We consider a general heterogeneous network in which, besides general propagation effects (shadowing and or fading), individual base stations can have different emitting powers and be subject to different parameters of Hata-like path-loss models (path-loss exponent and constant) due to, for example, varying antenna heights. We assume also that the stations may have varying parameters of, for example, the link layer performance (SINR threshold, etc). By studying the propagation processes of signals received by the typical user from all antennas marked by the corresponding antenna parameters, we show that seemingly different heterogeneous networks based on Poisson point processes can be equivalent from the point of view a typical user. These neworks can be replaced with a model where all the previously varying propagation parameters (including path-loss exponents) are set to constants while the only trade-off being the introduction of an isotropic base station density. This allows one to perform analytic comparisons of different network models via their isotropic representations. In the case of a constant path-loss exponent, the isotropic representation simplifies to a homogeneous modification of the constant intensity of the original network, thus generalizing a previous result showing that the propagation processes only depend on one moment of the emitted power and propagation effects. We give examples and applications to motivate these results and highlight an interesting observation regarding random path-loss exponents.
Our second result involves the equivalence of heterogeneous networks with random parameters, including path-loss exponents. For tractability, the aforementioned multi-tier results all assumed constant path-loss exponents across all tiers. @cite_9 extended this to a model with a different (but constant) path-loss exponent on each tier, but only assumed Rayleigh fading in their work and examined the SINR based on the base station with the smallest distance to the typical user. Also assuming different (but constant) path-loss exponents, @cite_6 generalized this approach to arbitrary propagation effects by using propagation invariance. For constant (but different) parameters across all tiers, they also showed that a multi-tier network is stochastically equivalent to a single-tier network with unity parameters while all the original parameters are incorporated into the density of the (inhomogeneous Poisson) propagation process. In the context of cellular networks or related fields, we are unaware of work involving random path-loss exponents or equivalence results to the level of generality (due to more randomized parameters) presented here.
@cite_9 @cite_6
2008364132 2134686390 2011266042 2034420299
We consider a general heterogeneous network in which, besides general propagation effects (shadowing and or fading), individual base stations can have different emitting powers and be subject to different parameters of Hata-like path-loss models (path-loss exponent and constant) due to, for example, varying antenna heights. We assume also that the stations may have varying parameters of, for example, the link layer performance (SINR threshold, etc). By studying the propagation processes of signals received by the typical user from all antennas marked by the corresponding antenna parameters, we show that seemingly different heterogeneous networks based on Poisson point processes can be equivalent from the point of view a typical user. These neworks can be replaced with a model where all the previously varying propagation parameters (including path-loss exponents) are set to constants while the only trade-off being the introduction of an isotropic base station density. This allows one to perform analytic comparisons of different network models via their isotropic representations. In the case of a constant path-loss exponent, the isotropic representation simplifies to a homogeneous modification of the constant intensity of the original network, thus generalizing a previous result showing that the propagation processes only depend on one moment of the emitted power and propagation effects. We give examples and applications to motivate these results and highlight an interesting observation regarding random path-loss exponents. Existing cellular network analyses, and even simulations, typically use the standard path loss model where received power decays like @math over a distance @math . This standard path loss model is quite idealized, and in most scenarios the path loss exponent @math is itself a function of @math , typically an increasing one. Enforcing a single path loss exponent can lead to orders of magnitude differences in average received and interference powers versus the true values. In this paper, we study multi-slope path loss models, where different distance ranges are subject to different path loss exponents. We focus on the dual-slope path loss function, which is a piece-wise power law and continuous and accurately approximates many practical scenarios. We derive the distributions of SIR, SNR, and finally SINR before finding the potential throughput scaling, which provides insight on the observed cell-splitting rate gain. The exact mathematical results show that the SIR monotonically decreases with network density, while the converse is true for SNR, and thus the network coverage probability in terms of SINR is maximized at some finite density. With ultra-densification (network density goes to infinity), there exists a phase transition in the near-field path loss exponent @math : if @math unbounded potential throughput can be achieved asymptotically; if $ 0 , ultra-densification leads in the extreme case to zero throughput. Using a multi-tier Poisson model, this paper studies the performance gain of successive interference cancellation (SIC) in the downlink of K-tier heterogeneous cellular networks (HCNs). For each tier, a fraction of base stations (BSs) is non-accessible. By using a framework based on the marked path loss process with fading and calculating the equivalent access probability, we analytically characterize the coverage probability, i.e., the probability of successfully connecting to at least one accessible BS, for a typical user equipment with finite or infinite SIC capability. The results show how the performance gain of SIC depends on many system parameters including path loss exponent, coding rate, fading distributions and BS accessibilities and densities. We show for contemporary OFDM-based HCNs, infinite SIC capability is often unnecessary. In fact, under typical system parameters, most of the gain of SIC comes from the ability of canceling only a single non-accessible BS. In this paper we develop a tractable framework for SINR analysis in downlink heterogeneous cellular networks (HCNs) with flexible cell association policies. The HCN is modeled as a multi-tier cellular network where each tier's base stations (BSs) are randomly located and have a particular transmit power, path loss exponent, spatial density, and bias towards admitting mobile users. For example, as compared to macrocells, picocells would usually have lower transmit power, higher path loss exponent (lower antennas), higher spatial density (many picocells per macrocell), and a positive bias so that macrocell users are actively encouraged to use the more lightly loaded picocells. In the present paper we implicitly assume all base stations have full queues; future work should relax this. For this model, we derive the outage probability of a typical user in the whole network or a certain tier, which is equivalently the downlink SINR cumulative distribution function. The results are accurate for all SINRs, and their expressions admit quite simple closed-forms in some plausible special cases. We also derive the average ergodic rate of the typical user, and the minimum average user throughput - the smallest value among the average user throughputs supported by one cell in each tier. We observe that neither the number of BSs or tiers changes the outage probability or average ergodic rate in an interference-limited full-loaded HCN with unbiased cell association (no biasing), and observe how biasing alters the various metrics.