Ramy H. Gohary

Noncoherent MIMO Communication: Grassmannian Constellations and Efficient Detection

This paper considers the design of both a transmitter and a receiver for noncoherent communication over a frequency-flat, richly scattered multiple-input multiple-output (MIMO) channel. The design is guided by the fact that at high signal-to-noise ratios (SNRs), the ergodic capacity of the channel can be achieved by input signals that are isotropically distributed on the (compact) Grassmann manifold. The first part of the paper considers the design of Grassmannian constellations that MIMIC the isotropic distribution. A subspace perturbation analysis is used to determine an appropriate metric for the distance between Grassmannian constellation points, and using this metric, greedy, direct and rotation-based techniques for designing constellations are proposed. These techniques offer different tradeoffs between the minimum distance of the constellation and the design complexity. In addition, the rotation-based technique results in constellations that have lower storage requirements and admit a natural ldquoquasi-set-partitioningrdquo binary labeling.

Optimal Tradeoff Between Sum-Rate Efficiency and Jain's Fairness Index in Resource Allocation

The focus of this paper is on studying the tradeoff between the sum efficiency and Jains fairness index in general resource allocation problems. Such problems are frequently encountered in wireless communication systems with M users. Among the commonly-used methods to approach these problems is the one based on the α-fair policy. Analyzing this policy, it is shown that it does not necessarily achieve the optimal Efficiency-Jain tradeoff (EJT) except for the case of M=2 users. When the number of users M>2, it is shown that the gap between the efficiency achieved by the α-fair policy and that achieved by the optimal EJT policy for the same Jains index can be unbounded. Finding the optimal EJT corresponds to solving a family of potentially difficult non-convex optimization problems. To alleviate this difficulty, we derive sufficient conditions which are shown to be sharp and naturally satisfied in various radio resource allocation problems. These conditions provide us with a means for identifying cases in which finding the optimal EJT and the rate vectors that achieve it can be reformulated as convex optimization problems. The new formulations are used to devise computationally-efficient resource schedulers that enable the optimal EJT to be achieved for both quasi-static and ergodic time-varying communication scenarios. Analytical findings are confirmed by numerical examples.

Robust IWFA for Open-Spectrum Communications

This correspondence considers a wireless open-spectrum communication system with N orthogonal narrowband tones and K users who compete to maximize their individual data rates. The correspondence proposes a robust version of the iterative water-filling algorithm (IWFA) that takes into account potential inaccuracies in the noise-plus-interference levels available at the transmitters. It is shown that, in comparison with the conventional version, the robust IWFA (RIWFA) can lead the users to behave in a less greedy fashion and to collaborate unintentionally in order to increase the network sum-rate. In particular, using an appropriately chosen RIWFA parameter, we show that RIWFA yields almost the same sum-rate as price-based IWFA (PIWFA) which requires collaboration of users.

Design of linear dispersion codes: asymptotic guidelines and their implementation

In this paper, a design method is developed for the class of linear-dispersion (LD) codes - a diverse set of space-time codes that subsumes several standard designs. The development begins by showing that for systems that employ a large number of transmit antennas, LD codes constructed from unitary coding matrices are asymptotically optimum from different design perspectives, viz., minimum mean square error (MMSE), mutual information, and average pairwise error probability (PEP). Those measures have a direct impact on the detection complexity, data rate, and error performance that a space-time code can achieve. Using the insight generated by the asymptotic result, a structured design technique for the LD coding matrices, that suits a broad class of configurations is provided. The resulting codes can support high data rates and provide performance advantages over current designs when decoded with a standard detector. Based on the asymptotic results, a row interleaving scheme is proposed, and it is shown to result in significant performance enhancement.

Noncoherent MIMO communication: Grassmannian constellations and efficient detection

We propose a greedy algorithm for designing Grassmannian constellations that mimic the distribution that achieves the high SNR capacity of a noncoherent MIMO fading channel. We also introduce a reduced complexity suboptimum detector whose performance is comparable to that of the optimal detector.

