Signal-to-interference-plus-noise Ratio Distribution Research Articles

The Meta Distribution of SINR in UAV-Assisted Cellular Networks

Mounting compact and lightweight base stations on unmanned aerial vehicles (UAVs) is a cost-effective and flexible solution to provide seamless coverage on the existing terrestrial networks. While the coverage probability in UAV-assisted cellular networks has been widely investigated, it provides only the first-order statistic of signal-to-interference-plus-noise ratio (SINR). In this paper, to analyze high-order statistics of SINR and characterize the disparity among individual links, we provide a meta distribution (MD)-based analytical framework for UAV-assisted cellular networks, in which the probabilistic line-of-sight channel and realistic antenna pattern are taken into account for air-to-ground transmissions. To accurately characterize the interference from UAVs, we relax the widely applied uniform off-boresight angle (OBA) assumption and derive the exact distribution of OBA. Using stochastic geometry, for both steerable and vertical antenna scenarios, we obtain mathematical expressions for the moments of condition success probability, the SINR MD, and the mean local delay. Moreover, we study the asymptotic behavior of the moments as network density approaches infinity. Numerical results validate the tightness of the theoretical results and show that the uniform OBA assumption underestimates the network performance, especially in the regime of moderate altitude of UAV. We also show that when UAVs are equipped with steerable antennas, the network coverage and user fairness can be optimized simultaneously by carefully adjusting the UAV parameters.

On the Distribution of SINR for Widely Linear MMSE MIMO Systems With Rectilinear or Quasi-Rectilinear Signals

Although the widely linear least mean square error (WLMMSE) receiver has been an appealing option for multiple-input-multiple-output (MIMO) wireless systems, a statistical understanding on its pose-detection signal-to-interference-plus-noise ratio (SINR) in detail is still missing. To this end, we consider a WLMMSE MIMO transmission system with rectilinear or quasi-rectilinear (QR) signals over the uncorrelated Rayleigh fading channel and investigate the statistical properties of its SINR for an arbitrary antenna configuration with $N_t$ transmit antennas and $N_r$ receive ones. We first derive an analytic probability density function (PDF) of the SINR in terms of the confluent hypergeometric function of the second kind, for WLMMSE MIMO systems with an arbitrary $N_r$ and $N_t=2, 3$. For a more general case in practice, i.e., $N_t>3$, we resort to the moment generating function to obtain an approximate but closed form PDF under some mild conditions, which, as expected, is more Gaussian-like as $2N_r-N_t$ increases. The so-derived PDFs are able to provide key insights into the WLMMSE MIMO receiver in terms of the outage probability, the symbol error rate, and the diversity gain, all presented in closed form. In particular, its diversity gain and the gain improvement over the conventional LMMSE one are explicitly quantified as $N_r-(N_t-1)/2$ and $(N_t-1)/2$, respectively. Finally, Monte Carlo simulations support the analysis.

Meta Distribution of the SINR for mmWave Cellular Networks With Clusters

In order to satisfy the requirement of extremely high data rate in traffic hotspot regions, millimeter wave (mmWave) has attracted significant attention in wireless communication networks. While the coverage performance of mmWave networks based on the distribution of signal-to-interference-plus-noise ratio (SINR) has been widely studied, it provides only very limited information on the link reliability. In this paper, we provide a fine-grained performance analysis of the mmWave networks with hotspots. Specifically, we first establish a general and tractable framework to investigate the performance of mmWave networks using the Poisson cluster process integrated with several features of the mmWave band. Both open and closed association strategies are considered. To show what fraction of users in the networks achieves target reliability when the SINR is given, we derive the tier association probability and the moments of the conditional SINR distribution, based on which the exact meta distributions of SINR are given. Interestingly, in clustered mmWave networks, the widely used standard and generalized beta approximations do not work well when the blockage effect is severe. To resolve this issue, we provide a modified approximation by scaling the standard beta distribution, which is shown to be closer to the exact results. We conduct extensive simulations to study the impact of mmWave and deployment features on the performance of clustered mmWave networks. Numerical results reveal that the optimal scattering variance of mmWave base stations scales with the cluster size to maximize the number of concurrent reliable links, and increasing the antenna directivity results in more reliable communications than elevating the transmit power of mmWave base stations.

