We introduce and characterize the Multi-cluster Fluctuating Two-Ray (MFTR) fading channel, generalizingboththe fluctuating two-ray (FTR) and the κ-μ shadowed fading models through a more general yet equally mathematically tractable model. We derive all the chief probability functions of the MFTR model such as probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) in closed-form, having a mathematical complexity similar to other fading models in the state-of-the-art. We also provide two additional analytical formulations for the PDF and the CDF: (i) in terms of a continuous mixture of κ-μ shadowed distributions, and (ii) as an infinite discrete mixture of Gamma distributions. Such expressions enable to conduct performance analysis under MFTR fading bydirectlyleveraging readily available results for the κ-μ shadowed or Nakagami-mcases, respectively. We demonstrate that the MFTR fading model provides a much better fit than FTR and κ-μ shadowed models for small-scale measurements of channel amplitude in outdoor Terahertz (THz) wireless links. Finally, the performance of wireless communications systems undergoing MFTR fading is exemplified in terms of classical benchmarking metrics like the outage probability, both in exact and asymptotic forms, and the amount of fading.

We introduce, characterize and validate the independent fluctuating two-ray (IFTR) fading model, which consists of two specular (dominant) components that fluctuate independently, plus a diffuse one resulting from the reception of multiple scattered waves. The IFTR model complements the fluctuating two-ray (FTR) model, in which the specular components are fully correlated and fluctuate jointly. The chief probability functions of the received SNR of this new model, including the PDF, CDF and MGF, are given in closed-form. The IFTR model is empirically validated using measured data from Line-Of-Sight (LOS) millimeter-wave channels, showing a better fit than the FTR model and other models previously used in these channels, and providing a remarkable improvement at 73 GHz.

We present a general and tractable fading model for line-of-sight (LOS) scenarios, which is based on the product of two independent and non-identically distributed κ-μ shadowed power envelopes. Simple closed-form expressions for the probability density function, cumulative distribution function and moment-generating function are derived, which are as tractable as the corresponding expressions derived from a product of Nakagami-m random variables. This model simplifies the challenging characterization of LOS product channels, as well as combinations of LOS channels with non-LOS ones. We leverage these results to analyze performance measures of interest in the contexts of wireless powered and backscatter communications, where both forward and reverse links are inherently of LOS nature, as well as in device-to-device communications subject to composite fading. In these contexts, the proposed model shows a higher flexibility when fitting field measurements with respect to conventional approaches based on product distributions with deterministic LOS, together with a more complete physical interpretation of the underlying propagation characteristics.

This letter introduces a new approach to the problem of approximating the probability density function (PDF) and the cumulative distribution function (CDF) of a positive random variable. The novel approximation strategy is based on the analysis of a suitably defined sequence of auxiliary variables which converges in distribution to the target variable. By leveraging such convergence, simple approximations for both the CDF and PDF of the target variable are given in terms of the derivatives of its moment generating function (MGF). In contrast to classical approximation methods based on truncated series of moments or cumulants, our approximations always represent a valid distribution and the relative error between variables is independent of the variable under analysis. The derived results are then used to approximate the statistics of positive-definite real Gaussian quadratic forms, comparing our proposed approach with other existing approximations in the literature.

We provide some comments and subsequent corrections to a paper recently published in this Journal (see ibid., vol. 33, no. 1, pp. 111-119, Jan. 2015). More precisely, we show that the pdf for the κ-μ shadowed fading model given by S.L. Cotton cannot be obtained from the underlying statistical model proposed therein. To support this observation, we present a detailed mathematical analysis as well as some Monte Carlo simulations. We also demonstrate that by simply adopting the underlying statistical model for the κ-μ shadowed fading distribution proposed in an earlier and independent work by J.F. Paris enables the κ-μ shadowed pdf later presented by S.L. Cotton to be obtained.