Optimal tradeoff between efficiency and Jain's fairness index in resource allocation

In this paper, we study tradeoff policies between efficiency and the Jains fairness index of the benefits received by M users in general resource allocation scenarios. Analyzing the commonly-used α-fair tradeoff policy, it is shown that, except for the case of M =2 users, this policy does not necessarily achieve the optimal Efficiency-Jain tradeoff. In particular, it is shown that, when the number of users M >;2, the gap between the efficiency achieved by the α-fair and the optimal Efficiency-Jain tradeoff policy can be unbounded, for the same Jains index. Finding the optimal Efficiency-Jain tradeoff for arbitrary set of admissible benefits is generally difficult. To alleviate this difficulty, we derive sufficient conditions, which, when satisfied by the set of admissible benefits, lead to efficiently computable optimal tradeoff and benefit vectors. Numerical results for a typical communication network scenario are provided to confirm analytical findings.

Coordinated Port Selection and Beam Steering Optimization in a Multi-Cell Distributed Antenna System using Semidefinite Relaxation

In this paper, we consider coordinated downlink transmission in a cellular system wherein each base station (BS) has multiple geographically dispersed antenna ports. Each port uses a fixed transmit power and the goal of the BSs is to collectively determine the subset of ports and the corresponding beam steering coefficients that maximize the minimum signal-to-interference-plus-noise ratio observed by the user terminals. This problem is NP-hard. To circumvent this difficulty, a two-stage polynomial-complexity technique that relies on semidefinite relaxation and Gaussian randomization is developed. It is shown that, for the considered scenarios, the port state vectors and beam steering coefficients generated by the proposed technique yield a performance comparable to that yielded by exhaustive search, but with a significantly less computational complexity. It is also shown that the proposed technique results in significant power savings when compared with other transmission strategies proposed in the literature.

On rate-optimal MIMO signalling with mean and covariance feedback

We consider a single-user multiple-input multiple-output (MIMO) communication system in which the transmitter has access to both the channel covariance and the channel mean. For this scenario, we provide an explicit second-order approximation of the ergodic capacity of the channel, and we use this approximation to show that when the channel has a non-zero mean, the basis of the optimal input covariance matrix depends on the input signal power. (This basis is independent of the signal power in the zero-mean case.) The second-order approximation also provides insight into the way in which the low-signal-to-noise-ratio (SNR) optimal input covariance matrix is related to the optimal input covariance matrix at arbitrary SNRs. Furthermore, we show that the design of the input covariance matrix that optimizes the second-order approximation can be cast as a convex optimization problem for which the Karush-Kuhn-Tucker (KKT) conditions completely characterize the optimal solution. Using these conditions, we provide an efficient algorithm for obtaining second-order optimal input covariance matrices. The resulting covariances confirm our theoretical observation that, in general, the low-SNR optimal signal basis does not coincide with the optimal basis at higher SNRs. Finally, we show how our second-order design algorithm can be used to efficiently obtain input covariance matrices that provide ergodic rates that approach the ergodic capacity of the system.

On efficient non-coherent detection of Grassmannian constellations

In this paper we derive analytic expressions for the boundaries of the search region of a recently proposed efficient detector for non-coherent reception of Grassmannian constellations. These boundaries are designed to ensure that the restriction of the detection search space to the enclosed region does not incur significant performance degradation. In addition, we show that the cardinality of the set of candidate constellation points, that is the number of constellation points that lie within the search space, approaches one at least as fast as the inverse of the square root of the received signal SNR

Design of linear dispersion codes: some asymptotic guidelines and their implementation

The family of linear dispersion (LD) codes is a diverse set of space-time block codes that subsumes several standard designs. In this paper, we provide a design technique for LD codes that generates codes which enable large capacities and perform well when decoded with a standard suboptimal detector. Our design technique is motivated by the observation that for an independent Rayleigh fading channel, as the number of transmit antennas grows, LD codes with a certain orthogonal structure simultaneously approach a maximized upper bound on the capacity, and a minimized lower bound on a certain mean square error performance measure. Using this asymptotic result as a guide, we impose the orthogonal structure on finite sized codes and optimize the resulting system. Imposing this structure significantly simplifies the design procedure, and as we demonstrate via simulation, leads to codes that perform well in practice. Using insight generated by our study of the asymptotic properties of LD codes, we also propose a row interleaving scheme which is shown to result in significant performance enhancement.