Interference-Based QoS and Capacity Analysis of VANETs for Safety Applications

Whether the current IEEE 802.11p communication system meets the stringent quality of service (QoS) requirements for safety applications or not is still not very clear. Signal-to-interference-plus-noise ratio (SINR) distribution plays a primary role in quantifying the QoS as well as link capacity of IEEE 802.11p in one-dimensional (1-D) highway and two-dimensional (2-D) intersection road. Most of the analytical models based on stochastic geometry assumed ALOHA access to analyze the SINR distribution, while few of the works developed the stochastic geometry based model considering CSMA access but derived the SINR distribution utilizing statistical estimator. On the other hand, the current interference based probability analytic model for the SINR distribution limit the 1-D extension to 2-D, due to the very high numerical computational complexity at 2-D. In this paper, we propose an analytic model under more general non-homogeneous Poisson process (NHPP) node distribution, more general channel fading model ( Nakagami ) with path loss, and noise, for the study of QoS and capacity of VANET for BSM based safety applications in both 1-D highway and 2-D intersection road. The proposed model derives QoS and capacity of VANET BSM broadcast through evaluation of SINR distribution using probability theory and ordered statistics, which has much lower computational complexity compared with the unordered statistic model. The proposed model is validated by NS2 simulation and extended to the derivation of other QoS metrics such as packet reception probability, packet reception ratio, and broadcast link capacity, etc. The performance comparisons between 1-D and 2-D are implemented, and the QoS sensitivity analyses regarding the extension to multi-intersection as well as enlarging interference range are discussed.

A Full Second-Order Analysis of the Widely Linear MVDR Beamformer for Noncircular Signals

A full performance analysis of the widely linear (WL) minimum variance distortionless response (MVDR) beamformer is introduced. While the WL MVDR is known to outperform its strictly linear counterpart, the Capon beamformer, for noncircular complex signals, the existing approaches provide limited physical insights, since they explicitly or implicitly omit the complementary second-order (SO) statistics of the output interferences and noise (IN). To this end, we exploit the full SO statistics of the output IN to introduce a full SO performance analysis framework for the WL MVDR beamformer. This makes it possible to separate the overall signal-to-interference plus noise ratio (SINR) gain of the WL MVDR beamformer w.r.t. the Capon one into the individual contributions along the in-phase (I) and quadrature (Q) channels. Next, by considering the reception of the unknown signal of interest (SOI) corrupted by an arbitrary number of orthogonal noncircular interferences, we further unveil the distribution of SINR gains in both the I and Q channels, and show that in almost all the spatial cases, these performance advantages are more pronounced when the SO noncircularity rate of the interferences increases. Illustrative numerical simulations are provided to support the theoretical results.

Optimum Combiner for Spatially Correlated Nakagami-m Fading Channels

This paper proposes a novel optimum combiner that raises the time-averaged signal-to-interference-plus-noise ratio (SINR) for maximal-ratio combining (MRC) reception over spatially correlated Nakagami-m fading channels. By exploiting the principal component analysis (PCA) with eigenvalue decomposition (EVD) of the covariance matrix analytically evaluated offline, a complete set of orthonormal basis functions can be obtained. A decorrelation process analyzes and then projects the received signal into the space spanned by the basis functions. In accordance with the theorem of irrelevance, a principal component selection combining (PCSC) method is proposed to remove components in a few dimensions in which SINRs are considered low to raise the resulting time-averaged SINR on the subsequent MRC reception. The proposed technique also avoids noise enhancement occurring with MRC reception in the scenario where noises on different branches are correlated. The SINR distribution, level-crossing rate (LCR) and average fade duration (AFD) are derived. Based on a novel scattering model interpretation, a simulator consisting of spatially correlated Nakagami-m fading channels is developed according to the analytically evaluated covariance matrix. Computer simulations show that the proposed optimum combiner not only decreases interference and noise from the irrelevant subspace to achieve higher time-averaged SINR and lower AFD but also significantly reduces the complexity required for subsequent signal processing.

Outage Analysis for MISO Zero-Forcing Precoding With Outdated CSI

Zero-forcing precoding is a commonly-used multiple-user, multiple-input multiple-output beamforming technique. Applying such precoding, the signal-to-interference-plus-noise ratio (SINR) statistics with outdated channel state information, which involve various projections related to the multi-dimensional channel vectors and precoding vectors, have never been explicitly derived. In this paper, for the multiple-input single-output scenario with uniform power allocation, the distributions of these projections are derived, and then the SINR distribution and the conditional outage probability can be computed using those distributions.