The incomplete moment generating function (IMGF) has paramount relevance in communication theory, since it appears in a plethora of scenarios when analyzing the performance of communication systems. We here present a general method for calculating the IMGF of any arbitrary fading distribution. Then, we provide exact closed-form expressions for the IMGF of the very general κ-μ shadowed fading model, which includes the popular κ-μ, η-μ, Rician shadowed, and other classical models as particular cases. We illustrate the practical applicability of this result by analyzing several scenarios of interest in wireless communications: 1) physical layer security in the presence of an eavesdropper; 2) outage probability analysis with interference and background noise; 3) channel capacity with side information at the transmitter and the receiver; and 4) average bit-error rate with adaptive modulation, when the fading on the desired link can be modeled by any of the aforementioned distributions.

Emerging cellular technologies such as those proposed for use in 5G communications will accommodate a wide range of usage scenarios with diverse link requirements. This will necessitate operation over a versatile set of wireless channels ranging from indoor to outdoor, from line-of-sight (LOS) to non-LOS, and from circularly symmetric scattering to environments which promote the clustering of scattered multipath waves. Unfortunately, many of the conventional fading models lack the flexibility to account for such disparate signal propagation mechanisms. To bridge the gap between theory and practical channels, we consider κ-μ shadowed fading, which contains as special cases the majority of the linear fading models proposed in the open literature. In particular, we propose an analytic framework to evaluate the average of an arbitrary function of the signal-to-noise-plus-interference ratio (SINR) over κ-μ shadowed fading channels by using an orthogonal expansion with tools from stochastic geometry. Using the proposed method, we evaluate the spectral efficiency, moments of the SINR, and outage probability of a K-tier heterogeneous cellular network with K classes of base stations (BSs), differing in terms of the transmit power, BS density, shadowing, and fading characteristics. Building upon these results, we provide important new insights into the network performance of these emerging wireless applications while considering a diverse range of fading conditions and link qualities.

We introduce the fluctuating two-ray (FTR) fading model, a new statistical channel model that consists of two fluctuating specular components with random phases plus a diffuse component. The FTR model arises as the natural generalization of the two-wave with diffuse power (TWDP) fading model; this generalization allows its two specular components to exhibit a random amplitude fluctuation. Unlike the TWDP model, all the chief probability functions of the FTR fading model (PDF, CDF, and MGF) are expressed in closed-form, having a functional form similar to other state-of-the-art fading models. We also provide approximate closed-form expressions for the PDF and CDF in terms of a finite number of elementary functions, which allow for a simple evaluation of these statistics to an arbitrary level of precision. We show that the FTR fading model provides a much better fit than Rician fading for recent small-scale fading measurements in 28 GHz outdoor mm-wave channels. Finally, the performance of wireless communication systems over FTR fading is evaluated in terms of the bit error rate and the outage capacity, and the interplay between the FTR fading model parameters and the system performance is discussed. Monte Carlo simulations have been carried out in order to validate the obtained theoretical expressions.

We investigate the dynamic behavior of the stationary random process defined by a central complex Wishart matrix W(t) as it varies along a certain dimension t. We characterize the second-order joint cumulative distribution function (cdf) of the largest eigenvalue, and the second-order joint cdf of the smallest eigenvalue of this matrix. We show that both cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order joint cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit (NT) and receive (NR) antennas is similar. However, as NT is increased while keeping NR fixed, we see how the best and worst channels tend to have a similar rate of change.

This paper presents a new connection between the generalized Marcum-Q function and the confluent hypergeometric function of two variables, Φ3. This result is then applied to the closed-form characterization of the bivariate Nakagami-m distribution and of the distribution of the minimum eigenvalue of correlated noncentral Wishart matrices, both important in communication theory. New expressions for the corresponding cumulative distributions are obtained and a number of communication-theoretic problems involving them are pointed out.

In multiple-input multiple-output (MIMO) systems the communication channel can be split into s-parallel single-input single-output eigenchannels. The channel gains associated with these eigenchannels depend on the magnitude of the eigenvalues of the complex random matrix that characterizes the MIMO channel. We present a general framework for the characterization of the dynamics of MIMO channels. In addition, we provide new analytical results for the distribution of the largest eigenvalue of two correlated Wishart matrices, which enable a direct evaluation of different system performance metrics such as the probability of two consecutive outages separated by a given time window, the level crossing rate and the average fade duration.

