Arbitrary Fading Channels Research Articles

Cell-Free Massive MIMO for URLLC: A Finite-Blocklength Analysis

We present a general framework for the characterization of the packet error probability achievable in cell-free Massive multiple-input multiple output (MIMO) architectures deployed to support ultra-reliable low-latency (URLLC) traffic. The framework is general and encompasses both centralized and distributed cell-free architectures, arbitrary fading channels and channel estimation algorithms at both network and user-equipment (UE) sides, as well as arbitrary combing and precoding schemes. The framework is used to perform numerical experiments on specific scenarios, which illustrate the superiority of cell-free architectures compared to cellular architectures in supporting URLLC traffic in uplink and downlink. Also, these numerical experiments provide the following insights into the design of cell-free architectures for URLLC: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) minimum mean square error (MMSE) spatial processing must be used to achieve the URLLC targets; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) for a given total number of antennas per coverage area, centralized cell-free solutions involving single-antenna access points (APs) offer the best performance in the uplink, thereby highlighting the importance of reducing the average distance between APs and UEs in the URLLC regime; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">iii</i> ) this observation applies also to the downlink, provided that the APs transmit precoded pilots to allow the UEs to estimate accurately the precoded channel.

Copula-Based Performance Analysis for Fluid Antenna Systems Under Arbitrary Fading Channels

Copula-Based Performance Analysis for Fluid Antenna Systems Under Arbitrary Fading Channels

A Low-Cost and Efficient Single Probe Based MIMO OTA Measurement Method

As the multiple-input–multiple-output (MIMO) technologies are increasingly emerging in the arena of modern wireless systems, their cost-effective and efficient over-the-air (OTA) performance verification under arbitrary fading channels, especially, for high-volume beam-reconfigurable product verifications, play a crucial role toward their technology adoption. The 2-D multi-probe anechoic chamber (MPAC) MIMO OTA measurement method has been well-developed, but requires both precise infrastructure and heavy calibration. Moreover, the extension to 3-D channel model appears impractical for the MPAC method with its significantly increased probe numbers in 3-D scenario. To address these challenges, we propose a novel single-probe anechoic chamber (SPAC) measurement method that transforms spatial synthesization of MPAC into time synthesization whereby the only source of measurement error can be restrained in time synchronization. The wireless community can be widely benefited with this proposed low-cost and efficient methodology, especially in the research and product prototyping stage. In this article, a proof-of-concept measurement system has been designed and implemented, which validates the efficiency of the proposed solution.

Performance analysis of space time coded generalized frequency division multiplexing system over generalized fading channels

AbstractDue to its low out‐of‐band emission and high spectral efficiency, the generalized frequency division multiplexing (GFDM) has been adopted as one of the most prominent waveform techniques for the 5G networks. To further combat the deep fading, the space time coding (STC) can be integrated with the GFDM system which provide high diversity gain that results into low symbol error rate at the receiver. In this article, a generalized model of space time coded GFDM system (STC‐GFDM) has been proposed. More precisely, a comprehensive analytical framework to compute the average symbol error rate (ASER) is introduced, which can be used for any MIMO configuration, code rate, and arbitrary fading channel. The proposed framework has wider applicability over generalized fading channels and having more accurate exact solution along with easy to evaluate approximate solution. Thus, the proposed framework extends the horizon of performance analysis of STC‐GFDM system over any fading scenario, that is not covered so far in the literature. In general, the closed from expressions of exact and approximate along with asymptotic ASER are derived for different fading channels using moment generating function (MGF) approach. Particularly, the ASER analysis has been performed analytically using derived expression over Rayleigh, TWDP, Nakagami‐q, and Nakagami‐m fading channels for ‐ary quadrature amplitude modulation (‐QAM). This analysis confirms that with the increase in transmit and receive antenna and decrease in modulation order, the ASER performance improves for all fading channels. Also, the improvement in ASER is observed as the power of specular components (ie, LOS paths) increases. Furthermore, these analytical results are validated using Monte‐Carlo simulation.