SINR and Rate Distributions for Downlink Cellular Networks

Signal-to-Interference-plus-Noise Ratio (SINR) measures the quality of the radio link between a base station and a User Equipment (UE). This quality indicator is important for the operator as it is used to measure and to optimize network coverage and the maximum user bitrate (which can be deduced from the SINR using the Shannon formula). In this paper, we study the SINR distribution for the downlink assuming that the received signals from serving and interfering cells undergo a path-loss and log-normal shadowing fading. We show that SINR can be approximated by a log-normal random variable and we give analytical expressions of characteristics parameters of its distribution. We then derive the average SINR expression. Also, we give a closed-expression of the rate probability density function and the outage probability and we obtain closed expressions of the average rate and lower and upper bounds of the average rate. For validation, we first compare theoretical results to Monte-Carlo network simulations and show that all the theoretical curves approximate well those obtained by simulations. Then using real measurements obtained by a measurement campaign, we validate the SINR distribution assumption. Based on a test of normality, we find that the recorded SINR samples are normally distributed in the logarithmic domain. We also show that the theoretical probability density function curves and the histogram of the measured samples of SINR are close.

Modeling and Analysis for Data Collection in Duty-Cycled Linear Sensor Networks With Pipelined-Forwarding Feature

Due to the vast demand for monitoring a structure or area in linear topology, linear sensor networks (LSNs) have recently attracted plenty of attention. Since sensor nodes are usually battery-powered, duty-cycling techniques have been widely studied to improve energy efficiency, which, however, introduces a significant issue known as sleep latency. Thereafter pipelined forwarding has been proposed in the literature as a promising way to alleviate this issue. This paper focuses on interference analysis for data collection services in a multihop LSN running a duty-cycling and pipelined-forwarding protocol, where multiple concurrent transmissions along a data collection path can severely interfere with each other. We first obtain the nodal distance distributions associated with all concurrent transmissions. Based on the obtained distance distributions and the path-loss model in an interference-limited environment, we analyze the distributions of signal-to-interference-plus-noise ratio (SINR) and link capacity. The obtained SINR distribution indicates the link outage probability at a given SINR threshold. By investigating the transmission which receives the strongest cumulative interference, our model can provide useful guidelines for duty cycle setting to achieve a desired network performance.

On the Distribution of SINR for MMSE MIMO Systems

While the performance analysis of linear zero-forcing (ZF) and minimum mean-square error (MMSE) receivers has received much attention, there has been no exact closed-form distribution of signal-to-interference-plus-noise ratio (SINR) for MMSE multiple-input multiple-output (MIMO) systems in the arbitrary fading environments for over the past 20 years. In this paper, an exact and general distribution of SINR for MMSE MIMO systems is presented under uncorrelated Rayleigh fading environments. We start our analysis by finding regular patterns from the probability density function (PDF) of SINR for small dimensions, and using the regular patterns, we extend the PDF to arbitrary dimensions. From the exact and general PDF of SINR for MMSE MIMO systems, the cumulative distribution function and the moment-generating function are derived in terms of the incomplete gamma function and the confluent hypergeometric function of the second kind, respectively. As applications, the error probability, outage probability, and achievable sum rate are investigated by using the distribution of SINR for MMSE MIMO systems. Most notably, the achievable sum rates for ZF and MMSE MIMO systems are defined by using the Meijer $G$ -function, which are the first closed-form expressions in the literature.

SINR and Rate Meta Distributions for HCNs With Joint Spectrum Allocation and Offloading

This paper focuses on the meta distributions of the signal-to-interference-plus-noise ratio (SINR) and user-perceived rate in heterogeneous cellular networks (HCNs) with multiple tiers of base stations. On the one hand, it is desirable to offload users to small cells to alleviate the congestion in macrocells; on the other hand, such offloading would in turn cause an SINR degradation of the offloaded users, which needs to be mitigated through interference avoidance based on resource partitioning. Thus, in consideration of both aspects, we provide a general framework for modeling and analyzing joint spectrum allocation and offloading in an HCN using the $K$ -tier homogeneous-independent Poisson model. With it, we derive the per-tier and overall moments of the conditional SINR and rate distribution given the point process, based on which the exact meta distributions are given. We show that the conventional SINR or rate performance evaluated at the typical user (averaging over all tiers and links in the HCN), by itself, is insufficient, and a much sharper version provided by the meta distribution is required in conjunction with the expected value to give a thorough assessment of the benefits of joint resource partitioning and offloading in HCNs.

