and identically distributed (i.i.d.) Gaussian entries. The parameter D provides a meaningful and tractable measure of the richness of scattering. We derive general bounds for the coherent ergodic capacity and investigate capacity scaling with the number of antennas and bandwidth. In the large antenna regime, we show that linear capacity scaling is possible if D scales linearly with the number of antennas. This, in turn, is possible if the number of resolvable paths grows quadratically with the number of antennas. The capacity saturates for linear growth in the number of paths (fixed D). The ergodic capacity does not depend on frequency selectivity of the channel in the wide-band case. Increasing bandwidth tightens the bounds and hastens the convergence of scaling behavior. For large bandwidth, the capacity scales linearly with the signal-to-noise ratio (SNR) as well. We also provide an explicit characterization of the wide-band slope recently proposed by Verdu. Numerical results are presented to illustrate the key theoretical results.

Capacity of Sparse Multipath Channels in the Ultra-Wideband Regime

This paper studies the ergodic capacity of time-and frequency-selective multipath fading channels in the ultrawide-band (UWB) regime when training signals are used for channel estimation at the receiver. Motivated by recent measurement results on UWB channels, we propose a model for sparse multipath channels. A key implication of sparsity is that the independent degrees of freedom in the channel scale sublinearly with the signal space dimension (product of signaling duration and bandwidth). Sparsity is captured by the number of resolvable paths in delay and Doppler. Our analysis is based on a training and communication scheme that employs signaling over orthogonal short-time Fourier (STF) basis functions. STF signaling naturally relates sparsity in delay-Doppler to coherence in time and frequency. We study the impact of multipath sparsity on two fundamental metrics of spectral efficiency in the wideband/low-SNR limit introduced by Verdu: first- and second-order optimality conditions. Recent results by Zheng et al. have underscored the large gap in spectral efficiency between coherent and noncoherent extremes and the importance of channel learning in bridging the gap. Building on these results, our results lead to the following implications of multipath sparsity: (1) the coherence requirements are shared in both time and frequency, thereby significantly relaxing the required scaling in coherence time with SNR; (2) sparse multipath channels are asymptotically coherent - for a given but large bandwidth, the channel can be learned perfectly and the coherence requirements for first- and second-order optimality met through sufficiently large signaling duration; and (3) the requirement of peaky signals in attaining capacity is eliminated or relaxed in sparse environments.

Sublinear Capacity Scaling Laws for Sparse MIMO Channels

Recent attention on performance analysis of single-user multiple-input-multiple-output (MIMO) systems has been on understanding the impact of the spatial correlation model on ergodic capacity. In most of these works, it is assumed that the statistical degrees of freedom (DoF) in the channel can be captured by decomposing it along a suitable eigenbasis and that the transmitter has perfect knowledge of the statistical DoF. With an increased interest in large-antenna systems in state-of-the-art technologies, these implicit channel modeling assumptions in the literature have to be revisited. In particular, multiantenna measurements have showed that large-antenna systems are sparse where only a few DoF are dominant enough to contribute towards capacity. Thus, in this work, it is assumed that the transmitter can only afford to learn the dominant statistical DoF in the channel. The focus is on understanding ergodic capacity scaling laws in sparse channels. Unlike classical results, where linear capacity scaling is implicit, sparsity of MIMO channels coupled with a knowledge of only the dominant DoF is shown to result in a new paradigm of sublinear capacity scaling that is consistent with experimental results and physical arguments. It is also shown that uniform-power signaling over all the antenna dimensions is wasteful and could result in a significant penalty over optimally adapting the antenna spacings in response to the sparsity level of the channel and transmit SNR.

Beamforming Tradeoffs for Initial UE Discovery in Millimeter-Wave MIMO Systems

Millimeter-wave (mmW) multi-input multi-output (MIMO) systems have gained increasing traction toward the goal of meeting the high data-rate requirements in next-generation wireless systems. The focus of this work is on low-complexity beamforming approaches for initial user equipment (UE) discovery in such systems. Toward this goal, we first note the structure of the optimal beamformer with per-antenna gain and phase control and establish the structure of good beamformers with per-antenna phase-only control. Learning these right singular vector (RSV)type beamforming structures in mmW systems is fraught with considerable complexities such as the need for a non-broadcast system design, the sensitivity of the beamformer approximants to small path length changes, inefficiencies due to power amplifier backoff, etc. To overcome these issues, we establish a physical interpretation between the RSV-type beamformer structures and the angles of departure/arrival (AoD/AoA) of the dominant path(s) capturing the scattering environment. This physical interpretation provides a theoretical underpinning to the emerging interest on directional beamforming approaches that are less sensitive to small path length changes. While classical approaches for direction learning such as MUltiple SIgnal Classification (MUSIC) have been well-understood, they suffer from many practical difficulties in a mmW context such as a non-broadcast system design and high computational complexity. A simpler broadcast-based solution for mmW systems is the adaptation of limited feedback-type directional codebooks for beamforming at the two ends. We establish fundamental limits for the best beam broadening codebooks and propose a construction motivated by a virtual subarray architecture that is within a couple of dB of the best tradeoff curve at all useful beam broadening factors. We finally provide the received SNR loss-UE discovery latency tradeoff with the proposed beam broadening constructions. Our results show that users with a reasonable link margin can be quickly discovered by the proposed design with a smooth roll-off in performance as the link margin deteriorates. While these designs are poorer in performance than the RSV learning approaches or MUSIC for cell-edge users, their low-complexity that leads to a broadcast system design makes them a useful candidate for practical mmW systems.

