We consider data transmission through a time-selective, correlated (first-order Markov) Rayleigh fading channel subject to an average power constraint. The channel is estimated at the receiver with a pilot signal, and the estimate is fed back to the transmitter. The estimate is used for coherent demodulation, and to adapt the data and pilot powers. We explicitly determine the optimal pilot and data power control policies in a continuous-time limit where the channel state evolves as an Ornstein-Uhlenbeck diffusion process, and is estimated by a Kalman filter at the receiver. The optimal pilot policy switches between zero and the maximum (peak-constrained) value (``bang-bang'' control), and approximates the optimal discrete-time policy at low Signal-to-Noise Ratios (equivalently, large bandwidths). The switching boundary is defined in terms of the system state (estimated channel mean and associated error variance), and can be explicitly computed. Under the optimal policy, the transmitter conserves power by decreasing the training power when the channel is faded, thereby increasing the data rate. Numerical results show a significant increase in achievable rate due to the adaptive training scheme with feedback, relative to constant (non-adaptive) training, which does not require feedback. The gain is more pronounced at relatively low SNRs and with fast fading. Results are further verified through Monte Carlo simulations.
The secrecy outage performance of wireless communication systems operating over spatially correlated composite fading channels is analyzed in this paper. We adopt a multiplicative composite channel model for both the legitimate communication link and the link between the eavesdropper and the legitimate transmitter, consisting of Nakagami-$m$ distributed small-scale fading and shadowing (large-scale fading) modeled by the Gamma distribution. We consider the realistic case where small-scale fading between the links is independent, but shadowing is arbitrarily correlated, and present novel analyt…
In this paper, we investigate the impact of side information (SI) on the performance of physical layer security (PLS) under correlated fading channels. By considering non-causally known SI at the transmitter and exploiting the copula technique to describe the fading correlation, we derive closed-from expressions for the average secrecy capacity (ASC) and secrecy outage probability (SOP) under positive/negative dependence conditions. We indicate that considering such knowledge at the transmitter is beneficial for system performance and ensures reliable communication with higher rates, as it imp…
This paper investigates the problem of power allocation for hybrid automatic repeat request (HARQ) schemes over time-correlated Nakagami-m fading channels under outage constraint. The presence of time correlation complicates the power allocation problem due to the involvement of multiple correlated fading channels. Under a general time-correlated Nakagami-m fading channel with exponential correlation, outage probabilities for three widely adopted HARQ schemes, including Type I HARQ, HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR), are first derived. With thes…
This paper proposes a general analytical approach to derive the outage probability of hybrid automatic repeat request with incremental redundancy (HARQ-IR) over correlated fading channels in closed-form. Unlike prior analyses, the consideration of channel correlation is one of the key reasons making the outage analysis involved. Using conditional Mellin transform, the outage probability of HARQ-IR over correlated Rayleigh fading channels is exactly expressed as a mixture of outage probabilities of HARQ-IR over independent Nakagami fading channels, where the weights are negative multinomial pro…
This paper considers the uplink (UL) of a multi-cell Massive MIMO (multiple-input multiple-output) system with spatially correlated Rician fading channels. The channel model is composed of a deterministic line-of-sight (LoS) path and a stochastic non-line-of-sight (NLoS) component describing a spatially correlated multipath environment. We derive the statistical properties of the minimum mean squared error (MMSE) and least-square (LS) channel estimates for this model. Using these estimates for maximum ratio (MR) combining, rigorous closed-form UL spectral efficiency (SE) expressions are derive…
This paper analyzes the performance of cooperative hybrid automatic repeat request with incremental redundancy (HARQ-IR) and proposes a new approach of outage probability approximation for performance analysis. A general time-correlated Nakagami fading channel covering fast fading and Rayleigh fading as special cases is considered here. An efficient inverse moment matching method is proposed to approximate the outage probability in closed-form. The effect of approximation degree is theoretically analyzed to ease its selection. Moreover, diversity order of cooperative HARQ-IR is analyzed. It is…
