Mahdi Hajiaghayi

Optimal channel assignment and power allocation for dual-hop multi-channel multi-user relaying

We consider the problem of jointly optimizing channel pairing, channel-user assignment, and power allocation in a single-relay multiple-access system. The optimization objective is to maximize the weighted sum-rate under total and individual power constraints on the transmitters. By observing the special structure of a three-dimensional assignment problem derived from the original problem, we propose a polynomial-time algorithm based on continuity relaxation and dual minimization. The proposed method is shown to be optimal for all relaying strategies that give a concave rate function in terms of power constraints.

Jointly Optimal Channel Pairing and Power Allocation for Multichannel Multihop Relaying

We study the problem of channel pairing and power allocation in a multichannel multihop relay network to enhance the end-to-end data rate. Both amplify-and-forward (AF) and decode-and-forward (DF) relaying strategies are considered. Given fixed power allocation to the channels, we show that channel pairing over multiple hops can be decomposed into independent pairing problems at each relay, and a sorted-SNR channel pairing strategy is sum-rate optimal, where each relay pairs its incoming and outgoing channels by their SNR order. For the joint optimization of channel pairing and power allocation under both total and individual power constraints, we show that the problem can be decoupled into two subproblems solved separately. This separation principle is established by observing the equivalence between sorting SNRs and sorting channel gains in the jointly optimal solution. It significantly reduces the computational complexity in finding the jointly optimal solution. It follows that the channel pairing problem in joint optimization can be again decomposed into independent pairing problems at each relay based on sorted channel gains. The solution for optimizing power allocation for DF relaying is also provided, as well as an asymptotically optimal solution for AF relaying. Numerical results are provided to demonstrate substantial performance gain of the jointly optimal solution over some suboptimal alternatives. It is also observed that more gain is obtained from optimal channel pairing than optimal power allocation through judiciously exploiting the variation among multiple channels. Impact of the variation of channel gain, the number of channels, and the number of hops on the performance gain is also studied through numerical examples.

Jointly Optimal Channel and Power Assignment for Dual-Hop Multi-Channel Multi-User Relaying

We consider the problem of jointly optimizing channel pairing, channel-user assignment, and power allocation, to maximize the weighted sum-rate, in a single-relay cooperative system with multiple channels and multiple users. Common relaying strategies are considered, and transmission power constraints are imposed on both individual transmitters and the aggregate over all transmitters. The joint optimization problem naturally leads to a mixed-integer program. Despite the general expectation that such problems are intractable, we construct an efficient algorithm to find an optimal solution, which incurs computational complexity that is polynomial in the number of channels and the number of users. We further demonstrate through numerical experiments that the jointly optimal solution can significantly improve system performance over its suboptimal alternatives.

Maximizing Lifetime in Relay Cooperation Through Energy-Aware Power Allocation

We study the problem of optimal power allocation among relays for lifetime maximization in a dual-hop cooperative network operated by amplify-and-forward relays with battery limitation. We first formulate the optimization problem for global noncausal power allocation and present a solution based on dual decomposition. In the special case of static channels, we provide a closed-form solution for lifetime maximization, which simply requires equally distributing energy over time for each participating relay. Based on this, we then develop a perceived lifetime (PLT) power allocation strategy, which can be viewed as a causal implementation of the noncausal solution by considering only the current channel state information. We also present a minimum weighted total power (MWTP) strategy that does not depend on the prediction of future channel state. PLT and MWTP are compared through analysis and simulation, and it is demonstrated that both result in lifetime performance close to that of the noncausal optimal solution, and that they significantly outperform the conventional strategy of minimizing the total power per transmission, especially when the link conditions are asymmetric or initial energy levels nonuniform among relays. We further extend the proposed power allocation strategies to relay cooperation with multiple sources and discuss how different network configurations affect relay power sharing among the sources.

Using Limited Feedback in Power Allocation Design for a Two-Hop Relay OFDM System

In this paper, we study power allocation (PA) in a single-relay OFDM system with limited feedback. We propose a PA scheme that uses a codebook of quantized PA vectors designed offline and known to the source, relay, and destination. The destination, which has full knowledge of channel side information (CSI), chooses one of the codebook vectors and conveys back to the source and relay. With the limited amount of available feedback, the design of an appropriate codebook is central to PA, which varies depending on the destinations strategy to choose the optimal PA vector. Assuming high received SNR on either link in the relay path, we first derive the optimal PA solutions as the function of channel realizations with two design criteria, maximizing capacity and minimizing error rate. It is found that when there is high received SNR in either the relay path or the direct path, the optimal solutions for both criteria reduce to simple forms. For maximizing capacity, the available power should be equally allocated to each OFDM subcarrier shared by the source and relay; while for minimum error rate, the available power should be allocated such that the received SNRs for all subcarriers at the destination are the same. The findings lead us to the sub-optimal solutions with great complexity reduction. We then present an adaptation of Lloyds algorithm to construct a codebook to quantize the optimal PA vectors subject to the amount of feedback. Simulations show that a mild to negligible performance loss can be achieved with only a few bits of feedback at different SNR values.

