Tharaka Samarasinghe

Optimal Selective Feedback Policies for Opportunistic Beamforming

This paper studies the structure of downlink sum-rate maximizing selective decentralized feedback policies for opportunistic beamforming under finite feedback constraints on the average number of mobile users feeding back. First, it is shown that any sum-rate maximizing selective decentralized feedback policy must be a threshold feedback policy. This result holds for all fading channel models with continuous distribution functions. Second, the resulting optimum threshold selection problem is analyzed in detail. This is a nonconvex optimization problem over finite-dimensional Euclidean spaces. By utilizing the theory of majorization, an underlying Schur-concave structure in the sum-rate function is identified, and the sufficient conditions for the optimality of homogenous threshold feedback policies are obtained. Applications of these results are illustrated for well-known fading channel models such as Rayleigh, Nakagami, and Rician fading channels. Rather surprisingly, it is shown that using the same threshold value at all mobile users is not always a rate-wise optimal feedback strategy, even for a network in which mobile users experience statistically the same channel conditions. For the Rayleigh fading channel model, on the other hand, homogenous threshold feedback policies are proven to be rate-wise optimal if multiple orthonormal data carrying beams are used to communicate with multiple mobile users simultaneously.

The Feedback-Capacity Tradeoff for Opportunistic Beamforming

Optimum capacity scaling in the downlink of a single-cell multiple-input-multiple-output communication system can be achieved by a communication strategy called opportunistic beamforming in which information carrying beams are randomly formed and users are opportunistically scheduled based on their partial channel state information. Even though opportunistic beamforming reduces the amount of feedback required to achieve optimum capacity scaling laws, the number of users feeding back in its plain implementations still grows linearly with the total number of users in the system, which is an onerous requirement on the feedback channel. In this paper, we focus on a more stringent but realistic O(1) feedback constraint on the feedback channel, and obtain the tradeoff curve tracing the Pareto optimal boundary between feasible and infeasible feedback-rate pairs. We show that any point on this tradeoff curve can be obtained by means of homogeneous decentralized thresholding policies, in which a user feeds back only if the received signal quality at her best link is good enough, and derive the form of these optimum policies. We further show that if the O(1) feedback constraint is relaxed, we can achieve the optimum capacity scaling by a feedback amount growing like O(log n)^epsilon for any epsilon in (0,1), where n is the number of users in the system.

The feedback-capacity tradeoff for opportunistic beamforming under optimal user selection☆

Opportunistic beamforming is a reduced feedback communication strategy for vector broadcast channels which requires partial channel state information (CSI) at the base station for its operation. Although reducing feedback, this strategy in its plain implementations displays a linear growth in the feedback load with the total number of users in the system n, which is an onerous requirement for large systems. This paper focuses on a more stringent but realistic O(1) feedback constraint on the feedback load. Starting with a set of statistically identical users, we obtain the tradeoff curve tracing the Pareto optimal boundary between feasible and infeasible feedback-capacity pairs for opportunistic beamforming. Any point on this tradeoff curve can be obtained by means of homogeneous decentralized threshold feedback policies, which are rate-wise optimal, in which a user feeds back only if the received signal quality is good enough. The paper includes the derivation of these optimum policies, and further shows to what extent the O(1) feedback constraint must be relaxed to achieve the same sum-rate scaling as with perfect CSI. Extensions of these results to heterogeneous communication environments in which different users experience non-identical path-loss gains are also provided. We also show how threshold feedback policies can be used to provide fairness in a heterogeneous system, while simultaneously achieving optimal capacity scaling. Although most of our results are asymptotic in the sense that they are derived by letting n grow large, they provide promising performance figures with a close match to the asymptotically optimal results when used in finite size systems.

Optimal SINR-Based Coverage in Poisson Cellular Networks with Power Density Constraints

This paper studies coverage maximization for cellular networks in which base station (BS) locations are modeled using a homogenous spatial Poisson point process, and user locations are arbitrary. A user is covered for communication if its received signal-to-interference-plus-noise-ratio (SINR) is above a given threshold value. Two coverage models are considered. In the first model, the coverage of a user is determined based on the received SINR only from the nearest BS. The nearest BS happens to be the BS maximizing the received SINR without fading. In the second model, on the other hand, the coverage of a user is determined based on the maximum SINR from all BSs in the network. The objective is to maximize the coverage probability under the constraints on transmit power density (per unit area). Using stochastic geometry, coverage probability expressions for both coverage models are obtained. Using these expressions, bounds on the coverage maximizing power per BS and BS density are obtained. These bounds truncate the search space of the optimization problem, and thereby simplify the numerical evaluation of optimum BS power and density values considerably. All results are derived for general bounded path loss models satisfying some mild conditions. Specific applications are also illustrated to provide further insights into the optimization problem of interest.

Wireless Energy Beamforming Using Received Signal Strength Indicator Feedback

Multiple antenna techniques that allow energy beamforming have been looked upon as a possible candidate for increasing the transfer efficiency between the energy transmitter (ET) and the energy receiver in wireless power transfer. This paper introduces a novel scheme that facilitates energy beamforming by utilizing received signal strength indicator (RSSI) values to estimate the channel. First, in the training stage, the ET will transmit using each beamforming vector in a codebook, which is predefined using a Cramer–Rao lower bound analysis. RSSI value corresponding to each beamforming vector is fed back to the ET, and these values are used to estimate the channel through a maximum likelihood analysis. The results that are obtained are remarkably simple, requires minimal processing, and can be easily implemented. The paper also validates the analytical results numerically, as well as experimentally, and it is shown that the proposed method achieves impressive results.

