Omar Mehanna

Feasible Point Pursuit and Successive Approximation of Non-Convex QCQPs

Quadratically constrained quadratic programs (QCQPs) have a wide range of applications in signal processing and wireless communications. Non-convex QCQPs are NP-hard in general. Existing approaches relax the non-convexity using semi-definite relaxation (SDR) or linearize the non-convex part and solve the resulting convex problem. However, these techniques are seldom successful in even obtaining a feasible solution when the QCQP matrices are indefinite. In this letter, a new feasible point pursuit successive convex approximation (FPP-SCA) algorithm is proposed for non-convex QCQPs. FPP-SCA linearizes the non-convex parts of the problem as conventional SCA does, but adds slack variables to sustain feasibility, and a penalty to ensure slacks are sparingly used. When FPP-SCA is successful in identifying a feasible point of the non-convex QCQP, convergence to a Karush-Kuhn-Tucker (KKT) point is thereafter ensured. Simulations show the effectiveness of our proposed algorithm in obtaining feasible and near-optimal solutions, significantly outperforming existing approaches.

Joint Multicast Beamforming and Antenna Selection

Multicast beamforming exploits subscriber channel state information at the base station to steer the transmission power towards the subscribers, while minimizing interference to other users and systems. Such functionality has been provisioned in the long-term evolution (LTE) enhanced multimedia broadcast multicast service (EMBMS). As antennas become smaller and cheaper relative to up-conversion chains, transmit antenna selection at the base station becomes increasingly appealing in this context. This paper addresses the problem of joint multicast beamforming and antenna selection for multiple co-channel multicast groups. Whereas this problem (and even plain multicast beamforming) is NP-hard, it is shown that the mixed l1,∞-norm squared is a prudent group-sparsity inducing convex regularization, in that it naturally yields a suitable semidefinite relaxation, which is further shown to be the Lagrange bi-dual of the original NP-hard problem. Careful simulations indicate that the proposed algorithm significantly reduces the number of antennas required to meet prescribed service levels, at relatively small excess transmission power. Furthermore, its performance is close to that attained by exhaustive search, at far lower complexity. Extensions to max-min-fair, robust, and capacity-achieving designs are also considered.

Frugal Sensing: Wideband Power Spectrum Sensing From Few Bits

Wideband spectrum sensing is a key requirement for cognitive radio access. It now appears increasingly likely that spectrum sensing will be performed using networks of sensors, or crowd-sourced to handheld mobile devices. Here, a network sensing scenario is considered, where scattered low-end sensors filter and measure the average signal power across a band of interest, and each sensor communicates a single bit (or coarsely quantized level) to a fusion center, depending on whether its measurement is above a certain threshold. The focus is on the underdetermined case, where relatively few bits are available at the fusion center. Exploiting non-negativity and the linear relationship between the power spectrum and the autocorrelation, it is shown that adequate power spectrum sensing is possible from few bits, even for dense spectra. The formulation can be viewed as generalizing classical nonparametric power spectrum estimation to the case where the data is in the form of inequalities, rather than equalities.

Channel Tracking and Transmit Beamforming With Frugal Feedback

Channel state feedback is a serious burden that limits deployment of transmit beamforming systems with many antennas in frequency-division duplex (FDD) mode. Transmit beamforming with limited feedback systems estimate the channel at the receiver and send quantized channel state or beamformer information to the transmitter. A different approach that exploits the spatio-temporal correlation of the channel is proposed here. The transmitter periodically sends a beamformed pilot signal in the downlink, while the receiver quantizes the corresponding received signal and feeds back the bits to the transmitter. Assuming an autoregressive (AR) channel model, Kalman filtering (KF) based on the sign of innovations (SOI) is proposed for channel tracking, and closed-form expressions for the channel estimation mean-squared error (MSE) are derived under certain conditions. For more general channel models, a novel tracking approach is proposed that exploits the quantization bits in a maximum a posteriori (MAP) formulation. Simulations show that close to optimum performance can be attained with only 2 bits per channel dwell time block, even for systems with many transmit antennas. This clears a hurdle for transmit beamforming with many antennas in FDD mode-which was almost impossible with the prior state-of-art.

Multicast beamforming with antenna selection

Multicast beamforming exploits subscriber channel state information at the base station to form multiple beams that steer radiated power towards users of interest, while minimizing leakage to other users and systems. Such functionality has been provisioned in the long-term evolution (LTE) enhanced multimedia broadcast multicast service (EMBMS). In this context, the present paper deals with joint multicast beamforming and antenna selection. Whereas this problem (and even plain multicast beamforming) is NP-hard, it is shown that using ℓ1-norm squared (instead of ℓ1-norm) as a surrogate for the ℓ0-norm yields a natural semidefinite programming relaxation - something not obvious with the ℓ1-norm. Simulations indicate that the proposed algorithm significantly reduces the number of antennas required to meet prescribed service levels, at a relatively small cost of excess transmission power. Furthermore, its performance is close to that attained by exhaustive search, at far lower complexity.