Efficient and practical resource block allocation for LTE-based D2D network via graph coloring

In this paper, we construct a practical framework for efficiently allocating long term evolution (LTE) resource blocks (RB) among the users in a device-to-device (D2D) network. For such network that presumably operates under the LTE cellular network, our aim is to improve the overall throughput of D2D connections using opportunistic or fairness-based approach. Taking the practical considerations into account, our proposed framework allows a number of connections to share a single RB whenever possible, thus utilizing the radio resources. To do so, our solution first identifies a superior set of the interference-free D2D reuse groups via graph modeling and graph coloring approach. In particular, we model a D2D network with a two-overlapping disk graph for which a suitable coloring algorithm is proposed and its performance bound is calculated. Once the reuse groups are known, our solution optimizes the RB allocation among these groups based on their reported channel condition as well as the scheduling criterion, whether it is fairness-based or opportunistic. Through numerical experiments, we show that our solution can significantly improve the throughput performance of a D2D network.

A 3-D Active Contour Method for Automated Segmentation of the Left Ventricle From Magnetic Resonance Images

Objective: This studys objective is to develop and validate a fast automated 3-D segmentation method for cardiac magnetic resonance imaging (MRI). The segmentation algorithm automatically reconstructs cardiac MRI DICOM data into a 3-D model (i.e., direct volumetric segmentation), without relying on prior statistical knowledge. Methods: A novel 3-D active contour method was employed to detect the left ventricular cavity in 33 subjects with heterogeneous heart diseases from the York University database. Papillary muscles were identified and added to the chamber using a convex hull of the left ventricle and interpolation. The myocardium was then segmented using a similar 3-D segmentation method according to anatomic information. A multistage approach was taken to determine the methods efficacy. Results: Our method demonstrated a significant improvement in segmentation performance when compared to manual segmentation and other automated methods. Conclusion and Significance: A true 3-D reconstruction technique without the need for training datasets or any user-driven segmentation has been developed. In this method, a novel combination of internal and external energy terms for active contour was utilized that exploits histogram matching for improving the segmentation performance. This method takes advantage of full volumetric imaging, does not rely on prior statistical knowledge, and employs a convex-hull interpolation to include the papillary muscles.

Unitary signal constellations for differential space-time modulation

In this letter, we introduce two matrix-signal constellations for differential unitary space time modulation. We also derive an approximation of the upper bound on the symbol error probability. The new constellations generalize several previously reported constellations and yield better performance when the number of transmitter antennas and the constellation size increase

Optimal Fixed Gain Linear Processing for Amplify-and-Forward Multichannel Relaying

In this correspondence, we consider the problem of linear processing design at the relay for amplified-and-forward relaying in a multichannel system. Assuming a fixed-gain power amplification at the relay, we study the linear processing structure to maximize the end-to-end achievable rate. For both the cases of relaying with or without direct path, we show that the optimal unitary processing matrix is of permutation structure, i.e., channel pairing is optimal. Furthermore, in each case, the explicit optimal channel pairing strategy is obtained based on sorting certain function of received SNR over the incoming and outgoing subchannels. This result is especially noticeable for the case with direct path, where the optimal linear processing was not known before under any power allocation. Specifically, we show that the pairing is according to the ordering of the relative SNR ratio on a subchannel over first hop to its direct path, and that of SNR strengths on subchannels over the second hop. Simulation results are presented to demonstrate the achievable gain of optimal channel pairing over non-optimal linear processing or no-pairing cases. It is also shown that the performance of channel pairing under the simple fixed-gain power allocation outperforms that under the traditional uniform power allocation.

Energy-aware power allocation for lifetime maximization in single-source relay cooperation

We study the problem of optimal power allocation (PA) among relays for lifetime maximization in a dual-hop cooperative network operated by amplify-and-forward relays with battery limitation. We first formulate the optimization problem for power allocation in a static channel case and present a closed-form solution with the objective of lifetime maximization. This solution simply requires equally distributing energy over time for each participating relay. Based on this, we then develop a perceived lifetime (PLT) PA strategy that can be used in time-varying channel scenarios. We also present a minimum weighted total power (MWTP) strategy that depends only on the current channel condition and residual energy information. PLT and MWTP are compared through analysis and simulations. It is demonstrated that both result in significant lifetime improvement compared to the conventional strategy of minimizing the total power per transmission, especially when the link conditions or initial energy levels are nonuniform among relays.