Millimeter-wave (mm-wave) communication opens up tens of giga-hertz spectrum in the mm-wave band for use by next-generation wireless systems, thereby solving the problem of spectrum scarcity. Maintaining connectivity stands out as a key design challenge for mm-wave networks deployed in urban regions due to the blockage effect characterizing mm-wave propagation. In this paper, we set out to investigate the blockage effect on the connectivity of mm-wave networks in a Manhattan-type urban region modeled using a random regular lattice, while base stations (BSs) are Poisson distributed in the plane. In particular, we analyze the connectivity probability that a typical user is within the transmission range of a BS and connected by a line-of-sight. First, we consider a single-tier network. By jointly applying the random lattice and stochastic geometry theories, a lower bound on the connectivity probability is derived as a function of building parameters (e.g., size and site occupancy probability) and BS parameters (e.g., transmission range and BS density). For the case of dense buildings, the bound is derived in a simpler form. Next, the preceding lower bounds are tightened based on the geometric technique of partitioning the irregular blockage-free region around the typical user. Moreover, the analysis is generalized to mm-wave channels with both LoS and NLoS paths. Finally, the results are extended to a K-tier heterogeneous network (HetNet), where building heights are random, and depending on its height, a building can block the signals transmitted by a subset of BS tiers but not all. The analysis shows that the connectivity probability of the K-tier HetNet increases linearly with the number of tiers. In general, our work quantifies the relation between the coverage of an mmwave network and the parameters of building and BS processes, providing useful guidelines for deploying practical networks in a Manhattan-type region.

The millimeter-wave (mmWave) communication exploits tens-of-GHz of available spectrum in the mmWave band for solving the problem of spectrum scarcity in next-generation wireless networks. Maintaining connectivity in urban mmWave networks is one key design challenge because of the blockage effect characterizing mmWave propagation. Specifically, mmWave signals can be blocked by buildings and other large urban objects. Thus, the type of urban model affects the performance of mmWave networks. In this paper, we make the first attempt to study the connectivity of mmWave networks in a Manhattan-type region modeled using a random lattice while base stations (BSs) are Poisson distributed in the plane. In particular, we define and analyze the connectivity probability that a typical user is within the transmission range of a BS and connected by a line-of-sight. By jointly applying random-lattice and stochastic-geometry theories, different lower bounds on the connectivity probability are derived as functions of the buildings' size and distribution as well as the BSs' transmission range and density. We also investigate the asymptotic connectivity probability for the case of dense buildings. Our study yields closed-form relations between the parameters of the building process and the BS process, providing useful guidelines for practical mmWave network deployment and opening up many directions for future extensions.

In order to improve the uplink performance of future cellular networks, the idea to decouple the downlink (DL) and uplink (UL) association has recently been shown to provide significant gain in terms of both coverage and rate performance. However, all the works are limited to a single input single output (SISO) network. Therefore, to study the gain provided by the DL and UL decoupling in multi-antenna base stations (BSs) setup, we study a two tier heterogeneous network consisting of multi-antenna BSs, and single antenna user equipments (UEs). We use maximal ratio combining (MRC) as a linear receiver at the BSs and tools from stochastic geometry, and we derive tractable expressions for both signal-to-interference ratio (SIR) coverage probability and rate coverage probability. We observe that as the disparity in the beamforming gain of both tiers increases, the gain in terms of SIR coverage probability provided by the decoupled association over non-decoupled association decreases. We further observe that when there is asymmetry in the number of antennas of both tiers, then we need further biasing toward femto-tier on the top of decoupled association to balance the load and get optimal rate coverage probability.

Caching and multicasting at base stations are two promising approaches to supporting massive content delivery over wireless networks. However, existing analysis and designs do not fully explore and exploit the potential advantages of the two approaches. In this paper, we consider the analysis and optimization of caching and multicasting in a large-scale cache-enabled wireless network. We propose a random caching and multicasting design. By carefully handling different types of interferers and adopting appropriate approximations, we derive a tractable expression for the successful transmission probability in the general region, utilizing tools from stochastic geometry. We also obtain a closed-form expression for the successful transmission probability in the high signal-to-noise ratio (SNR) and user density region. Then, we consider the successful transmission probability maximization, which is a very complex nonconvex problem in general. Using optimization techniques, we develop an iterative numerical algorithm to obtain a local optimal caching and multicasting design in the general region. To reduce complexity and maintain superior performance, we also derive an asymptotically optimal caching and multicasting design in the asymptotic region, based on a two-stage optimization framework. Finally, numerical simulations show that the asymptotically optimal design achieves a significant gain in successful transmission probability over some baseline schemes in the general region.

