We derive a general and closed-form result for the success probability in downlink multiple-antenna (MIMO) heterogeneous cellular networks (HetNets), utilizing a novel Toeplitz matrix representation. This main result, which is equivalently the signal-to-interference ratio (SIR) distribution, includes multiuser MIMO, single-user MIMO and per-tier biasing for @math different tiers of randomly placed base stations (BSs), assuming zero-forcing precoding and perfect channel state information. The large SIR limit of this result admits a simple closed form that is accurate at moderate SIRs, e.g., above 5 dB. These results reveal that the SIR-invariance property of SISO HetNets does not hold for MIMO HetNets; instead the success probability may decrease as the network density increases. We prove that the maximum success probability is achieved by activating only one tier of BSs, while the maximum area spectral efficiency (ASE) is achieved by activating all the BSs. This reveals a unique tradeoff between the ASE and link reliability in multiuser MIMO HetNets. To achieve the maximum ASE while guaranteeing a certain link reliability, we develop efficient algorithms to find the optimal BS densities. It is shown that as the link reliability requirement increases, more BSs and more tiers should be deactivated.
The link reliability vs. ASE tradeoff discussed in this paper is related to the notion of transmission capacity'' in wireless ad hoc networks @cite_39 @cite_41 , with related multi-antenna results such as @cite_10 @cite_31 @cite_20 @cite_14 . In wireless ad hoc networks, to maximize the spatial throughput, i.e. ASE, while guaranteeing the link reliability at a certain SINR, the density of transmitters cannot exceed a certain value, which is called the @cite_41 . Naturally, allowing more simultaneous transmitters will increase the spatial reuse efficiency, but the interference to the receivers will become higher and so the SINR and thus link reliability will decrease, similar to the ASE vs. link reliability tradeoff studied in this paper.
@cite_14 @cite_41 @cite_39 @cite_31 @cite_10 @cite_20
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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. In this paper, we investigate the optimal caching policy, respectively, maximizing the success probability and area spectral efficiency (ASE) in a cache-enabled heterogeneous network (HetNet), where a tier of multi-antenna macro base stations (MBSs) is overlaid with a tier of helpers with caches. Under the probabilistic caching framework, we resort to stochastic geometry theory to derive the success probability and ASE. After finding the optimal caching policies, we analyze the impact of critical system parameters and compare the ASE with traditional HetNet where the MBS tier is overlaid by a tier of pico BSs (PBSs) with limited-capacity backhaul. Analytical and numerical results show that the optimal caching probability is less skewed among helpers to maximize the success probability when the ratios of MBS-to-helper density, MBS-to-helper transmit power, user-to-helper density, or the rate requirement are small, but is more skewed to maximize the ASE in general. Compared with traditional HetNet, the helper density is much lower than the PBS density to achieve the same target ASE. The helper density can be reduced by increasing cache size. With given total cache size within an area, there exists an optimal helper node density that maximizes the ASE. In ad hoc networks, it may be helpful to suppress transmissions by nodes around the desired receiver in order to increase the likelihood of successful communication. This paper introduces the concept of a guard zone, defined as the region around each receiver where interfering transmissions are inhibited. Using stochastic geometry, the guard zone size that maximizes the transmission capacity for spread spectrum ad hoc networks is derived - narrowband transmission (spreading gain of unity) is a special case. A large guard zone naturally decreases the interference, but at the cost of inefficient spatial reuse. The derived results provide insight into the design of contention resolution algorithms by quantifying the optimal tradeoff between interference and spatial reuse in terms of the system parameters. A capacity increase relative to random access (ALOHA) in the range of 2 - 100 fold is demonstrated through an optimal guard zone; the capacity increase depending primarily on the required outage probability, as higher required QoS increasingly rewards scheduling. Compared to the ubiquitous carrier sense multiple access (CSMA) which essentially implements a guard zone around the transmitter rather than the receiver - we observe a capacity increase on the order of 30 - 100