In this paper, we derive exact closed-form expressions for the bivariate Nakagami-m cumulative distribution function (CDF) with positive integer fading severity index m in terms of a class of hypergeometric functions. Particularly, we show that the bivariate Nakagami-m CDF can be expressed as a finite sum of elementary functions and bivariate confluent hypergeometric Φ3functions. Direct applications which arise from the proposed closed-form expression are the outage probability (OP) analysis of a dual-branch selection combiner in correlated Nakagami-m fading, or the calculation of the level crossing rate (LCR) and average fade duration (AFD) of a sampled Nakagami-m fading envelope.

In this paper exact closed-form expressions are derived for the outage probability (OP) in scenarios where the signal of interest (SoI) experiences η-μ or κ-μ fading, the interfering signals are subject to η-μ fading and the background noise can be neglected. With the only assumption that the μ parameter is a positive integer number for the interfering signals, the derived expressions when the SoI is either η-μ or κ-μ distributed are given in elementary terms for maximal ratio combining (MRC) with independent branches. If the pre-combining SoI power signals are η-μ distributed with their corresponding μ parameters being positive integer or half-integer numbers, the previous analysis is extended for spatially correlated MRC at the receiver.

The statistical properties of Wishart matrices have been extensively used to analyze the performance of multiple-input multiple-output (MIMO) systems. In particular, the signal-to-noise ratio (SNR) output statistics of several MIMO systems depends on the diagonal distribution of a complex Wishart matrix. In this paper, we derive the joint density of the diagonal elements of a complex Wishart matrix, which follows a multivariate chi-square distribution. The density expression is in the form of an infinite series representation which converges rapidly and is easy to compute. This expression is used to obtain the distribution of the maximum of the diagonal elements, which allows analyzing the performance of two different MIMO systems under practical conditions. First, our statistical results are applied to the outage probability characterization of MIMO systems with receive antenna selection in spatially correlated Rayleigh fading. Then, the same results are used to analyze the outage probability of transmit beamforming systems under limited-rate feedback.

In this paper, we derive an exact closed-form expression for the bit error rate (BER) of orthogonal frequency division multiplexing (OFDM) systems impaired by transmit (TX) and receive (RX) in-phase/quadrature (IQ) imbalances and imperfect channel state information (ICSI), in Rayleigh fading channels. Since the decision metric in this scenario can be expressed as a quadratic form D in Gaussian complex-valued non-circularly symmetric random variables (RVs) with zero mean, we provide a general expression for the calculation of Pr{D <; 0}. In addition, two approximate closed-form expressions for the BER are obtained, which are demonstrated to be extremely accurate for practical values of IQ imbalances. Results show that TX IQ imbalance is in general less detrimental than RX IQ imbalance, and confirm that the correlation between the channel response at the observed subcarrier frequency and the mirror subcarrier has a significant impact in the BER.

The performance of multiple-input multiple-output (MIMO) systems using spatial multiplexing is analyzed under channel prediction errors. We derive exact closed-form expressions for the conditional and average bit error rate (BER) for both fixed and adaptive modulation. We apply our analysis to design a rate adaptation policy that optimally adapts antenna use between beamforming and spatial multiplexing. Our results indicate that the prediction error degrades BER in MIMO systems with spatial multiplexing much more than in MIMO systems with beamforming due to the self-interference that arises from channel coupling. In particular, if interference between eigenchannels is high, spatial multiplexing should not utilize the weakest eigenchannels. In our policy, beamforming is used when prediction error is high to avoid interference, whereas multiplexing is used when it is low to achieve the maximum multiplexing gain. We show that this policy improves performance over prior adaptive policies that have been proposed in the literature.

Exact closed-form expressions are obtained for the outage probability of Nakagami-q (Hoyt) fading channels under co-channel interference (CCI). The scenario considered in this work assumes the joint presence of background white Gaussian noise and independent Rayleigh interferers with arbitrary powers.

Multiple input multiple output (MIMO) systems, in conjunction with orthogonal frequency division multiplexing (OFDM), are extensively used in modern communication systems in order to improve throughput and robustness in multipath fading environments. However, for an optimal operation of these techniques, channel state information (CSI) must be available in both the transmitter and receiver sides. In this paper, an exact closed-form expression for the bit error rate (BER) in MIMO-OFDM systems with transmit beamforming and maximal ratio combining (MRC) reception is obtained, under imperfect channel prediction and interpolation, in multipath Rayleigh fading. This expression is used to evaluate the BER performance of the system for different antenna configurations, prediction and interpolation filters, and channel conditions.

