The problem of determining asymptotic bounds on the capacity of a random ad hoc network is considered. Previous approaches assumed a threshold-based link layer model in which a packet transmission is successful if the SINR at the receiver is greater than a fixed threshold. In reality, the mapping from SINR to packet success probability is continuous. Hence, over each hop, for every finite SINR, there is a non-zero probability of packet loss. With this more realistic link model, it is shown that for a broad class of routing and scheduling schemes, a fixed fraction of hops on each route have a fixed non-zero packet loss probability. In a large network, a packet travels an asymptotically large number of hops from source to destination. Consequently, it is shown that the cumulative effect of per-hop packet loss results in a per-node throughput of only O(1 n) (instead of Theta(1 sqrt n log n )) as shown previously for the threshold-based link model). A scheduling scheme is then proposed to counter this effect. The proposed scheme improves the link SINR by using conservative spatial reuse, and improves the per-node throughput to O(1 (K_n sqrt n log n )), where each cell gets a transmission opportunity at least once every K_n slots, and K_n tends to infinity as n tends to infinity.
In @cite_9 , the authors discuss the limitations of the work in @cite_4 , by taking a network information theoretic approach. The authors discuss how several co-operative strategies such as interference cancellation, network coding, etc. could be used to improve the throughput. However these tools cannot be exploited fully with the current technology which relies on point-to-point coding, and treats all forms of interference as noise. The authors also discuss how the problem of determining the network capacity from an information theoretic view-point is a difficult problem, since even the capacity of a three node relay network is unknown. In Theorem 3.6 in @cite_9 , the authors determine the same bound on the capacity of a random network as obtained in @cite_4 .
@cite_9 @cite_4
2121223271 2952966314 2129533376 2115094114
This paper deals with throughput scaling laws for random ad hoc wireless networks in a rich scattering environment. We develop schemes to optimize the ratio lambda(n) of achievable network sum capacity to the sum of the point-to-point capacities of source-destinations (S-D) pairs operating in isolation. Our focus in this paper is on fixed signal-to-noise ratio (SNR) networks, i.e., networks where the worst case SNR over the S-D pairs is fixed independent of n. For such fixed SNR networks, which include fixed area networks as a special case, we show that collaborative strategies yield a scaling law of lambda(n)=Omega(1 n1 3) in contrast to multihop strategies which yield a scaling law of lambda(n)=Theta(1 radicn). While networks where worst case SNR goes to zero do not preclude the possibility of collaboration, multihop strategies achieve optimal throughput. The plausible reason is that the gains due to collaboration cannot offset the effect of vanishing receive SNR. This suggests that for fixed SNR networks, a network designer should look for network protocols that exploit collaboration A generalization of the Gaussian dirty-paper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa's strategies (i.e. by a random binning scheme induced by Costa's auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies ("lattice precoding") can achieve positive rates independent of the interferences, and in fact in some cases - which depend on the noise variance and power constraints - they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the Korner-Marton modulo-two sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a "helper" to the other user), and for the "common interference" case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit. Recently, the capacity region of a multiple-input multiple-output (MIMO) Gaussian broadcast channel, with Gaussian codebooks and known-interference cancellation through dirty paper coding, was shown to equal the union of the capacity regions of a collection of MIMO multiple-access channels. We use this duality result to evaluate the system capacity achievable in a cellular wireless network with multiple antennas at the base station and multiple antennas at each terminal. Some fundamental properties of the rate region are exhibited and algorithms for determining the optimal weighted rate sum and the optimal covariance matrices for achieving a given rate vector on the boundary of the rate region are presented. These algorithms are then used in a simulation study to determine potential capacity enhancements to a cellular system through known-interference cancellation. We study both the circuit data scenario in which each user requires a constant data rate in every frame and the packet data scenario in which users can be assigned a variable rate in each frame so as to maximize the long-term average throughput. In the case of circuit data, the outage probability as a function of the number of active users served at a given rate is determined through simulations. For the packet data case, long-term average throughputs that can be achieved using the proportionally fair scheduling algorithm are determined. We generalize the zero-forcing beamforming technique to the multiple receive antennas case and use this as the baseline for the packet data throughput evaluation. This paper addresses three issues in the field of ad hoc network capacity: the impact of (i) channel fading, (ii) channel inversion power control, and (iii) threshold-based scheduling on capacity. Channel inversion and threshold scheduling may be viewed as simple ways to exploit channel state information (CSI) without requiring cooperation across transmitters. We use the transmission capacity (TC) as our metric, defined as the maximum spatial intensity of successful simultaneous transmissions subject to a constraint on the outage probability (OP). By assuming the nodes are located on the infinite plane according to a Poisson process, we are able to employ tools from stochastic geometry to obtain asymptotically tight bounds on the distribution of the signal-to-interference (SIR) level, yielding in turn tight bounds on the OP (relative to a given SIR threshold) and the TC. We demonstrate that in the absence of CSI, fading can significantly reduce the TC and somewhat surprisingly, channel inversion only makes matters worse. We develop a threshold-based transmission rule where transmitters are active only if the channel to their receiver is acceptably strong, obtain expressions for the optimal threshold, and show that this simple, fully distributed scheme can significantly reduce the effect of fading.