In heterogeneous networks (HetNets), strong interference due to spectrum reuse affects each user's signal-to-interference ratio (SIR), and hence is one limiting factor of network performance. In this paper, we propose a user-centric interference nulling (IN) scheme in a downlink large-scale HetNet to improve coverage/outage probability by improving each user's SIR. This IN scheme utilizes at most maximum IN degree of freedom (DoF) at each macro-base station to avoid interference to uniformly selected macro (pico) users with signal-to-individual-interference ratio below a macro (pico) IN threshold, where the maximum IN DoF and the two IN thresholds are three design parameters. Using tools from stochastic geometry, we first obtain a tractable expression of the coverage (equivalently outage) probability. Then, we obtain the asymptotic expressions of the coverage/outage probability in the low and high SIR threshold regimes. The analytical results indicate that the maximum IN DoF can affect the order gain of the outage probability in the low SIR threshold regime, but cannot affect the order gain of the coverage probability in the high SIR threshold regime. Moreover, we characterize the optimal maximum IN DoF, which optimizes the asymptotic coverage/outage probability. Finally, numerical results show that the proposed scheme can achieve good gains in coverage/outage probability over some baseline schemes.

We derive an asymptotic outage probability expression for multiple-input multiple-output maximum-ratiocombining (MIMO-MRC) systems considering Rician fading channels with both transmit and receive spatial correlation. This result is facilitated by a new asymptotic expression which we obtain for the cumulative distribution function of the maximum eigenvalue of a noncentral quadratic form in complex Gaussian matrices. Based on our analysis, we demonstrate that for a rank-1 line-of-sight (LoS) path, the interaction with the correlation matrices may yield improved or degraded performance. The relative effect depends largely on the geometric alignment of the LoS path with the eigenvectors of the correlation matrices. Generally speaking, when the LoS path aligns with the weak eigenvectors (i.e., those corresponding to the smallest eigenvalues), both a stronger LoS component, characterized by a higher Rician K factor, and a higher correlation lead to improved performance. In contrast, when the LoS path aligns with the strong eigenvectors, we demonstrate that there exists distinct regions for which increasing the Rician K factor has a beneficial or deleterious effect. Our results, in general, provide novel insight into how the mutual interactions of LoS and spatial correlation components impact the performance of MIMO-MRC systems.

Caching and multicasting at base stations are two promising approaches to support massive content delivery over wireless networks. However, existing analysis and designs do not fully explore and exploit the potential advantages of the two approaches. In this paper, we jointly consider caching and multicasting to maximize the successful transmission probability in large-scale information-centric networks. We propose a random caching and multicasting scheme with a design parameter. Utilizing tools from stochastic geometry, we derive a tractable expression and a closed-form expression for the successful transmission probability in the general and high signal-to-noise ratio (SNR) regions, respectively. Then, using optimization techniques, we derive a simple asymptotically optimal design in the high SNR region, which provides important design insights. Finally, by numerical simulations, we show that the asymptotically optimal design also achieves a significant performance gain over some baseline schemes in the general SNR region, and hence is applicable and effective in practical cache-enabled information-centric networks.

Heterogeneous networks (HetNets) with offloading is considered as an effective way to meet the high data rate demand of future wireless service. However, the offloaded users suffer from strong inter-tier interference, which reduces the benefits of offloading and is one of the main limiting factors of the system performance. In this paper, we investigate the use of an interference nulling (IN) beamforming scheme to improve the system performance by carefully managing the inter-tier interference to the offloaded users in downlink two-tier HetNets with multi-antenna base stations. Utilizing tools from stochastic geometry, we derive a tractable expression for the rate coverage probability of the IN scheme. Then, we optimize the design parameter, i.e., the degrees of freedom that can be used for IN, to maximize the rate coverage probability. Specifically, in the asymptotic scenario where the rate threshold is small, by studying the order behavior of the rate coverage probability, we characterize the optimal design parameter. For the general scenario, we show some properties of the optimal design parameter. Finally, by numerical simulations, we show the IN scheme can outperform both the simple offloading scheme without interference management and the almost blank subframes scheme in 3GPP LTE, especially in large antenna regime.

Heterogeneous networks (HetNets) have strong interference due to spectrum reuse. This affects the signal-to-interference ratio (SIR) of each user, and hence is one of the limiting factors of network performance. However, in previous works, interference management approaches in HetNets are mainly based on interference level, and thus cannot effectively utilize the limited resource to improve network performance. In this paper, we propose a user-centric interference nulling (IN) scheme in downlink two-tier HetNets to improve network performance by improving each user's SIR. This scheme has three design parameters: the maximum degree of freedom for IN (i.e., maximum IN DoF), and the IN thresholds for the macro and pico users, respectively. Using tools from stochastic geometry, we first obtain a tractable expression of the coverage (equivalently outage) probability. Then, we characterize the asymptotic behavior of the outage probability in the high reliability regime. The asymptotic results show that the maximum IN DoF can affect the order gain of the asymptotic outage probability, while the IN thresholds only affect the coefficient of the asymptotic outage probability. Moreover, we show that the IN scheme can linearly improve the outage performance, and characterize the optimal maximum IN DoF which minimizes the asymptotic outage probability.

