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
2031116206 2963847582 2095796369 2150450717 2137079066 2102473388
The tremendous capacity gains promised by space division multiple access (SDMA) depend critically on the accuracy of the transmit channel state information. In the broadcast channel, even without any network interference, it is known that such gains collapse due to interstream interference if the feedback is delayed or low rate. In this paper, we investigate SDMA in the presence of interference from many other simultaneously active transmitters distributed randomly over the network. In particular we consider zero-forcing beamforming in a decentralized (ad hoc) network where each receiver provides feedback to its respective transmitter. We derive closed-form expressions for the outage probability, network throughput, transmission capacity, and average achievable rate and go on to quantify the degradation in network performance due to residual self-interference as a function of key system parameters. One particular finding is that as in the classical broadcast channel, the per-user feedback rate must increase linearly with the number of transmit antennas and SINR (in dB) for the full multiplexing gains to be preserved with limited feedback. We derive the throughput-maximizing number of streams, establishing that single-stream transmission is optimal in most practically relevant settings. In short, SDMA does not appear to be a prudent design choice for interference-limited wireless networks. Transmission capacity (TC) is a performance metric for wireless networks that measures the spatial intensity of successful transmissions per unit area, subject to a constraint on the permissible outage probability (where outage occurs when the signal to interference plus noise ratio (SINR) at a receiver is below a threshold). This volume gives a unified treatment of the TC framework that has been developed by the authors and their collaborators over the past decade. The mathematical framework underlying the analysis (reviewed in Section 2) is stochastic geometry: Poisson point processes model the locations of interferers, and (stable) shot noise processes represent the aggregate interference seen at a receiver. Section 3 presents TC results (exact, asymptotic, and bounds) on a simple model in order to illustrate a key strength of the framework: analytical tractability yields explicit performance dependence upon key model parameters. Section 4 presents enhancements to this basic model — channel fading, variable link distances (VLD), and multihop. Section 5 presents four network design case studies well-suited to TC: (i) spectrum management, (ii) interference cancellation, (iii) signal threshold transmission scheduling, and (iv) power control. Section 6 studies the TC when nodes have multiple antennas, which provides a contrast vs. classical results that ignore interference. In this paper, upper and lower bounds on the transmission capacity of spread-spectrum (SS) wireless ad hoc networks are derived. We define transmission capacity as the product of the maximum density of successful transmissions multiplied by their data rate, given an outage constraint. Assuming that the nodes are randomly distributed in space according to a Poisson point process, we derive upper and lower bounds for frequency hopping (FH-CDMA) and direct sequence (DS-CDMA) SS networks, which incorporate traditional modulation types (no spreading) as a special case. These bounds cleanly summarize how ad hoc network capacity is affected by the outage probability, spreading factor, transmission power, target signal-to-noise ratio (SNR), and other system parameters. Using these bounds, it can be shown that FH-CDMA obtains a higher transmission capacity than DS-CDMA on the order of M sup 1-2 spl alpha , where M is the spreading factor and spl alpha >2 is the path loss exponent. A tangential contribution is an (apparently) novel technique for obtaining tight bounds on tail probabilities of additive functionals of homogeneous Poisson point processes. Receivers with N antennas in single-hop, ad-hoc wireless networks with nodes randomly distributed on an infinite plane with uniform area density are studied. Transmitting nodes have single antennas and transmit simultaneously in the same frequency band with power P that decays with distance via the commonly-used inverse-polynomial model with path-loss- exponent (PLE) greater than 2. This model applies to shared spectrum systems where multiple links share the same frequency band. In the interference-limited regime, the average spectral efficiency of a representative link E[C] (b s Hz link) is found to grow as log(N) and linearly with PLE, and its variance decays as 1 N. The average signal-to-interference-plus-noise-ratio (SINR) on a representative link is found to grow faster than linearly with N. With multiple-input-multiple-output (MIMO) links where transmit nodes have multiple antennas without Channel- State-Information, it is found that E[C] in the network can be improved if nodes transmit using the optimum number of antennas compared to the optimum selfish strategy of transmitting equal-power streams from every antenna. The results are extended to random code-division-multiple-access systems where the optimum spreading factor for a given link length is found. These results are developed as asymptotic expressions using infinite random matrix theory and are validated by Monte-Carlo simulations. This paper derives the outage probability and transmission capacity of ad hoc wireless networks with nodes employing multiple antenna diversity techniques, for a general class of signal distributions. This analysis allows system performance to be quantified for fading or non-fading environments. The transmission capacity is given for interference-limited uniformly random networks on the entire plane with path loss exponent alpha > 2 in which nodes use: (1) static beamforming through M sectorized antennas, for which the increase in transmission capacity is shown to be thetas(M2) if the antennas are without sidelobes, but less in the event of a nonzero sidelobe level; (2) dynamic eigenbeamforming (maximal ratio transmission combining), in which the increase is shown to be thetas(M 2 alpha ); (3) various transmit antenna selection and receive antenna selection combining schemes, which give appreciable but rapidly diminishing gains; and (4) orthogonal space-time block coding, for which there is only a small gain due to channel hardening, equivalent to Nakagami-m fading for increasing m. It is concluded that in ad hoc networks, static and dynamic beamforming perform best, selection combining performs well but with rapidly diminishing returns with added antennas, and that space-time block coding offers only marginal gains. The benefit of multi-antenna receivers is investigated in wireless ad hoc networks, and the main finding is that network throughput can be made to scale linearly with the number of receive antennas N_r even if each transmitting node uses only a single antenna. This is in contrast to a large body of prior work in single-user, multiuser, and ad hoc wireless networks that have shown linear scaling is achievable when multiple receive and transmit antennas (i.e., MIMO transmission) are employed, but that throughput increases logarithmically or sublinearly with N_r when only a single transmit antenna (i.e., SIMO transmission) is used. The linear gain is achieved by using the receive degrees of freedom to simultaneously suppress interference and increase the power of the desired signal, and exploiting the subsequent performance benefit to increase the density of simultaneous transmissions instead of the transmission rate. This result is proven in the transmission capacity framework, which presumes single-hop transmissions in the presence of randomly located interferers, but it is also illustrated that the result holds under several relaxations of the model, including imperfect channel knowledge, multihop transmission, and regular networks (i.e., interferers are deterministically located on a grid).