Reinforcement algorithms refer to the schemes where the results of the previous trials and a reward-punishment rule are used for parameter setting in the next steps. In this paper, we use the concept of reinforcement algorithms to develop different data transmission models in wireless networks. Considering temporally-correlated fading channels, the results are presented for the cases with partial channel state information at the transmitter (CSIT). As demonstrated, the implementation of reinforcement algorithms improves the performance of communication setups remarkably, with the same feedback…
This study investigates the mean capacity of multiple-input multiple-output (MIMO) systems for spatially semi-correlated flat fading channels. In reality, the capacity degrades dramatic due to the channel covariance (CC) when correlations exist at the transmitter or receiver or on both sides. Most existing works have so far considered the traditional channel covariance matrices that have not been entirely constructed. Thus, we propose an iterative channel covariance (ICC) matrix using a matrix splitting (MS) technique with a guaranteed zero correlations coefficient in the case of the downlink …
Time-varying fast fading channels present a major challenge in the design of wireless communication systems. Pilot Symbol Assisted Modulation (PSAM) has been introduced to mitigate the effects of fading and allow coherent demodulation. Our work studies the performance of \emph{non-feedback} adaptive PSAM scheme over time-varying Rayleigh fading channels. A modular method is introduced for computing the rates in an efficient manner. Moreover, four transmission policies are analyzed and we show how optimal training in terms of duration and power allocation varies with the channel conditions and …
We develop a characterization of fading models, which assigns a number called logarithmic Jensen's gap to a given fading model. We show that as a consequence of a finite logarithmic Jensen's gap, approximate capacity region can be obtained for fast fading interference channels (FF-IC) for several scenarios. We illustrate three instances where a constant capacity gap can be obtained as a function of the logarithmic Jensen's gap. Firstly for an FF-IC with neither feedback nor instantaneous channel state information at transmitter (CSIT), if the fading distribution has finite logarithmic Jensen's…
In this paper, performance of hybrid automatic repeat request with incremental redundancy (HARQ-IR) over Rayleigh fading channels is investigated. Different from prior analysis, time correlation in the channels is considered. Under time-correlated fading channels, the mutual information in multiple HARQ transmissions is correlated, making the analysis challenging. By using polynomial fitting technique, probability distribution function of the accumulated mutual information is derived. Three meaningful performance metrics including outage probability, average number of transmissions and long te…
VLSF Decoding with Reliability Guarantees over Correlated Noncoherent Fading Channels
Inria（法国国家信息与自动化研究所）；Université de la Polynésie française（法属波利尼西亚大学）；Princeton University（普林斯顿大学）；Univ. Rennes, INSA, CNRS, IETR UMR 6164（雷恩大学、国立应用科学学院、法国国家科学研究中心、信息电子工程研究所）；Inria, INSA Lyon, CITI Laboratory（法国国家信息与自动化研究所、里昂国立应用科学学院、信息与通信技术创新实验室）
This paper analyzes Type I hybrid automatic repeat request (HARQ) over time-correlated Rayleigh fading channels. Due to the presence of channel time correlation, the analysis is more challenging than the prior analysis in the literature. Outage probability is first derived as a weighted sum of joint CDF of multiple independent Gamma random variables based on an infinite series representation. A truncation method is proposed for efficient computation of the outage probability and it is proved that the truncation error decreases exponentially with the truncation order. Asymptotic outage probabil…
This paper addresses the problem of rate selection for the cooperative hybrid automatic repeat request with chase combination (HARQ-CC) system, where time correlated Nakagami-m fading channels are considered. To deal with this problem, the closed-form cumulative distribution function (CDF) for the combine SNRs through maximal ratio combining (MRC) is first derived as a generalized Fox's $\bar H$ function. By using this result, outage probability and delay-limited throughput (DLT) are derived in closed forms, which then enables the rate selection for maximum DLT. These analytical results are va…