Statistical Beamforming on the Grassmann Manifold for the Two-User Broadcast Channel

A Rayleigh fading spatially correlated broadcast setting with M = 2 antennas at the transmitter and two users (each with a single antenna) is considered. It is assumed that the users have perfect channel information about their links, whereas the transmitter has only statistical information of each users link (covariance matrix of the vector channel). A low-complexity linear beamforming strategy that allocates equal power and one spatial eigenmode to each user is employed at the transmitter. Beamforming vectors on the Grassmann manifold that depend only on statistical information are to be designed at the transmitter to maximize the ergodic sum-rate delivered to the two users. Toward this goal, the beamforming vectors are first fixed and a closed-form expression is obtained for the ergodic sum-rate in terms of the covariance matrices of the links. This expression is nonconvex in the beamforming vectors ensuring that the classical Lagrange multiplier technique is not applicable. Despite this difficulty, the optimal solution to this problem is shown to be the same as the solution to the maximization of an appropriately defined average signal-to-interference and noise ratio metric for each user. This solution is the dominant generalized eigenvector of a pair of positive-definite matrices where the first matrix is the covariance matrix of the forward link and the second is an appropriately designed “effective” interference covariance matrix. In this sense, our work is a generalization of optimal signalling along the dominant eigenmode of the transmit covariance matrix in the single-user case. Finally, the ergodic sum-rate for the general broadcast setting with M antennas at the transmitter and M-users (each with a single antenna) is obtained in terms of the covariance matrices of the links and the beamforming vectors.

Why Does the Kronecker Model Result in Misleading Capacity Estimates

Many recent works that study the performance of multiple-input-multiple-output (MIMO) systems in practice assume a Kronecker model where the variances of the channel entries, upon decomposition on to the transmit and the receive eigenbases, admit a separable form. Measurement campaigns, however, show that the Kronecker model results in poor estimates for capacity. Motivated by these observations, a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better. In this paper, we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates, the transmit and/or the receive eigenbases. Using tools from random matrix theory, we then establish the theoretical basis behind the Kronecker mismatch at the low-and the high-SNR extremes: 1) sparsity of the dominant statistical degrees of freedom (DoF) in the true channel at the low- SNR extreme, and 2) nonregularity of the sparsity structure (disparities in the distribution of the DoF across the rows and the columns) at the high-SNR extreme.

Quickest Change Detection of a Markov Process Across a Sensor Array

Recent attention in quickest change detection in the multisensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption. In this work, a more general scenario is considered where the change propagates across the sensors, and its propagation can be modeled as a Markov process. A centralized, Bayesian version of this problem is considered, with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process. The problem of minimizing the average detection delay subject to false alarm constraints is formulated in a dynamic programming framework. Insights into the structure of the optimal stopping rule are presented. In the limiting case of rare disruptions, it is shown that the structure of the optimal test reduces to thresholding the a posteriori probability of the hypothesis that no change has happened. Under a certain condition on the Kullback-Leibler (K-L) divergence between the post- and the pre-change densities, it is established that the threshold test is asymptotically optimal (in the vanishing false alarm probability regime). It is shown via numerical studies that this low-complexity threshold test results in a substantial improvement in performance over naive tests such as a single-sensor test or a test that incorrectly assumes that the change propagates instantaneously.

Capacity of space-time wireless channels: a physical perspective

Existing results on MIMO channel capacity assume a rich scattering environment in which the channel power scales quadratically with the number of antennas, resulting in linear capacity scaling with the number of antennas. However, such scaling in channel power is physically impossible indefinitely. We thus address the following fundamental question: for a given channel power scaling law, what is the best achievable capacity scaling law? For a channel power scaling, /spl rho//sub c/(N) = O(N/sup /spl gamma//), /spl gamma/ /spl isin/ (0,2], we argue that the channel capacity cannot scale faster than C(N) = O(/spl radic/(/spl rho//sub c/(N))) = O(N/sup /spl gamma//2/). Our approach is based on a family of space-time channels corresponding to different distributions of channel power in the spatial signal space dimensions. We develop the concept of an ideal MIMO channel that achieves the optimal scaling law for a given /spl rho//sub c/(N). For a given number of antennas, unlike existing results that either emphasize the low or high SNR regimes, we propose a methodology for capacity-optimal signaling at any SNR. The methodology is based on creating the ideal channel from any given physical scattering environment via adaptive-resolution array configurations.

Semiunitary Precoding for Spatially Correlated MIMO Channels

The focus of this paper is on spatial precoding in correlated multiantenna channels where the number of data-streams is adapted independent of the number of transmit antennas. Towards the goal of a low-complexity implementation, a statistical semiunitary precoder is studied where the precoder matrix evolves fairly slowly with respect to the channel evolution. While prior work on statistical precoding has focussed on information-theoretic limits, most of these computations result in complicated functional dependencies of the mutual information with the channel statistics that do not explicitly reveal the impact of statistics on performance. In contrast, estimates that are directly in terms of the channel statistics are obtained here for the relative mutual information loss of a semiunitary precoder with respect to a perfect channel information benchmark. Based on these estimates, matching metrics are developed that capture the degree of matching of a channel to the precoder structure continuously and allow ordering two matrix channels in terms of their mutual information performance. While these metrics are based on bounds, numerical studies are used to show that the proposed metrics capture the performance tradeoffs accurately. The main conclusion of this work is a simple-to-state fundamental principle in the context of signaling design for single-user MIMO systems: the best channel for the statistical precoder is the channel that is matched to it.