Delay Analysis of Wireless Federated Learning Based on Saddle Point Approximation and Large Deviation Theory

Federated learning (FL) is a collaborative machine learning paradigm, which enables deep learning model training over a large volume of decentralized data residing in mobile devices without accessing clients’ private data. Driven by the ever increasing demand for model training of mobile applications or devices, a vast majority of FL tasks are implemented over wireless fading channels. Due to the time-varying nature of wireless channels, however, random delay occurs in both the uplink and downlink transmissions of FL. How to analyze the overall time consumption of a wireless FL task, or more specifically, a FL’s delay distribution, becomes a challenging but important open problem, especially for delay-sensitive model training. In this paper, we present a unified framework to calculate the approximate delay distributions of FL over arbitrary fading channels. Specifically, saddle point approximation, extreme value theory (EVT), and large deviation theory (LDT) are jointly exploited to find the approximate delay distribution along with its tail distribution, which characterizes the quality-of-service of a wireless FL system. Simulation results will demonstrate that our approximation method achieves a small approximation error, which vanishes with the increase of training accuracy.

Interference Analysis in Wireless Networks Operating over Arbitrary Fading Channels with Heterogeneous Poisson Fields of Transmitters and Interferers

In this letter, we analyze statistics of signal-to-interference ratio in wireless networks operating over arbitrary fading channels in interference-limited scenarios with heterogeneous Poisson fields of transmitters and interferers. First, we derive expressions for the moment generating functions of aggregate interference and its negative fractional power. Then, we obtain a formula for the outage probability. Depending on an operational scenario, this formula presents either an exact expression or an upper bound. Some obtained results are given in terms of Mittag-Leffler's function. This special function is implemented in standard software, which makes the presented results convenient for analysis and design of wireless networks.

Performance Analysis of Energy Detection for MIMO Decision Fusion in Wireless Sensor Networks Over Arbitrary Fading Channels

In this paper, we consider a wireless sensor network (WSN) with sensors simultaneously reporting their decision to a fusion center (FC) equipped with multiple antennas. A Gaussian mixture channel model is used to obtain a general fading characterization of the channels ensemble between the sensors and the FC. Energy detection is studied as an appealing low-complexity sub-optimal alternative to the (computationally expensive) optimal test based on log-likelihood ratio. Closed-form theoretical performance is obtained for the energy test and furthermore asymptotic analysis for both tests is derived in order to provide a detailed characterization of large-system scenarios. Finally, the simulation results are provided to confirm the theoretical results and compare performance trends of the two tests.

Outage performance of MIMO cooperative networks with selective OFDMA relaying

The multiple-input multiple-output (MIMO) cooperative networks with selective orthogonal frequency division multiplexing access (OFDMA) relaying, where transmit beamforming and maximum ratio combining are carried out at source transmission and destination reception, respectively, are considered. The closed-form expression of outage probability is investigated to statistically assess the performance of systems. The impact of number of relays on the outage performance under arbitrary Nakagmi-m fading channels is analysed. Results reveal that increasing the number of relays is not always necessary for the improvement of outage performance and there has been the right relay configuration to guarantee the outage performance and reduce the complexity for relay networks.

One Bit Feedback for CDF-Based Scheduling with Resource Sharing Constraints

Cumulative distribution function (CDF)-based scheduling (CS) is known to be effective in meeting the different channel access ratio (CAR) requirements of users in a multi-user wireless system. In this paper, we propose a one-bit-feedback scheme for CS (OBCS) to reduce the feedback overhead from users in a cell. In OBCS, each user sets its individual threshold to decide whether to send one-bit feedback to the base station (BS). The BS randomly generates numbers for all users based on their feedback behavior and selects a user who is assigned with the largest value. We further propose OBCS with reduced complexity, OBCS-RC, which employs a universal threshold for all users, and relieves the BS to generate random numbers only for the users who have sent feedback. Both OBCS and OBCS-RC inherit the properties of CS in meeting diverse CAR requirements of users in arbitrary fading channels. Extensive analytical and simulation results indicate that simply setting the OBCS-RC threshold to 0.1 is adequate for good throughput performance compared to OBCS with the optimal threshold for each user. Although OBCS and OBCS-RC induce a throughput loss due to the reduced feedback overhead, their throughput still grows in a double-logarithmic manner as CS in Nakagami-m channels when the number of users increases to infinity.

Link Performance Bounds of MIMO Transmit Beamforming Systems Operating over Generalized Fading Channels

In this letter, we prove that link performance bounds of multiple-input multiple-output transmit beamforming systems employing maximal ratio combining at the receiver and operating over arbitrary ergodic fading channels can be obtained by analyzing receiver diversity systems operating over specially constructed virtual radio channels.

