In recent work, Ozgur, Leveque, and Tse (2007) obtained a complete scaling characterization of throughput scaling for random extended wireless networks (i.e., n nodes are placed uniformly at random in a square region of area n). They showed that for small path-loss exponents alpha isin (2,3], cooperative communication is order optimal, and for large path-loss exponents alpha > 3, multihop communication is order optimal. However, their results (both the communication scheme and the proof technique) are strongly dependent on the regularity induced with high probability by the random node placement. In this paper, we consider the problem of characterizing the throughput scaling in extended wireless networks with arbitrary node placement. As a main result, we propose a more general novel cooperative communication scheme that works for arbitrarily placed nodes. For small path-loss exponents alpha isin (2,3], we show that our scheme is order optimal for all node placements, and achieves exactly the same throughput scaling as in Ozgur. This shows that the regularity of the node placement does not affect the scaling of the achievable rates for alpha isin (2,3]. The situation is, however, markedly different for large path-loss exponents alpha > 3. We show that in this regime the scaling of the achievable per-node rates depends crucially on the regularity of the node placement. We then present a family of schemes that smoothly ldquointerpolaterdquo between multihop and cooperative communication, depending upon the level of regularity in the node placement. We establish order optimality of these schemes under adversarial node placement for alpha > 3.
Since @cite_1 , the problem has received a considerable amount of attention. One stream of work @cite_13 @cite_7 @cite_12 @cite_5 @cite_3 @cite_9 @cite_11 has progressively broadened the conditions on the channel model and the communication model, under which multi-hop communication is order optimal. Specifically, with a power loss of @math for signals sent over distance @math , it has been established that under signal attenuation @math and random node placement, the best achievable per-node rate @math for random source-destination pairing scales essentially like @math and that this scaling is achievable with multi-hop communication.
@cite_7 @cite_9 @cite_1 @cite_3 @cite_5 @cite_13 @cite_12 @cite_11
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We develop a new metric for quantifying end-to-end throughput in multihop wireless networks, which we term random access transport capacity, since the interference model presumes uncoordinated transmissions. The metric quantifies the average maximum rate of successful end-to-end transmissions, multiplied by the communication distance, and normalized by the network area. We show that a simple upper bound on this quantity is computable in closed-form in terms of key network parameters when the number of retransmissions is not restricted and the hops are assumed to be equally spaced on a line between the source and destination. We also derive the optimum number of hops and optimal per hop success probability and show that our result follows the well-known square root scaling law while providing exact expressions for the preconstants, which contain most of the design-relevant network parameters. Numerical results demonstrate that the upper bound is accurate for the purpose of determining the optimal hop count and success (or outage) probability. In recent work, Ozgur, Leveque, and Tse (2007) obtained a complete scaling characterization of throughput scaling for random extended wireless networks (i.e., n nodes are placed uniformly at random in a square region of area n). They showed that for small path-loss exponents alpha isin (2,3], cooperative communication is order optimal, and for large path-loss exponents alpha > 3, multihop communication is order optimal. However, their results (both the communication scheme and the proof technique) are strongly dependent on the regularity induced with high probability by the random node placement. In this paper, we consider the problem of characterizing the throughput scaling in extended wireless networks with arbitrary node placement. As a main result, we propose a more general novel cooperative communication scheme that works for arbitrarily placed nodes. For small path-loss exponents alpha isin (2,3], we show that our scheme is order optimal for all node placements, and achieves exactly the same throughput scaling as in Ozgur. This shows that the regularity of the node placement does not affect the scaling of the achievable rates for alpha isin (2,3]. The situation is, however, markedly different for large path-loss exponents alpha > 3. We show that in this regime the scaling of the achievable per-node rates depends crucially on the regularity of the node placement. We then present a family of schemes that smoothly ldquointerpolaterdquo between multihop and cooperative communication, depending upon the level of regularity in the node placement. We establish order optimality of these schemes under adversarial node placement for alpha > 3. The goal of this paper is to establish which practical routing schemes for wireless networks are most suitable for power-limited and bandwidth-limited communication regimes. We regard channel state information (CSI) at the receiver and point-to-point capacity-achieving codes for the additive white Gaussian noise (AWGN) channel as practical features, interference cancellation (IC) as possible, but less practical, and synchronous cooperation (CSI at the transmitters) as impractical. We consider a communication network with a single source node, a single destination node, and N-1 intermediate nodes placed equidistantly on a line between them. We analyze the minimum total transmit power needed to achieve a desired end-to-end rate for several schemes and demonstrate that multihop communication with spatial reuse performs very well in the power-limited regime, even without IC. However, within a class of schemes not performing IC, single-hop transmission (directly from source to destination) is more suitable for the bandwidth-limited regime, especially when higher spectral efficiencies are required. At such higher spectral efficiencies, the gap between single-hop and multihop can be closed by employing IC, and we present a scheme based upon backward decoding that can remove all interference from the multihop system with an arbitrarily small rate loss. This new scheme is also used to demonstrate that rates of O(log N) are achievable over linear wireless networks even without synchronous cooperation. The authors obtain the optimum transmission ranges to maximize throughput for a direct-sequence spread-spectrum multihop packet radio network. In the analysis, they model the network self-interference as a random variable which is equal to the sum of the interference power of all other terminals plus background noise. The model is applicable to other spread-spectrum schemes where the interference of one user appears as a noise source with constant power spectral density to the other users. The network terminals are modeled as a random Poisson field of interference power emitters. The statistics of the interference power at a receiving terminal are obtained and shown to be the stable distributions of a parameter that is dependent on the propagation power loss law. The optimum transmission range in such a network is of the form CK sup alpha where C is a constant, K is a function of the processing gain, the background noise power spectral density, and the degree of error-correction coding used, and alpha is related to the power loss law. The results obtained can be used in heuristics to determine optimum routing strategies in multihop networks. >