Coverage and Cell-Edge Sum-Rate Analysis of mmWave Massive MIMO Systems With ORP Schemes and MMSE Receivers

In this study, we consider the downlink of millimeter-wave massive multiple-input multiple-output systems that employ orthogonal random precoding (ORP) and minimum-mean-square-error (MMSE) receivers. In the ORP scheme, a precoding matrix consisting of orthogonal vectors is utilized at the transmitter, which provides beamforming gains to enhance the maximum signal-to-interference-plus-noise ratio (SINR) at the receivers. In this study, the ability of the ORP scheme with MMSE receivers to extend the cell coverage and its sum-rate performance for cell-edge users are investigated. In particular, we first derive the approximate distribution of the maximum SINR at the output of the MMSE receiver. Then, to analyze and optimize the ORP scheme with MMSE receivers in terms of coverage and sum-rate performance, the analytical expressions for the downlink coverage probability and sum rate are derived. It is shown that there is a tradeoff between coverage and sum-rate performance in the ORP scheme. In particular, a smaller number of precoding vectors provides larger coverage; however, it leads to a lower sum rate. To achieve optimal tradeoff between coverage and sum rate for the ORP scheme, we propose using multiple random precoder groups over multiple time slots. It is shown that the proposed scheme is capable of significantly enhancing coverage performance while preserving an acceptable sum rate for cell-edge users. The simulation results validate the analytical findings.

Performance analysis for 5G beamforming heterogeneous networks

The heterogeneous network (HetNet) is an attractive solution to solve limited spectral efficiency, the increasing traffic demands, and crowded coverage. In 5G, massive multiple-input multiple-output and millimeter-wave technologies are considered to explore high array gain and alleviate high path loss with beamforming. In this paper, we propose a general tractable model for signal-to-interference-plus-noise ratio (SINR) analysis with cell expansion and beamforming for 5G. In this HetNet, each layer is characterized by particular parameters such as base station (BS) density, transmission power, beam gain, beamwidth, propagation loss, and bias factor. In our model, the expressions of outage probability for each layer and the whole network, which represent the SINR distributions, are derived through a typical user. We also analyze the rate performance by the minimum average user rates and the rate coverage probabilities. Furthermore, the spectrum reuse strategy, some layers are spectrum separation while others are spectrum sharing, are considered to consistent with the existing and future cellular network. From the simulations, system performance can be greatly improved by beamforming and affected by beamwidth, and the optimal bias changes with BS density and path loss. Furthermore, the proposed method provides practical deployment guidelines with some determined parameters.

Closed-formed distribution for the SINR of MMSE-detected MIMO systems and performance analysis

In this paper, we investigate the error performance of multiple-input multiple-output (MIMO) wireless communications systems using minimum mean-square error (MMSE) detection. Particularly, a new closed-form statistical distribution for the output signal-to-interference-plus-noise ratio (SINR) of MMSE receiver is derived, for independent Rayleigh fading channels. The expression for the distribution of SINR is shown to be a linear combination of gamma distributions and polynomial of 11+x, where x is the SINR. Base on the derived distribution for the SINR, closed-form and approximated expressions for the symbol error probability (SEP) of quadrature amplitude modulation (QAM) and phase shift keying (PSK) signaling are obtained, respectively. The derived SINR density and SEP are valid for arbitrary number of transmit and receive antennas. Furthermore, a reduced complexity approximation is introduced to obtain the SINR distribution and SEP performance of MMSE-Detected MIMO Systems with a large number of antennas. The provided simulation results confirm the validity of our theoretical analysis for both the SINR and SEP.

SINR Distributions for Robust MIMO TX-Power Minimization With Controlled Outage

We offer a simple and comprehensive alternative to existing robust network optimization methods as a solution to the long-standing problem of cellular network optimization under imperfect channel state information at the transmitter (CSIT) conditions. Specifically, instead of relying on a relaxation of statistical constraints into deterministic convex equivalents, as done in current literature and which leads to tradeoffs between robustness and optimality, we derive accurate models for the distributions of users’ signal-to-interference-plus-noise ratio (SINRs), conditioned on constraint-matching SINR estimates obtained under imperfect CSIT. Using these distributions, precise accounting and compensation for imperfection on CSIT, as well as statistical outage matching, can be achieved directly via the design of deterministic, instantaneous, and convex SINR constraints. Simulated comparison with the state of the art demonstrates the significant performance gain achieved by the proposed solution.