To enhance the multiplexing gain of two-receiver Multiple-Input-Single-Output Broadcast Channel with imperfect channel state information at the transmitter (CSIT), a class of Rate-Splitting (RS) approaches has been proposed recently, which divides one receiver's message into a common and a private part, and superposes the common message on top of Zero-Forcing precoded private messages. In this paper, with quantized CSIT, we study the ergodic sum rate of two schemes, namely RS-S and RS-ST, where the common message(s) are transmitted via a space and space-time design, respectively. Firstly, we upper-bound the sum rate loss incurred by each scheme relative to Zero-Forcing Beamforming (ZFBF) with perfect CSIT. Secondly, we show that, to maintain a constant sum rate loss, RS-S scheme enables a feedback overhead reduction over ZFBF with quantized CSIT. Such reduction scales logarithmically with the constant rate loss at high Signal-to-Noise-Ratio (SNR). We also find that, compared to RS-S scheme, RS-ST scheme offers a further feedback overhead reduction that scales with the discrepancy between the feedback overhead employed by the two receivers when there are alternating receiver-specific feedback qualities. Finally, simulation results show that both schemes offer a significant SNR gain over conventional single-user/multiuser mode switching when the feedback overhead is fixed.

Heterogeneous networks (HetNets) with offloading is considered as an effective way to meet the high data rate demand of future wireless service. However, offloaded users suffer from strong inter-tier interference, which reduces the benefits of offloading and is one of the main limiting factors of system performance. In this paper, we investigate an interference nulling (IN) scheme in improving system performance by carefully managing the inter-tier interference to the offloaded users in downlink two-tier HetNets with multi-antenna base stations. Utilizing tools from stochastic geometry, we first derive a tractable expression for the rate coverage probability of the IN scheme. Then, by studying its order, we obtain the optimal design parameter, i.e., the degree of freedom that can be used for IN, to maximize the rate coverage probability. Finally, we analyze the rate coverage probabilities of the simple offloading scheme without interference management and the multi-antenna version of the almost blank subframes (ABS) scheme in 3GPP LTE, and compare the performance of the IN scheme with these two schemes. Both analytical and numerical results show that the IN scheme can achieve good performance gains over both of these two schemes, especially in the large antenna regime.

We investigate the impact of channel estimation on the performance of downlink random cellular networks. First, we derive a new closed-form expression for the coverage probability under certain practical conditions. We show that the coverage probability is dependent on the user and base station (BS) densities solely through their ratio for arbitrary pilot-training length. Next, we derive the optimal pilot-training length that maximizes the area spectral efficiency (ASE) in several asymptotic regimes, and capture the dependence of this optimal length on the ratio between the user and BS densities. The ASE loss due to training is shown to be less significant in small cell networks with a larger base station density.

We investigate the impact of channel estimation (CE) on the performance of point-to-point transmission schemes in wireless ad hoc networks. We first derive a new closed-form expression for the outage probability when the minimum mean square error estimator is utilized for CE, and show that the training-pilot length should increase as a linear function of the network intensity to maintain a fixed CE quality. Next, we derive the optimal training-pilot length which maximizes the transmission capacity under interference-limited conditions, and show that this optimal length increases with the frame length according to a square-root law.

We develop a general framework for the analysis of a broad class of point-to-point linear multiple-input multiple-output (MIMO) transmission schemes in decentralized wireless ad hoc networks. New general closed-form expressions are derived for the outage probability, throughput and transmission capacity. For the throughput, we investigate the optimal number of data streams in various asymptotic regimes, which is shown to be dependent on different network parameters. For the transmission capacity, we prove that it scales linearly with the number of antennas, provided that the number of data streams also scales linearly with the number of antennas, in addition to meeting some mild technical conditions. We also characterize the optimal number of data streams for maximizing the transmission capacity. To make our discussion concrete, we apply our general framework to investigate three popular MIMO schemes, each requiring different levels of feedback. In particular, we consider eigenmode selection with MIMO singular value decomposition, multiple transmit antenna selection, and open-loop spatial multiplexing. Our analysis of these schemes reveals that significant performance gains are achieved by utilizing feedback under a range of network conditions.

In this paper, we investigate the benefits of providing limited-feedback and using transmit antenna selection (TAS) in ad hoc networks. We find that the TAS scheme can provide throughput gains of up to 50% compared to the non-feedback scheme. We also find that the performance gains of the TAS scheme are more significant for low path loss exponents and single-antenna transmission. Our results are obtained by deriving new closed-form expressions for the network throughput and transmission capacity. Moreover, we also propose design guidelines for TAS to determine the optimal number of antennas used for transmission.