Masoud Ebrahimi

Power Allocation and Asymptotic Achievable Sum-Rates in Single-Hop Wireless Networks

A network of n communication links operating over a shared wireless channel is considered. Power management is crucial to such interference-limited networks to improve the aggregate throughput. We consider sum-rate maximization of the network by optimum power allocation when conventional linear receivers (without interference cancellation) are utilized. It is shown that in the case of n=2 links, the optimum power allocation strategy is such that either both links use their maximum power or one of them uses its maximum power and the other keeps silent. An asymptotic analysis for large n is carried out to show that in a Rayleigh fading channel the average sum-rate scales at least as log(n). This is obtained by deriving an on-off power allocation strategy. The same scaling law is obtained in the work of Gowaikar et al., where the number of links, their end-points (source-destination pairs), and the relay nodes are optimally chosen all by a central controller. However, our proposed strategy can be implemented in a decentralized fashion for any number of links, arbitrary transmitter-receiver pairs, and without any relay nodes. It is shown that the proposed power allocation scheme is optimum among all on-off power allocation strategies in the sense that no other strategies can achieve an average sum-rate of higher order.

Throughput Scaling Laws for Wireless Networks With Fading Channels

A network of n communication links, operating over a shared wireless channel, is considered. Fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. It is assumed that each link can be active and transmit with a constant power P or remain silent. The objective is to maximize the throughput over the selection of active links. By deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading: (i) the maximum throughput scales like log n; (ii) the maximum throughput is achievable in a distributed fashion. The upper bound is obtained using probabilistic methods, where the key point is to upper bound the throughput of any random set of active links by a chi-squared random variable. To obtain the lower bound, a decentralized link activation strategy is proposed and analyzed.

Characterization of SINR Region for Interfering Links With Constrained Power

In this paper, a communication system including n interfering additive white Gaussian noise (AWGN) links is considered. Each transmitter uses a Gaussian codebook and each receiver only decodes the data of the corresponding transmitter. For the case that the transmit powers are subject to arbitrary linear constraints, a mathematical expression for the boundary points of the signal-to-interference-plus-noise-ratio (SINR) region is obtained. Moreover, when the channels are time-varying and the average powers are constrained, the zero-outage SINR region of the system is derived. In addition, a scenario where the demanded SINR of the users is out of the SINR region is considered. A common approach is to remove a subset of the users such that the demanded SINR can be provided for the remaining users; the removed users are serviced in a later time slot. With the aim of maximizing the number of serviced users in each time slot, a suboptimal algorithm is developed, which outperforms the other known alternatives.

A New Decentralized Power Allocation Strategy in Single-Hop Wireless Networks

In this paper, a simple decentralized power allocation strategy is proposed, which relies on the local information in a single-hop wireless network with n links. The main goal of the strategy is to improve the average sum-rate. We first define a new utility-based framework, in which each user takes into account the negative impact of its power increment on the other users performance. For large n and by knowing only the direct channel gain hii, the optimum strategy for user i is to transmit with full power or remain silent. The transmission policy is to compare hii with a prespecified threshold taun that is a function of n. Under a Rayleigh fading channel condition, it is demonstrated that among n pairs of nodes, the average number of active links is of order log n. Also, the average sum-rate scales as Theta(log n). The performance of the proposed strategy is compared with that of the centralized power allocation scheme and the non-cooperative power control games through simulation and the analytical arguments. The proposed on-off power allocation scheme has the advantage of not requiring a central controller. The proposed strategy relies on a one shot game with a simple structure, rather than the iterative mechanism used in the pricing algorithm. These properties make our scheme more practical in time-varying networks.

Characterization of Rate Region in Interference Channels with Constrained Power

In this paper, an n-user Gaussian interference channel under arbitrary linear power constraints is considered. Using Perron-Frobenius theorem, a closed-form expression for the boundary points of the rate region of such a channel is derived. This is a generalization of the well-known result on the maximum rate that some interfering links can simultaneously achieve when the power is unbounded. Moreover, this result is extended to the time-varying channels with constraints on the average power.