Massive MIMO Uplink Scheme Design and System-Level Performance Analysis

The intercell interference in massive multiple-input-multiple-output uplink consists of both correlated and uncorrelated components, where the former is due to pilot contamination and the latter is usually neglected in most of the existing literature. In this paper, we show that the uncorrelated intercell interference is actually not negligible for reasonably many antennas at the base station. Hence, a novel and general uplink performance analysis framework is established to take the uncorrelated interference into account. Specifically, we investigate the tradeoff between pilot overhead and uplink signal-to-interference-plus-noise ratio (SINR) in four uplink transmission schemes. Without cell coordination, the conventional uplink scheme and the soft pilot reuse scheme are evaluated. Compared with the former one, the soft pilot reuse scheme has higher mitigation efficiency on correlated intercell interference. However, the uncorrelated intercell interference cannot be mitigated without cell coordination. With cell coordination, we first evaluate the scheme that the pilot information can be shared via backhaul. Hence, both the correlated and uncorrelated interference can be canceled effectively. We also propose and analyze a novel pilot extension scheme in the cell coordination scenario, which could address different preferences of both cell-edge and cell-center users. In all the above four schemes, the asymptotic expressions of uplink SINR for arbitrary user are first obtained. Based on them, we derive the distribution of uplink SINR by considering the randomness of interfering users’ locations. It is shown that the analytical results match the numerical simulation tightly. Besides, both analytical and numerical results demonstrate the performance gain of the proposed scheme.

Semianalytical Approach to the PDF of SINR in HPHT and LPLT Single-Frequency Networks

Single-frequency networks (SFN) are widely adopted in terrestrial broadcast networks based on high-power high-tower (HPHT) deployments. The mobile broadcasting standard Evolved Multimedia Broadcast Multicast Service (eMBMS) has been enhanced in Release 14 to enable SFN operation with larger CP duration which may allow for the deployment of large area SFNs and even the combined operation between HPHT and low-power low-tower (LPLT) cellular stations. The knowledge of the signal-to-interference-plus-noise ratio (SINR) distribution over an SFN area may facilitate the selection of transmission parameters according to the network topology. This paper presents a semianalytical method for the calculation of the SINR distribution in SFNs with low computational complexity compared to Monte Carlo simulations. The method, which builds on previous work developed for cellular communications, is applied to HPHT+LPLT SFNs and evaluated against different transmission and network parameters.

A Fine-Grained Analysis of Millimeter-Wave Device-to-Device Networks

Enabling device-to-device (D2D) communications in millimeter-wave (mm-wave) networks is of critical importance for the next-generation mobile networks to support very high data rates (multi-gigabits-per-second) for mobile devices. In this paper, we provide a fine-grained performance analysis of the mm-wave D2D communication networks. Specifically, we first establish a general and tractable framework to investigate the performance of mm-wave D2D networks using the Poisson bipolar model integrated with several features of the mm-wave band. To show what fraction of users in the network achieve target reliability if the required signal-to-interference-plus-noise ratio (SINR) (or QoS requirement) is given, we derive the meta distributions of the SINR and the data rate. Interestingly, in mm-wave D2D networks, the standard beta approximation for the meta distribution does not work very well when highly directional antenna arrays are used or the node density is small. To resolve this issue, we provide a modified approximation by using higher moments of the conditional SINR distribution, which is shown to be closer to the exact result. On this basis, we also derive the mean local delay and spatial outage capacity to provide a comprehensive investigation on the impact of mm-wave features on the performance of D2D communication.

Location-based achievable signal-to-interference-plus-noise ratio in visible light communication network with different topology parameters

In visible light communication (VLC) networks, light-emitting diodes (LEDs) as transmitters are densely deployed so that the interference between cells is serious. A variety of methods about interference management have been proposed to improve the signal-to-interference-plus-noise ratio (SINR). However, the achievable SINR has not been studied yet. We obtain the achievable signal-to-interference ratio and improve the SINR with the derived results. A simple analytic solution is provided to show the achievable SINR of two cells under a linear model. Furthermore, we discuss the effect of different parameters of the SINR distribution under the linear model.

Closed-Form Performance Bounds for Stochastic Geometry-Based Cellular Networks

In this paper, we study the performance of partial-fading and Rayleigh fading wireless networks using stochastic geometry. The aim is to provide closed-form bounds for the signal-to-interference-plus-noise ratio (SINR) distribution, average Shannon rate, and outage rate. We first characterize the SINR distribution of partial-fading channels through the Laplace transform of the inverted SINR. Since most communication systems are interference limited, we also consider the case of negligible noise power, and derive the upper and lower bounds for the signal-to-interference ratio distribution under both partial fading and fading cases. These bounds are of closed forms and thus more convenient for theoretical analysis. Based on these derivations, we obtain closed-form bounds for the average Shannon and outage rates. These results are useful for investigating the fifth-generation communication systems, for example massive multi-antenna networks as described in our illustrative example.