Rahul Vaze

Analysis of blockage effects on urban cellular networks

Large-scale blockages such as buildings affect the performance of urban cellular networks, especially at higher frequencies. Unfortunately, such blockage effects are either neglected or characterized by oversimplified models in the analysis of cellular networks. Leveraging concepts from random shape theory, this paper proposes a mathematical framework to model random blockages and analyze their impact on cellular network performance. Random buildings are modeled as a process of rectangles with random sizes and orientations whose centers form a Poisson point process on the plane. The distribution of the number of blockages in a link is proven to be a Poisson random variable with parameter dependent on the length of the link. Our analysis shows that the probability that a link is not intersected by any blockages decays exponentially with the link length. A path loss model that incorporates the blockage effects is also proposed, which matches experimental trends observed in prior work. The model is applied to analyze the performance of cellular networks in urban areas with the presence of buildings, in terms of connectivity, coverage probability, and average rate. Our results show that the base station density should scale superlinearly with the blockage density to maintain the network connectivity. Our analyses also show that while buildings may block the desired signal, they may still have a positive impact on the SIR coverage probability and achievable rate since they can block significantly more interference.

On the Capacity and Diversity-Multiplexing Tradeoff of the Two-Way Relay Channel

In a two-way relay channel, two sources use one or more relay nodes to exchange data with each other. This paper considers a multiple input multiple output (MIMO) two-way relay channel, where each relay node has one or more antennas. Optimal relay transmission strategies for the two-way relay channel are derived to maximize the achievable rate with amplify and forward (AF) at each relay and to achieve the optimal diversity-multiplexing tradeoff (DM-tradeoff). To maximize the achievable rate with AF, an iterative algorithm is proposed which solves a power minimization problem subject to minimum signal-to-interference-and-noise ratio constraints at every step. The power minimization problem is nonconvex. The Karush Kuhn Tucker conditions, however, are shown to be sufficient for optimality. Capacity scaling law of the two-way relay channel with increasing number of relays is also established by deriving a lower and upper bound on the capacity region of the two-way relay channel. To achieve the optimal DM-tradeoff, a compress and forward strategy is proposed and its DM-tradeoff is derived. For the full-duplex two-way relay channel, the proposed strategy achieves the optimal DM-tradeoff, while for the half-duplex case the proposed strategy is shown to achieve the optimal DM-tradeoff under some conditions.

Transmission Capacity of Ad-hoc Networks With Multiple Antennas Using Transmit Stream Adaptation and Interference Cancellation

The transmission capacity of an ad-hoc network is the maximum density of active transmitters in an unit area, given an outage constraint at each receiver for a fixed rate of transmission. Assuming channel state information is available at the receiver, this paper presents bounds on the transmission capacity as a function of the number of antennas used for transmission, and the spatial receive degrees of freedom used for interference cancelation at the receiver. Canceling the strongest interferers, using a single antenna for transmission together with using all but one spatial receive degrees of freedom for interference cancelation is shown to maximize the transmission capacity. Canceling the closest interferers, using a single antenna for transmission together with using a fraction of the total spatial receive degrees of freedom for interference cancelation depending on the path loss exponent, is shown to maximize the transmission capacity.

Optimal amplify and forward strategy for two-way relay channel with multiple relays

An iterative algorithm is proposed to achieve the optimal rate region in a two-way relay channel, where two nodes want to exchange data with each other using multiple relays, and each relay employs an amplify and forward strategy. The iterative algorithm solves a power minimization problem at every step, subject to minimum signal-to-interference-and-noise ratio constraints, which is non-convex, however, for which the Karush Kuhn Tucker conditions are sufficient for optimality. Using simulations, the achievable rate region of the iterative algorithm is compared with the cut-set upper bound; the gap is shown to be quite small for most cases.

Capacity Scaling for MIMO Two-Way Relaying

This paper considers capacity scaling in the recently proposed two-way MIMO (multiple input multiple output) relay channel. In the two-way relay channel, two nodes use a relay for exchanging data with each other. Under the assumption that each node has perfect receive channel state information and all nodes work only in half duplex mode, this paper shows that the sum capacity scales linearly with the number of transmit antennas and logarithmically with the number of relays, as the number of relays grows large. This result shows that with two- way relay channels it is possible to asymptotically (in the number of relays) obtain full-duplex performance while using only half-duplex nodes.

