We present a stochastic model for analyzing the performance of multiple-input multiple-output (MIMO) diversity in a downlink heterogeneous cellular network. Multi-antenna receivers are assumed to perform maximal-ratio combining (MRC). We consider interference-blind (IB) MRC and interference-aware (IA) MRC, where the latter takes the interference power at each antenna into account. Using tools from stochastic geometry, we derive the coverage probability for both types of MRC as a function of various tier-specific system parameters, including the number of base station transmit antennas in each tier. The model is then used to compare the performance of IB-MRC and IA-MRC. One important insight is that IA-MRC becomes less favorable than IB-MRC in a transmit-diversity system due to a larger interference correlation across receive antennas.

We study multiple-input-multiple-output (MIMO)-based downlink heterogeneous cellular networks (HetNets) with joint transmit-receive diversity using orthogonal space-time block coding at the base stations (BSs) and maximal-ratio combining (MRC) at the users. MIMO diversity with MRC receivers is particularly appealing in cellular networks due to the relatively low hardware complexity at both the BS and the user device. Using stochastic geometry, we develop a tractable stochastic model for analyzing such HetNets taking into account the irregular and multitier BS deployment. We derive the coverage probability for both interference-blind (IB) and interference-aware (IA) MRC as a function of the relevant tier-specific system parameters such as BS density and transmit (Tx) power, number of Tx antennas, and path-loss law. Important insights arising from our analysis for typical HetNets are as follows: 1) IA-MRC becomes less favorable than IB-MRC with Tx diversity due to the smaller interference variance and increased interference correlation across receive (Rx) antennas; 2) ignoring spatial interference correlation significantly overestimates the performance of IA-MRC; and 3) for a small number of Rx antennas, selection combining may offer a better performance-complexity tradeoff than MRC.

Base station (BS) cooperation is set to play a key role in managing interference in dense heterogeneous cellular networks (HCNs). Non-coherent joint transmission (JT) is particularly appealing due to its low complexity, smaller overhead, and ability for load balancing. However, a general analysis of this technique is difficult mostly due to the lack of tractable models. This paper addresses this gap and presents a tractable model for analyzing non-coherent JT in HCNs, while incorporating key system parameters such as user-centric BS clustering and channel-dependent cooperation activation. Assuming all BSs of each tier follow a stationary Poisson point process, the coverage probability for non-coherent JT is derived. Using the developed model, it is shown that for small cooperative clusters of small-cell BSs, non-coherent JT by small cells provides spectral efficiency gains without significantly increasing cell load. Further, when cooperation is aggressively triggered intra-cluster frequency reuse within small cells is favorable over intra-cluster coordinated scheduling.

Understanding the performance of cognitive relay networks (CRNs) is of great interest. Recently, stochastic geometry is being used to model and characterize the performance of CRNs. It is a known fact that sensing is an integral part of the CRN, however, in most cases it is not perfect. Moreover, the model inaccuracies caused by simplifications and/or approximations when deriving the analytical expressions for characterizing CRNs may distort their true performance. With no sensing in the system, we determine a lower performance bound (LPB) that can be used to judge the reliability of other systems that include sensing and model approximations. Based on the LPB, the operating characteristics (OC) for the CRN are obtained, which determine the joint performance of the primary and secondary system. Finally, OC are used to investigate the system performance under different scenarios.

Despite being ubiquitous in practice, the performance of maximal-ratio combining (MRC) in the presence of interference is not well understood. Because the interference received at each antenna originates from the same set of interferers but partially decorrelates over the fading channel, it possesses a complex correlation structure. This paper develops a realistic analytic model that accurately accounts for the interference correlation using stochastic geometry. Modeling interference by a Poisson shot noise process with independent Nakagami fading, we derive the link success probability for dual-branch interference-aware MRC. Using this result, we show that the common assumption that all receive antennas experience equal interference power underestimates the true performance, although this gap rapidly decays with increasing the Nakagami parameter mIof the interfering links. In contrast, ignoring interference correlation leads to a highly optimistic performance estimate for MRC, especially for large mI. In the low outage probability regime, our success probability expression can be considerably simplified. Observations based from the analysis include the following: 1) For small path loss exponents, MRC and minimum mean square error combining exhibit similar performance, and 2) the gains of MRC over selection combining are smaller in the interference-limited case than in the well-studied noise-limited case.

While the performance of maximum ratio combining (MRC) is well understood for a single isolated link, the same is not true in the presence of interference, which is typically correlated across antennas due to the common locations of interferers. For tractability, prior work focuses on the two extreme cases where the interference power across antennas is either assumed to be fully correlated or fully uncorrelated. In this paper, we address this shortcoming and characterize the performance of MRC in the presence of spatially-correlated interference across antennas. Modeling the interference field as a Poisson point process, we derive the exact distribution of the signal-to-interference ratio (SIR) for the case of two receive antennas, and upper and lower bounds for the general case. Using these results, we study the diversity behavior of MRC and characterize the critical density of simultaneous transmissions for a given outage constraint. The exact SIR distribution is also useful in benchmarking simpler correlation models. We show that the full-correlation assumption is considerably pessimistic (up to 30% higher outage probability for typical values) and the no-correlation assumption is significantly optimistic compared to the true performance.