The existing investigations on artificial noise (AN) security systems assumed that only null spaces is used to send AN signals, and all eigen-subchannels should be used to transmit messages. Our previous work proposed an AN scheme that allocates some of eigen-subchannels to transmit AN signals for improving secrecy rates. Nevertheless, our previous work considered only uncorrelated MIMO Rayleigh fading channels. In fact, the correlations among antennas exist in realistic scattering channel environments. In this paper, we extend our previous AN scheme to spatially correlated Rayleigh fading cha…
This paper considers multi-cell Massive MIMO (multiple-input multiple-output) systems where the channels are spatially correlated Rician fading. The channel model is composed of a deterministic line-of-sight (LoS) path and a stochastic non-line-of-sight (NLoS) component describing a practical spatially correlated multipath environment. We derive the statistical properties of the minimum mean squared error (MMSE), element-wise MMSE (EW-MMSE), and least-square (LS) channel estimates for this model. Using these estimates for maximum ratio (MR) combining and precoding, rigorous closed-form uplink …
In this paper, we investigate the impact of correlated fading on the performance of wireless multiple access channels (MAC) in the presence and absence of side information (SI) at transmitters, where the fading coefficients are modeled according to the Fisher-Snedecor F distribution. Specifically, we represent two scenarios: (i) clean MAC (i.e, without SI at transmitters), (ii) doubly dirty MAC (i.e., with the non-causally known SI at transmitters). For both system models, we derive the closedform expressions of the outage probability (OP) as well as the average capacity (AC) under independent…
In this paper, outage performance of hybrid automatic repeat request with incremental redundancy (HARQ-IR) is analyzed. Unlike prior analyses, time-correlated Nakagami-$m$ fading channel is considered. The outage analysis thus involves the probability distribution analysis of a product of multiple correlated shifted Gamma random variables and is more challenging than prior analyses. Based on the finding of the conditional independence of the received signal-to-noise ratios (SNRs), the outage probability is exactly derived by using conditional Mellin transform. Specifically, the outage probabil…
The downlink of a wireless network where multi-antenna base stations (BSs) communicate with single-antenna mobile stations (MSs) using maximal ratio transmission (MRT) is considered here. The locations of BSs are modeled by a homogeneous Poisson point process (PPP) and the channel gains between the multiple antennas of each BS and the single antenna of each MS are modeled as spatially arbitrarily correlated Rayleigh random variables. We first present novel closed-form expressions for the distribution of the power of the interference resulting from the coexistence of one intended and one uninte…
Most of the prior works on designing codebooks for limited feedback systems have not considered the presence of strong line-of-sight (LOS) channel component. This paper proposes the design of polar-cap codebook (PCC) for multipleinput single-output (MISO) limited feedback systems subject to Rician fading channels. The codewords of the designed PCC are adaptively constructed according to the instantaneous strength of the LOS channel component. Simulation results show that the codebook can significantly enhance the performance of transmit beamforming in terms of received signal-to-noise ratio (S…
In cognitive multiple access networks, feedback is an important mechanism to convey secondary transmitter primary base station (STPB) channel gains from the primary base station (PBS) to the secondary base station (SBS). This paper investigates the optimal sum-rate capacity scaling laws for cognitive multiple access networks in feedback limited communication scenarios. First, an efficient feedback protocol called $K$-smallest channel gains ($K$-SCGs) feedback protocol is proposed in which the PBS feeds back the $\K$ smallest out of $N$ STPB channel gains to the SBS. Second, the sum-rate perfor…
Massive multiple-input--multiple-output (MIMO) systems can suffer from coherent intercell interference due to the phenomenon of pilot contamination. This paper investigates a two-layer decoding method that mitigates both coherent and non-coherent interference in multi-cell Massive MIMO. To this end, each base station (BS) first estimates the channels to intra-cell users using either minimum mean-squared error (MMSE) or element-wise MMSE (EW-MMSE) estimation based on uplink pilots. The estimates are used for local decoding on each BS followed by a second decoding layer where the BSs cooperate t…