In this paper we analyze the performance of multiple-input multiple-output (MIMO) multiplexing for BPSK and square M-QAM under Rayleigh fading. We derive exact closed-form expressions of the bit error rate (BER) assuming channel prediction error. Our analysis indicates that prediction error degrades MIMO multiplexing BER much more than MIMO beamforming BER. This is not surprising since prediction error in MIMO multiplexing leads to eigenchannel interference, which has a much greater impact on BER than the imperfect beamforming coefficients that result from such errors. Our numerical results also reveal that non-uniform rate allocation between ordered eigenchannels dramatically improves the BER.

Significant throughput improvements can be obtained in multiple-input multiple-output (MIMO) fading channels by merging beamforming at the transmitter and maximal ratio combining (MRC) at the receiver. In general, accurate channel state information (CSI) is required to achieve these performance gains. In this paper, we analyze the impact of channel prediction error on the bit error rate (BER) of combined beamforming and MRC in slow Rayleigh fading channels. Exact closed-form BER expressions are obtained in terms of elementary functions. Numerical results show that imperfect CSI causes little BER degradation using channel prediction of moderate complexity.

Important throughput improvements in multiple- input multiple-output (MIMO) fading channels can be obtained by merging beamforming at the transmitter and maximal ratio combining (MRC) at the receiver. However, to attain these performance gains it is important to obtain accurate channel state information (CSI). For this purpose a channel estimation technique is used at the receiver: channel prediction to feed back to the transmitter for beamforming, and channel interpolation for MRC at the receiver. In this paper, the impact of imperfect channel prediction on bit error probability (BEP) is analyzed in Rayleigh fading, taking into account the channel response variations over the frame interval. An exact closed-form expression for BEP is obtained, and we evaluate this expression assuming both time-variant and time-invariant channel models. These results indicate that the BEP performance degrades on the order of 1.5 dB due to channel variations.

Adaptive modulation schemes for fading channels are usually required to fulfill certain long-term average BER targets. However, for simplicity and mathematical tractability, these schemes are often designed by fixing the short-term instantaneous BER to the target value. In this paper, the analysis and design of variable-rate variable-power QAM schemes with average BER constraints are tackled for a MIMO beamforming system with MRC and imperfect CSI. The SISO system is considered as a special case of these more general results. Approximate closed-form policies are derived for continuous rate and power adaptation which are compared to fully discrete policies designed numerically. Closed-form expressions for the ASE of the proposed policies are derived and evaluated. Our results indicate that imperfect CSI and discrete rate and power constraints do not significantly degrade performance.

Adaptive modulation schemes for fading channels are usually required to fulfill certain long-term average BER targets. However, for simplicity and mathematical tractability, these schemes are often designed by fixing the short-term instantaneous BER to the target value. In this paper, the analysis and design of variable-rate variable-power QAM schemes with average BER constraints are tackled for MIMO multiplexing with imperfect CSI. The SISO system is considered as a special case of these more general results. Approximate closed-form policies are derived for continuous rate and power adaptation which are compared to the fully discrete policies. Our results indicate that MIMO multiplexing is much more sensitive to imperfect CSI than MIMO beamforming due to the self-interference that arises from channel coupling. In particular, if interference between eigenchannels is large, MIMO multiplexing should utilize only one of its eigenchannels, in which case all multiplexing gain is lost.

The impact of non-ideal adaptive modulation for Nakagami-m flat fading channels is studied. First, the consequences of bounded feedback information rate, not feasible with continuous power or rate variation, are tackled. An optimum fully-discrete AQAM scheme is derived and the signaling information rate is evaluated. Later, degradation due to noisy and delayed pilot symbol assisted channel estimation is analyzed and compared to that of continuous schemes.

Presented here is an approach to analyzing the effect of imperfect channel estimation on adaptive modulation. The sensitivity of the main performance parameters to short-term and long-term estimation error sources is summarized in a set of new formulas that are either closed-form expressions or simple to compute numerically.