Optimal SNR-based coverage in Poisson cellular networks with power density constraints

This paper studies coverage maximization for cellular networks in which base station (BS) locations are modeled using a homogenous spatial Poisson point process, and user locations are arbitrary. A user is covered for communication if its received signal-to-interference-plus-noise-ratio (SINR) is above a given threshold value. Two coverage models are considered. In the first model, the coverage of a user is determined based on the received SINR only from the nearest BS. The nearest BS happens to be the BS maximizing the received SINR without fading. In the second model, on the other hand, the coverage of a user is determined based on the maximum SINR from all BSs in the network. The objective is to maximize the coverage probability under the constraints on transmit power density (per unit area). Using stochastic geometry, coverage probability expressions for both coverage models are obtained. Using these expressions, bounds on the coverage maximizing power per BS and BS density are obtained. These bounds truncate the search space of the optimization problem, and thereby simplify the numerical evaluation of optimum BS power and density values considerably. All results are derived for general bounded path loss models satisfying some mild conditions. Specific applications are also illustrated to provide further insights into the optimization problem of interest.

On the Outage Capacity of Opportunistic Beamforming With Random User Locations

This paper studies the outage capacity of a network consisting of a multitude of heterogeneous mobile users and operating according to the classical opportunistic beamforming framework. The base station is located at the center of the cell, which is modeled as a disk of finite radius. The random user locations are modeled using a homogeneous spatial Poisson point process. The received signals are impaired by both fading and location dependent path loss. For this system, we first derive an expression for the beam outage probability. This expression holds for all path loss models that satisfy some mild conditions. Then, we focus on two specific path loss models (i.e., an unbounded model and a more realistic bounded one) to illustrate the applications of our results. In the large system limit, where the cell radius tends to infinity, the beam outage capacity and its scaling behavior are derived for the selected specific path loss models. This paper also studies opportunistic schemes that achieve fairness among the heterogeneous users. Numerical evaluations are performed to give further insights and to illustrate the applicability of the outage capacity results even to a cell having a small finite radius.

Optimizing User Selection Schemes in Vector Broadcast Channels

In this paper, we focus on the ergodic downlink sum-rate performance of a system consisting of a set of heterogeneous users. We study three user selection schemes to group near-orthogonal users for simultaneous transmission. The first scheme is a random selection policy that achieves fairness, but does not exploit multi-user diversity. The second scheme is a greedy selection policy that fully exploits multi-user diversity, but does not achieve fairness, and the third scheme achieves fairness while partially exploiting multi-user diversity. We also consider two beamforming methods for data transmission, namely, maximum-ratio transmission and zero-forcing beamforming. In all scheduling schemes studied in the paper, there is a key parameter that controls the degrees of orthogonality of channel directions between co-scheduled users. We focus on optimally setting this parameter for each scheduling scheme such that the ergodic downlink sum-rate is maximized. To this end, we derive analytical expressions for the ergodic downlink sum-rate considering each scheduling scheme. Numerical results are also presented to provide further insights.

Transmission rank selection for opportunistic beamforming with Quality of Service constraints

In this paper, we consider a multi-cell multi-user MISO broadcast channel. The system operates according to the opportunistic beamforming framework in a multi-cell environment with variable number of transmit beams (may alternatively be referred as the transmission rank) at each base station. The maximum number of co-scheduled users in a cell is equal to its transmission rank, thus increasing it will have the effect of increasing the multiplexing gain. However, this will simultaneously increase the amount of interference in the network, which will decrease the rate of communication. This paper focuses on optimally setting the transmission rank at each base station such that a set of Quality of Service (QoS) constraints, that will ensure a guaranteed minimum rate per beam at each base station, is not violated. Expressions representing the achievable region of transmission ranks are obtained considering different network settings. The achievable transmission rank region consists of all achievable transmission rank tuples that satisfy the QoS constraints. Numerical results are also presented to provide further insights on the feasibility problem.

Modeling and Analysis of Opportunistic Beamforming for Poisson Wireless Networks

This paper introduces a model to study both single tier and multitier wireless communication systems consisting of a multitude of wireless access points (AP), and operating according to the classical opportunistic beamforming framework. The AP locations in the proposed network model are determined by using planar Poisson point processes. The extreme value distribution of signal-to-interference-plus-noise-ratio (SINR) on a beam is of fundamental importance for obtaining performance bounds for such an opportunistic communication system. Two tight distribution approximation results are provided for the distribution of maximum SINR on a beam, which is hard to obtain due to correlation structure of the underlying inter-AP interference field, using key tools from stochastic geometry. These approximations hold for general path loss models that satisfy some mild conditions. Simulations and numerical evaluations are presented to validate the results, to provide further insights into the derived approximate maximum beam SINR distributions, and to illustrate the utility of these approximations in obtaining performance bounds for opportunistic communication systems having multiple interfering APs. In particular, key performance measures such as beam outage probability and ergodic aggregate data rate of an AP are derived by utilizing the approximated distributions.