Prior asymptotic performance analyses are based on the series expansion of the moment-generating function (MGF) or the probability density function (PDF) of channel coefficients. However, these techniques fail for lognormal fading channels because the Taylor series of the PDF of a lognormal random variable is zero at the origin and the MGF does not have an explicit form. Although lognormal fading model has been widely applied in wireless communications and free-space optical communications, few analytical tools are available to provide elegant performance expressions for correlated lognormal c…
We consider large-scale fading precoding (LSFP), which is a two-layer precoding scheme in the downlink of multi-cell massive MIMO (multiple-input multiple-output) systems to suppress inter-cell interference. We obtain the closed-form spectral efficiency (SE) with LSFP at the central network controller and maximum ratio precoding at the base stations (BSs) using the linear minimum mean-squared error or least squares channel estimators. The LSFP weights are designed based on the long-term channel statistics and two important performance metrics are optimized under the per-BS transmit power const…
We propose pilot reuse (PR) in single cell for massive multiuser multiple-input multiple-output (MIMO) transmission to reduce the pilot overhead. For spatially correlated Rayleigh fading channels, we establish a relationship between channel spatial correlations and channel power angle spectrum when the base station antenna number tends to infinity. With this channel model, we show that sum mean square error (MSE) of channel estimation can be minimized provided that channel angle of arrival intervals of the user terminals reusing the pilots are non-overlapping, which shows feasibility of PR ove…
The proposed research performs an analysis of the capacity higher-order statistics for a single-input multiple-output multiantenna wireless communication system equipped with a maximum-ratio combining scheme. It was assumed that the propagation multipath channel is described with the $κ-μ$ fading model with the correlated dominant components. Closed-form and asymptotic expressions were derived and applied to the problem of minimum capacity reliability (due to channel fluctuations, thus possible rate deterioration) and corresponding signal-to-noise ratio analysis. The performed computer simulat…
We carry out a theoretical analysis of the uplink (UL) of a massive MIMO system with per-user channel correlation and Rician fading, using two processing approaches. Firstly, we examine the linear minimum-mean-square-error receiver under training-based imperfect channel estimates. Secondly, we propose a statistical combining technique that is more suitable in environments with strong Line-of-Sight (LoS) components. We derive closed-form asymptotic approximations of the UL spectral efficiency (SE) attained by each combining scheme in single and multi-cell settings, as a function of the system p…
This paper proposes a unified framework for the effective rate analysis over arbitrary correlated and not necessarily identical multiple inputs single output (MISO) fading channels, which uses moment generating function (MGF) based approach and H transform representation. The proposed framework has the potential to simplify the cumbersome analysis procedure compared to the probability density function (PDF) based approach. Moreover, the effective rates over two specific fading scenarios are investigated, namely independent but not necessarily identical distributed (i.n.i.d.) MISO hyper Fox's H…
This paper presents a detailed secrecy outage performance analysis of correlated multi-antenna wiretap channels with three popular diversity combining schemes, namely maximal ratio combining, selection combining, and equal gain combining at the legitimate receiver. For single input multiple output wiretap channels, both exact and asymptotic expressions are derived for the secrecy outage probability (SOP) of these systems. The findings suggest that, compared with the scenario where all the channels are independent, correlation of the main channels alone increases the SOP by a factor of 1/ det(U…
We study the uplink performance of massive multiple-input multiple-output (MIMO) when users are equipped with multiple antennas. To this end, we consider a generalized channel model that accounts for line-of-sight propagation and spatially correlated multipath fading. Most importantly, we employ the Weichselberger correlation model, which has been shown to alleviate the deficiencies of the popular Kronecker model. The main contribution of this paper is a rigorous closed-form expression for the uplink spectral efficiency using maximum-ratio combining and minimum mean square error channel estima…