Rate-Constrained Wireless Networks With Fading Channels: Interference-Limited and Noise-Limited Regimes

A network of n wireless communication links is considered in a Rayleigh fading environment. It is assumed that each link can be active and transmit with a constant power P or remain silent. The objective is to maximize the number of active links such that each active link can transmit with a constant rate λ. In a Rayleigh fading environment, an upper bound is derived that shows the number of active links scales at most like 1/λ log n. To obtain a lower bound, a decentralized link activation strategy is described and analyzed. It is shown that for small values of λ, the number of supported links by this strategy meets the upper bound; however, as λ grows, this number becomes far below the upper bound. To shrink the gap between the upper bound and the achievability result, a modified link activation strategy is proposed and analyzed based on some results from random graph theory. It is shown that this modified strategy performs very close to the optimum. Specifically, this strategy is asymptotically almost surely optimum when λ approaches ∞ or 0. It turns out that the optimality results are obtained in an interference-limited regime. It is demonstrated that, by proper selection of the algorithm parameters, the proposed scheme also allows the network to operate in a noise-limited regime in which the transmission rates can be adjusted by the transmission powers. The price for this flexibility is a decrease in the throughput scaling law by a multiplicative factor of loglogn. Finally, both decentralized and centralized schemes are evaluated in a distance-dependent fading environment with a path loss exponent of m and are shown to achieve throughput that scale like Θ( n(m/m+2) log n ) and Θ(n[(m(2)+2m)/( m(2)+2m+4)]), respectively.

Sum-Rate Maximization in Single-Hop Wireless Networks with the On-Off Power Scheme

A single-hop wireless network with K links is considered, where the links are partitioned into M clusters, each operating in a subchannel with bandwidth W/M. We assume that the links in each cluster perform the on-off power allocation strategy proposed in [1]. The problem is to analyze the average sum-rate of the network in terms of M and under the shadow- fading effect with probability a. It is demonstrated that for M ~ o(K) and 0 < alpha les 1, where alpha is a fixed parameter, the average sum-rate of the network scales as W/alpha log K. For M ~ Theta(K), we present an upper bound for the average sum-rate. It is proved that the maximum average sum-rate of the network for every value of 0 < alpha les 1 is achieved at M = 1. In fact, in the proposed model, partitioning the bandwidth W into M subchannels has no gain in terms of enhancing the throughput.

Virtual Cooperation for Throughput Maximization in Distributed Large-Scale Wireless Networks

A distributed wireless network with links is considered, where the links are partitioned into clusters each operating in a subchannel with bandwidth . The subchannels are assumed to be orthogonal to each other. A general shadow-fading model described by the probability of shadowing and the average cross-link gains is considered. The main goal is to find the maximum network throughput in the asymptotic regime of , which is achieved by: (i) proposing a distributed power allocation strategy, where the objective of each user is to maximize its best estimate (based on its local information) of the average network throughput and (ii) choosing the optimum value for . In the first part, the network throughput is defined as the average sum-rate of the network, which is shown to scale as . It is proved that the optimum power allocation strategy for each user for large is a threshold-based on-off scheme. In the second part, the network throughput is defined as the guaranteed sum-rate, when the outage probability approaches zero. It is demonstrated that the on-off power scheme maximizes the throughput, which scales as . Moreover, the optimum spectrum sharing for maximizing the average sum-rate and the guaranteed sum-rate is achieved at .

Interference-Limited versus Noise-Limited Communication Over Dense Wireless Networks

A network of n wireless communication links is considered. Rayleigh fading is assumed to be the dominant factor affecting the strength of the channels between nodes. In previous works it is shown that the maximum throughput of this network over all link activation strategies scales as logn. However, it is achieved by assigning a vanishingly small rate to each active link. The objective of this paper is to analyze the achievable throughput of the network when the data rate of each active link is constrained to be a constant lambda > 0. A link activation strategy is proposed and analyzed using random graph theory. In the interference-limited regime, a throughput scaling as tau log n is achievable, where the scaling factor tau approaches 1 as lambda rarr 0 or lambda rarr infin. This implies the asymptotic optimality of the proposed scheme. In the noise-limited regime, it is shown that rate-per-links scaling as log(Delta0rho) are achievable, where Delta0 is a constant and rho is the transmit signal to noise ratio. However, in this case the throughput decreases by a factor of log log n as compared to the interference-limited regime.

An Efficient User Removal Algorithm for Limited-Power Interference Channels

In this paper, the problem of maximizing the number of active users satisfying a required quality of service (QoS) in n-user interference channels is investigated. This problem is known as an NP-complete problem. We introduce an efficient suboptimal algorithm, relying on the results for the boundary of the rate region we derived in [1]. The algorithm is developed for different sorts of constraints on the transmit powers, including constraint on the power of the individual transmitters and constraint on the total power of the transmitters. Simulation results show that the performance of the proposed algorithm is very close to the optimum solution, and outperforms alternative algorithms.