This paper addresses the following question, which is of interest in the design and deployment of a multiuser decentralized network. Given a total system bandwidth of W Hz and a fixed data rate constraint of R bps for each transmission, how many frequency slots N of size W N should the band be partitioned into to maximize the number of simultaneous transmissions in the network? In an interference-limited ad-hoc network, dividing the available spectrum results in two competing effects: on the positive side, it reduces the number of users on each band and therefore decreases the interference level which leads to an increased SINR, while on the negative side the SINR requirement for each transmission is increased because the same information rate must be achieved over a smaller bandwidth. Exploring this tradeoff between bandwidth and SINR and determining the optimum value of N in terms of the system parameters is the focus of the paper. Using stochastic geometry, we analytically derive the optimal SINR threshold (which directly corresponds to the optimal spectral efficiency) on this tradeoff curve and show that it is a function of only the path loss exponent. Furthermore, the optimal SINR point lies between the low-SINR (power-limited) and high-SINR (bandwidth-limited) regimes. In order to operate at this optimal point, the number of frequency bands (i.e., the reuse factor) should be increased until the threshold SINR, which is an increasing function of the reuse factor, is equal to the optimal value.
The problem studied in this work is essentially the optimization of frequency reuse in uncoordinated spatial (ad hoc) networks, which is a well studied problem in the context of cellular networks (see for example @cite_1 and references therein). In both settings the tradeoff is between the bandwidth utilized per cell transmission, which is inversely proportional to the frequency reuse factor, and the achieved SINR per transmission. A key difference is that in cellular networks, regular frequency reuse patterns can be planned and implemented, whereas in an ad hoc network this is impossible and so the best that can be hoped for is uncoordinated frequency reuse. Another crucial difference is in terms of analytical tractability. Although there has been a tremendous amount of work on optimization of frequency reuse for cellular networks, these efforts do not, to the best of our knowledge, lend themselves to clean analytical results. On the contrary, in this work we are able to derive very simple analytical results in the random network setting that very cleanly show the dependence of the optimal reuse factor on system parameters such as path loss exponent and rate.
@cite_1
2127242306 1970103089 2149151217 2148562694
In CSMA CA-based, multi-hop, multi-rate wireless networks, spatial reuse can be increased by tuning the carrier-sensing threshold (Tcs) to reduce the carrier sense range (dcs). While reducing dcs enables more concurrent transmissions, the transmission quality suffers from the increased accumulative interference contributed by concurrent transmissions outside dcs. As a result, the data rate at which the transmission can sustain may decrease. How to balance the interplay of spatial reuse and transmission quality (and hence the sustainable data rate) so as to achieve high network capacity is thus an important issue. In this paper, we investigate this issue by extending Cali's model and devising an analytical model that characterizes the transmission activities as governed by IEEE 802.11 DCF in a single-channel, multi-rate, multi-hop wireless network. The systems throughput is derived as a function of Tcs, SINR, beta, and other PHY MAC systems parameters. We incorporate the effect of varying the degree of spatial reuse by tuning the Tcs. Based on the physical radio propagation model, we theoretically estimate the potential accumulated interference contributed by concurrent transmissions and the corresponding SINR. For a given SINR value, we then determine an appropriate data rate at which a transmission can sustain. To the best of our knowledge, this is perhaps the first effort that considers tuning of PHY characteristics (transmit power and data rates) and MAC parameters (contention backoff timer) jointly in an unified framework in order to optimize the overall network throughput. Analytical results indicate that the systems throughput is not a monotonically increasing decreasing function of Tcs, but instead exhibits transitional points where several possible choices of Tcs can be made. In addition, the network capacity can be further improved by choosing the backoff timer values appropriately. The importance of spatial reuse in wireless ad-hoc networks has been long recognized as a key to improving the network capacity. One can increase the level of spatial reuse by either reducing the transmit power or increasing the carrier sense threshold (thereby reducing the carrier sense range). On the other hand, as the transmit power decreases or the carrier sense threshold increases, the SINR decreases as a result of the smaller received signal or the increased interference level. Consequently, the data rate sustained by each transmission may decrease. This leads naturally to the following questions:(1)How can the trade-off between the increased level of spatial reuse and the decreased data rate each node can sustain be quantified? In other words,is there an optimal range of transmit power carrier sense threshold in which the network capacity is maximized? (2)What is the relation between the transmit power and the carrier sense threshold.In this paper, we study both problems, and show that (i)in the case that the achievable channel rate follows the Shannon capacity, spatial reuse depends only on the ratio of the transmit power to the carrier sense threshold; and (ii) in the case that only a set of discrete data rates are available, tuning the transmit power offers several advantages that tuning the carrier sense threshold cannot, provided that there is a sufficient number of power levels available. Based on the findings, we then propose a decentralized power and rate control algorithm to enable each node to adjust, based on its signal interference level, its transmit power and data rate. The transmit power is so determined that the transmitter can sustain a high data rate, while keeping the adverse interference effect on the other neighboring concurrent transmissions minimal. Simulation results have shown that, as compared to existing carrier sense threshold tuning algorithms, the proposed power and rate control algorithm yields higher network capacity. The importance of spatial reuse in wireless ad hoc networks has been long recognized as a key to improving the network capacity. In this paper, we show that 1) in the case that the achievable channel rate follows the Shannon capacity, spatial reuse depends only on the ratio of the transmit power to the carrier sense threshold and 2) in the case that only a set of discrete data rates are available, as a control knob for sustaining achievable data rates, tuning the transmit power provides more sophisticated rate control over tuning the carrier sense threshold, provided that there is a sufficient number of power levels available. Based on the findings, we then propose a decentralized power and rate control algorithm to enable each node to adjust, based on its signal interference level, its transmit power and data rate. The transmit power is so determined that the transmitter can sustain a high data rate while keeping the adverse interference effect on the other neighboring concurrent transmissions minimal. Simulation results have shown that compared to existing carrier sense threshold tuning algorithms, the proposed power and rate control algorithm yields higher network capacity. This paper considers the joint optimization of frequency reuse and base-station (BS) bias for user association in downlink heterogeneous networks for load balancing and intercell interference management. To make the analysis tractable, we assume that BSs are randomly deployed as point processes in multiple tiers, where BSs in each tier have different transmission powers and spatial densities. A utility maximization framework is formulated based on the user coverage rate, which is a function of the different BS biases for user association and different frequency reuse factors across BS tiers. Compared to previous works where the bias levels are heuristically determined and full reuse is adopted, we quantitatively compute the optimal user association bias and obtain the closed-form solution of the optimal frequency reuse. Interestingly, we find that the optimal bias and the optimal reuse factor of each BS tier have an inversely proportional relationship. Further, we also propose an iterative method for optimizing these two factors. In contrast to system-level optimization solutions based on specific channel realization and network topology, our approach is off-line and is useful for deriving deployment insights. Numerical results show that optimizing user association and frequency reuse for multi-tier heterogeneous networks can effectively improve cell-edge user rate performance and utility.