This paper examines the impact of system parameters such as access point density and bandwidth partitioning on the performance of randomly deployed, interference-limited, dense wireless networks. While much progress has been achieved in analyzing randomly deployed networks via tools from stochastic geometry, most existing works either assume a very large user density compared to that of access points which does not hold in a dense network, and or consider only the user signal-to-interference-ratio as the system figure of merit which provides only partial insight on user rate, as the effect of multiple access is ignored. In this paper, the user rate distribution is obtained analytically, taking into account the effects of multiple access as well as the SIR outage. It is shown that user rate outage probability is dependent on the number of bandwidth partitions (subchannels) and the way they are utilized by the multiple access scheme. The optimal number of partitions is lower bounded for the case of large access point density. In addition, an upper bound of the minimum access point density required to provide an asymptotically small rate outage probability is provided in closed form.
A few recent works have attempted to address these issues. Specifically, the UE distribution is taken into account in @cite_12 @cite_0 by incorporating in the analysis the probability of an AP being inactive (no UE present within its cell). However, analysis considers only the SIR. In @cite_8 @cite_13 the UE distribution is employed for computation of user rates under time-division-multiple-access (TDMA) without considering the effect of SIR outage. In addition, TDMA may not be the best multiple access scheme under certain scenarios.
@cite_0 @cite_13 @cite_12 @cite_8
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The calculation of the SIR distribution at the typical receiver (or, equivalently, the success probability of transmissions over the typical link) in Poisson bipolar and cellular networks with Rayleigh fading is relatively straightforward, but it only provides limited information on the success probabilities of the individual links. This paper focuses on the meta distribution of the SIR, which is the distribution of the conditional success probability @math given the point process, and provides bounds, an exact analytical expression, and a simple approximation for it. The meta distribution provides fine-grained information on the SIR and answers questions such as “What fraction of users in a Poisson cellular network achieve 90 link reliability if the required SIR is 5 dB?” Interestingly, in the bipolar model, if the transmit probability @math is reduced while increasing the network density @math such that the density of concurrent transmitters @math stays constant as @math , @math degenerates to a constant, i.e., all links have exactly the same success probability in the limit, which is the one of the typical link. In contrast, in the cellular case, if the interfering base stations are active independently with probability @math , the variance of @math approaches a non-zero constant when @math is reduced to 0 while keeping the mean success probability constant. We develop a general downlink model for multi-antenna heterogeneous cellular networks (HetNets), where base stations (BSs) across tiers may differ in terms of transmit power, target signal-to-interference-ratio (SIR), deployment density, number of transmit antennas and the type of multi-antenna transmission. In particular, we consider and compare space division multiple access (SDMA), single user beamforming (SU-BF), and baseline single-input single-output (SISO) transmission. For this general model, the main contributions are: (i) ordering results for both coverage probability and per user rate in closed form for any BS distribution for the three considered techniques, using novel tools from stochastic orders, (ii) upper bounds on the coverage probability assuming a Poisson BS distribution, and (iii) a comparison of the area spectral efficiency (ASE). The analysis concretely demonstrates, for example, that for a given total number of transmit antennas in the network, it is preferable to spread them across many single-antenna BSs vs. fewer multi-antenna BSs. Another observation is that SU-BF provides higher coverage and per user data rate than SDMA, but SDMA is in some cases better in terms of ASE. This paper analyzes the impact of user mobility in multi-tier heterogeneous networks. We begin by obtaining the handoff rate for a mobile user in an irregular cellular network with the access point locations modeled as a homogeneous Poisson point process. The received signal-to-interference-ratio (SIR) distribution along with a chosen SIR threshold is then used to obtain the probability of coverage. To capture potential connection failures due to mobility, we assume that a fraction of handoffs result in such failures. Considering a multi-tier network with orthogonal spectrum allocation among tiers and the maximum biased average received power as the tier association metric, we derive the probability of coverage for two cases: 1) the user is stationary (i.e., handoffs do not occur, or the system is not sensitive to handoffs); 2) the user is mobile, and the system is sensitive to handoffs. We derive the optimal bias factors to maximize the coverage. We show that when the user is mobile, and the network is sensitive to handoffs, both the optimum tier association and the probability of coverage depend on the user's speed; a speed-dependent bias factor can then adjust the tier association to effectively improve the coverage, and hence system performance, in a fully-loaded network. For an arbitrarily-located user terminal (UE) in a multi-tier heterogeneous cellular wireless network, the joint distribution of the downlink SINR at the UE from the candidate serving base stations (BSs) in the accessible tiers of the network has been derived in closed form for the cases where the candidate serving BS from each accessible tier is chosen as either the one nearest to the UE [1] or the one that is received strongest (equivalently, with maximum SINR) at the UE [2], when the locations of the BSs in the tiers are modeled by independent Poisson Point Processes, and the fading on all links is assumed independent identically distributed (iid) and Rayleigh. The actual serving BS for the UE is chosen as the nearest strongest max-SINR candidate serving BS after imposing selection bias across the tiers. The above joint distributions can be used to yield the distribution of the actual SINR at the UE (i.e., when receiving from this serving BS) when no selection bias exists across tiers. However, for the practically important case of selection bias, analytical calculation of the distribution of the actual SINR presents significant challenges. This work derives and summarizes the distribution of actual downlink SINR for all the above criteria for selection of the serving BS accounting for selection bias. We then explore some implications of these results for design and operation of a heterogeneous network.