Throughput-Delay-Reliability Tradeoff with ARQ in Wireless Ad Hoc Networks

Delay-reliability (D-R), and throughput-delay-reliability (T-D-R) tradeoffs in an ad hoc network are derived for single hop and multi-hop transmission with automatic repeat request (ARQ) on each hop. The delay constraint is modeled by assuming that each packet is allowed at most D retransmissions end-to-end, and the reliability is defined as the probability that the packet is successfully decoded in at most D retransmissions. The throughput of the ad hoc network is characterized by the transmission capacity, where the transmission capacity is defined to be the maximum density of spatial transmissions that can be simultaneously supported in an ad hoc network under quality of service (QoS) constraints (maximum retransmissions and reliability). The transmission capacity captures the T-D-R tradeoff as it incorporates the dependence between the throughput, the maximum delay, and the reliability. Given an end-to-end retransmission constraint of D, the optimal allocation of the number of retransmissions allowed at each hop is derived that maximizes a lower bound on the transmission capacity. Optimizing over the number of hops, single hop transmission is shown to be optimal for maximizing a lower bound on the transmission capacity in the sparse network regime.

Transmission capacity of ad-hoc networks with multiple antennas using transmit stream adaptation and interference cancelation

The transmission capacity of an ad-hoc network is the maximum density of active transmitters per unit area, given an outage constraint at each receiver for a fixed rate of transmission. Assuming that the transmitter locations are distributed as a Poisson point process, this paper derives upper and lower bounds on the transmission capacity of an ad-hoc network when each node is equipped with multiple antennas. The transmitter either uses eigen multi-mode beamforming or a subset of its antennas without channel information to transmit multiple data streams, while the receiver uses partial zero forcing to cancel certain interferers using some of its spatial receive degrees of freedom (SRDOF). The receiver either cancels the nearest interferers or those interferers that maximize the post-cancellation signal-to-interference ratio. Using the obtained bounds, the optimal number of data streams to transmit, and the optimal SRDOF to use for interference cancellation are derived that provide the best scaling of the transmission capacity with the number of antennas. With beamforming, single data stream transmission together with using all but one SRDOF for interference cancellation is optimal, while without beamforming, single data stream transmission together with using a fraction of the total SRDOF for interference cancellation is optimal.

Using random shape theory to model blockage in random cellular networks

Shadow fading is severe in downtown areas where buildings are densely located. This paper proposes a stochastic model to quantify blockages due to shadowing, using methods from random shape theory. Buildings inside a cell are modeled as line segments with random sizes and orientations, with locations from a spatial Poisson point process. Dense urban areas can be modeled by the parameters of the line process. Based on this construction, the distribution of the power loss caused by shadowing in a particular path is expressed in closed form. The distribution can be used to compute several performance metrics of interest in random systems. Simulations illustrate coverage and connectivity as a function of the metrics of blockages, such as the density and the average size of buildings.

Critical database size for effective caching

Replicating or caching popular content in memories distributed across the network is a technique to reduce peak network loads. Conventionally, the performance gain of caching was thought to result from making part of the requested data available closer to end users. Recently, it has been shown that by using a carefully designed technique to store the contents in the cache and coding across data streams a much more significant gain can be achieved in reducing the network load. Inner and outer bounds on the network load v/s cache memory tradeoff were obtained in [1]. We give an improved outer bound on the network load v/s cache memory tradeoff. We also address the question of to what extent caching is effective in reducing the server load when the number of files becomes large as compared to the number of users. We show that the effectiveness of caching become small when the number of files becomes comparable to the square of the number of users.

Dynamic power allocation for maximizing throughput in energy-harvesting communication system

The design of online algorithms for maximizing the achievable rate in a wireless communication channel between a source and a destination over a fixed number of slots is considered. The source is assumed to be powered by a natural renewable source, and the most general case of arbitrarily varying energy arrivals is considered, where neither the future energy arrival instants or amount nor their distribution is known. The fading coefficients are also assumed to be arbitrarily varying over time, with only causal information available at the source. For a maximization problem, the utility of an online algorithm is tested by finding its competitive ratio or competitiveness that is defined to be the maximum of the ratio of the gain of the optimal offline algorithm and the gain of the online algorithm over all input sequences. We show that the lower bound on the optimal competitive ratio for maximizing the achievable rate is arbitrarily close to the number of slots. Conversely, we propose a simple strategy that invests available energy uniformly over all remaining slots until the next energy arrival, and show that its competitive ratio is equal to the number of slots, to conclude that it is an optimal online algorithm.