This paper presents a tractable model for analyzing noncoherent joint-transmission base station (BS) cooperation, taking into account the irregular BS deployment typically encountered in practice. In addition to cellular-network specific aspects, such as BS density, channel fading, average path loss, and interference, the model also captures relevant cooperation mechanisms, including user-centric BS clustering and channel-dependent cooperation activation. The locations of all BSs are modeled by a Poisson point process. Using tools from stochastic geometry, the signal-to-interference-plus-noise ratio (SINR) distribution with cooperation is precisely characterized in a generality-preserving form. The result is then applied to practical design problems of recent interest. We find that increasing the network-wide BS density improves the SINR, while the gains increase with the path loss exponent. For pilot-based channel estimation, the average spectral efficiency saturates at cluster sizes of around seven BSs for typical values, irrespective of backhaul quality. Finally, it is shown that intra-cluster frequency reuse is favorable in moderately loaded cells with generous cooperation activation, while intra-cluster coordinated scheduling may be better in lightly loaded cells with conservative cooperation activation.

This work analyzes the gains of cooperative relaying in interference-limited networks, in which outages can be due to interference and fading. A stochastic model based on point process theory is used to capture the spatial randomness present in contemporary wireless networks. Using a modification of the diversity order metric, the reliability gain of selection decode-and-forward is studied for several cases. The main results are as follows: the achievable spatial-contention diversity order (SC-DO) is equal to one irrespective of the type of channel which is due to the ineffectiveness of the relay in the MAC-phase (transmit diversity). In the BC-phase (receive diversity), the SC-DO depends on the amount of fading and spatial interference correlation. In the absence of fading, there is a hard transition between SC-DO of either one or two, depending on the system parameters.

We discuss the performance of an adaptive FH-CDMA ad hoc network under the influence of external interference where node positions are modeled by a homogeneous Poisson point process. The optimum channel assignment that balances internal network interference due to spatial reuse and external interference is derived analytically for a path loss and Rayleigh fading model. The performances of the resulting hopping strategies are then compared to various suboptimal hopping strategies such as non-adaptive hopping and min-max allocation with constant QoS. It is found that adaptivity offers a benefit only at low to medium node densities and that a good suboptimal strategy can be based on hard exclusion of bad channels (thresholding) with optional min-max allocation to balance the load of active channels.

We study the interference and outage statistics in a slotted Aloha ad hoc network, where the spatial distribution of nodes is non-stationary and isotropic. In such a network, outage probability and local throughput depend on both the particular location in the network and the shape of the spatial distribution. We derive in closed-form certain distributional properties of the interference that are important for analyzing wireless networks as a function of the location and the spatial shape. Our results focus on path loss exponents 2 and 4, the former case not being analyzable before due to the stationarity assumption of the spatial node distribution. We propose two metrics for measuring local throughput in non-stationary networks and discuss how our findings can be applied to both analysis and optimization.

We consider a single-hop frequency hopping (FH) mobile ad hoc network (MANET). To increase throughput orthogonal FH (O-FH) with hop-synchronous hopping can be used, thereby allowing collision-free transmissions under certain circumstances. However, as the MANET grows, hopping sequences must be re-used. As a result, nodes sharing the same sequence will experience deterministic collisions while others having a unique sequence will still communicate collision-free. This results in an \emph{unfair} interference situation and makes performance guarantees difficult to meet for all nodes simultaneously. In this paper, we propose a \emph{collision-balancing} FH (CB-FH) scheme to overcome this drawback. The CB scheme builds on O-FH and adapts the sequence set to balance interference among the nodes. We analytically study the characteristics of the adaptive sequences and analyze the resulting interference situation at the nodes. The performance is compared to uncoordinated FH (U-FH) and O-FH. It is found that CB-FH solves the problem of unfairness present in O-FH. Compared to U-FH, CB-FH yields considerable improvements in a wide range. Practical issues are discussed.

This paper investigates the performance of a wireless ad hoc network capable of dynamically coordinating a set of orthogonal frequency channels such that every receiver and its nearest interferer operate in different channels. The distribution of the ratio of the interference powers of the second and first interferer is derived to show that the nearest interferer has dominant character, particularly in the absence of fading. Lower and upper bounds on outage probability are derived for the path loss model. For Rayleigh fading, an approximation is presented. Simulation results show that nearest neighbor scheduling is beneficial, thereby avoiding interference effectively. In contrast to other techniques such as successive interference cancellation, the complexity of nearest neighbor scheduling remains comparatively low.

This paper studies the performance of ad hoc networks with local FDMA scheduling using stochastic point processes. In such networks, the Poisson assumption is not justified due to interdependencies between points introduced by scheduling. For this reason, an upper bound on the second reduced moment measure is derived. Using this result, two lower bounds on the success probability are given, based on the second order product density and a non-homogeneous Poisson approximation. The relative performance of local FDMA is compared to random channel access. It is shown that the relative outage probability reduction of local FDMA highly depends on the SIR threshold as well as on the ratio of transmission distance to orthogonalization distance. If these two quantities are small, the improvement is high; the number of channels has only a minor effect on the relative improvement.

Statistical models for handover scenarios are necessary in order to identify key parameters and to allow proper benchmarking for handover techniques. This is quite a difficult task, since many assumptions have to be made, resulting in a loss of generality. Efforts towards the generation of such models were already made. Although these models show insights into trade offs, they leave some open questions. It is our purpose to extend previous work by presenting a new model for the macro cellular environment which is based on relative received signal strength technique employing a hysteresis margin and exponential smoothing. This model also incorporates implicitly the effect of the velocity of the mobile terminal on the handover system performance as well as the statistical dependency of consecutive signal strength measurements. We evaluate handover performance parameters such as handover probability, handover delay, expected number of handovers and outage probability. The outcome of this analysis is presented through numerical evaluations of the proposed model.