Parametric Frugal Sensing of Power Spectra for Moving Average Models

Wideband spectrum sensing is a fundamental component of cognitive radio and other applications. A novel frugal sensing scheme was recently proposed as a means of crowdsourcing the task of spectrum sensing. Using a network of scattered low-end sensors transmitting randomly filtered power measurement bits to a fusion center, a non-parametric approach to spectral estimation was adopted to estimate the ambient power spectrum. Here, a parametric spectral estimation approach is considered within the context of frugal sensing. Assuming a Moving-Average (MA) representation for the signal of interest, the problem of estimating admissible MA parameters, and thus the MA power spectrum, from single bit quantized data is formulated. This turns out being a non-convex quadratically constrained quadratic program (QCQP), which is NP-Hard in general. Approximate solutions can be obtained via semi-definite relaxation (SDR) followed by randomization; but this rarely produces a feasible solution for this particular kind of QCQP. A new Sequential Parametric Convex Approximation (SPCA) method is proposed for this purpose, which can be initialized from an infeasible starting point, and yet still produce a feasible point for the QCQP, when one exists, with high probability. Simulations not only reveal the superior performance of the parametric techniques over the globally optimum solutions obtained from the non-parametric formulation, but also the better performance of the SPCA algorithm over the SDR technique.

Maximum Likelihood Passive and Active Sensing of Wideband Power Spectra From Few Bits

Wideband power spectrum sensing is essential for cognitive radio and many other applications. Aiming to crowdsource spectrum sensing operations, a novel frugal sensing framework was recently proposed, employing a network of low duty-cycle sensors (e.g., running in background mode on consumer devices) reporting randomly filtered broadband power measurement bits to a fusion center, which in turn estimates the ambient power spectrum. Frugal sensing is revisited here from a statistical estimation point of view. Taking into account fading and insufficient sample averaging considerations, maximum likelihood (ML) formulations are developed which outperform the original minimum power and interior point solutions when the soft power estimates prior to thresholding are noisy. Assuming availability of a downlink channel that the fusion center can use to send threshold information, active sensing strategies are developed that quickly narrow down and track the power spectrum estimate, using ideas borrowed from cutting plane methods to develop active ML solutions. Simulations show that satisfactory wideband power spectrum estimates can be obtained with passive ML sensing from few bits, and much better performance can be attained using active sensing. Various other aspects, such as known emitter spectral shapes and different types of non-negativity constraints, are also considered.

On achievable rates of the two-user symmetric Gaussian interference channel

We study the Han-Kobayashi (HK) achievable sum rate for the two-user symmetric Gaussian interference channel. We find the optimal power split ratio between the common and private messages (assuming no time-sharing), and derive a closed form expression for the corresponding sum rate. This provides a finer understanding of the achievable HK sum rate, and allows for precise comparisons between this sum rate and that of orthogonal signaling. One surprising finding is that despite the fact that the channel is symmetric, allowing for asymmetric power split ratio at both users (i.e., asymmetric rates) can improve the sum rate significantly. Considering the high SNR regime, we specify the interference channel value above which the sum rate achieved using asymmetric power splitting outperforms the symmetric case.

Line spectrum estimation from broadband power detection bits

Line spectrum estimation from analog signal samples is a classic problem with numerous applications. However, sending analog or finely quantized signal sample streams to a fusion center is a burden in distributed sensing scenarios. Instead, it is appealing to estimate the frequency lines from a few randomly filtered broadband power measurement bits taken using a network of cheap sensors. This leads to a new problem: line spectrum estimation from inequalities. Three different techniques are proposed for this estimation task. In the first two, the autocorrelation function is first estimated nonparametrically, then a parametric method is used to estimate the sought frequencies. The third is a direct maximum likelihood (ML) parameter estimation approach that uses coordinate descent. Simulations show that the underlying frequencies can be accurately estimated using the proposed techniques, even from relatively few bits; and that the ML estimates obtained with the third technique can meet the Cramer-Rao lower bound (also derived here), when the number of sensors is sufficiently large.

Frugal channel tracking for transmit beamforming

Channel state feedback is a serious burden for transmit beamforming systems with many antennas in FDD mode. Instead of estimating the channel at the receiver and feeding back quantized beamformer information, a different approach that exploits the spatio-temporal correlation of the channel is proposed. The transmitter periodically sends a beamformed pilot signal, while the receiver feeds back the quantized innovation derived from either a Kalman filtering or a MAP tracking loop. Simulations show that close to optimum performance can be attained with only 2 bits per channel dwell, clearing a hurdle for transmit beamforming with many antennas in FDD mode.