Statistical assessment of selection-based dual-hop semi-blind amplify-and-forward cooperative networks

For multiple-relay cooperative networks with multiple antennas deployed at source and destination nodes, we investigate the outage performance of selection based semi-blind amplify-and-forward (AF) relaying, where transmit beamforming (TB) is conducted at source transmission and maximum ratio combining (MRC) at destination reception. Based on the Kolmogorov-Smirnov test, we analyze the impact of the configuration of destination antennas on the outage performance under arbitrary Nakagami-m fading channels. Results reveal that increasing the number of destination antennas is not necessary for an improvement of outage performance with any Nakagami-m parameter. Inspired by this fact, an approximation is proposed for the optimal selection. Simulation results show that the approximation is an efficient selection method.

Design Criteria of Two-Hop Based Wireless Networks with Non-Regenerative Relays in Arbitrary Fading Channels

In this paper we evaluate outage performances of multirelay amplify and forward (AF) transmission over fading channels. We focus on the uplink of a two-hop based network where N (with N ges 1) single antenna relay stations (RSs) serve as non-regenerative repeaters for the message transmitted by a single antenna source node (or mobile station MS). Performances are derived at high SNR for arbitrary fading distributions over each cooperative link. In Rayleigh fading the high price of cooperation in terms of signalling (e.g. during MS-to-RSs transmissions and control messages broadcasts) causes a significant loss in spectral efficiency. Instead, provided that the RSs can be strategically positioned to benefit from a channel with marginal diffusive fading component compared to Rayleigh, this paper shows that this loss in efficiency can be significantly alleviated depending on the particular propagation environment. Closed form conditions on the fading statistics for the relayed links are derived to guarantee that collaborative transmission performs as if the MS node would benefit from the same diversity and bandwidth efficiency provided by multi-antenna transmission. The proposed conditions are computed for arbitrary distributed fading for the relays-to-BS link and are specialized for Rice faded RSs-to-BS links.

Tight closed-form approximation for the ergodic capacity of orthogonal STBC

In this letter we derive a simple and tight closed-form approximation for the ergodic capacity of orthogonal space-time block coding in arbitrary fading channels. The expression is an analytical function of the power covariance matrix of the channel. In the case of uncorrelated channels the expression only depends on the variances of the channel power gains. These channel statistics can be easily obtained from both analytical and physical fading channel models. Simulations results show the accuracy of the proposed expression

Stochastic gradient algorithms for design of minimum error-rate linear dispersion codes in MIMO wireless systems

Linear dispersion (LD) codes are a good candidate for high-data-rate multiple-input multiple-ouput (MIMO) signaling. Traditionally LD codes were designed by maximizing the average mutual information, which cannot guarantee good error performance. This paper presents a new design scheme for LD codes that directly minimizes the block error rate (BLER) in MIMO channels with arbitrary fading statistics and various detection algorithms. For MIMO systems employing LD codes, the error rate does not admit an explicit form. Therefore, we cannot use deterministic optimization methods to design the minimum-error-rate LD codes. In this paper, we propose a simulation-based optimization methodology for the design of LD codes through stochastic approximation and simulation-based gradient estimation. The gradient estimation is done using the score function method originally developed in the discrete-event-system community. The proposed method can be applied to design the minimum-error-rate LD codes for a variety of detector structures including the maximum-likelihood (ML) detector and several suboptimal detectors. It can also design optimal codes under arbitrary fading channel statistics; in particular, it can take into account the knowledge of spatial fading correlation at the transmitter and receiver ends. Simulation results show that codes generated by the proposed new design paradigm generally outperform the codes designed based on algebraic number theory.

SEP Performance of Coherent MPSK Over Fading Channels in the Presence of Phase/Quadrature Error and I-Q Gain Mismatch

This letter presents a joint approach to the symbol-error probability (SEP) of coherent M-ary phase-shift keying in a situation where the phase error, quadrature error, and in-phase-quadrature (I-Q) gain mismatch problems take place all concurrently over an additive white Gaussian noise and arbitrary fading channel. A set of equations that characterizes the conditional SEP on an instantaneous fading signal-to-noise ratio is derived in the form of the Craig representation.

Bit error probability for MDPSK and NCFSK over arbitrary Rician fading channels

In this paper, we analyze the bit error probability (BEP) of binary and quaternary differential phase shift keying (2/4 DPSK) and noncoherent frequency shift keying (NCFSK) with postdetection diversity combining in arbitrary Rician fading channels. The model is quite general in that it accommodates fading correlation and noise correlation between different diversity branches as well as between adjacent symbol intervals. We show that the relevant decision statistic can be expressed in a noncentral Gaussian quadratic form, and its moment generating function (MGF) is derived. Using the MGF and the saddle point technique, we give an efficient numerical quadrature scheme to compute the BEP. The most significant contribution of the paper, however, lies in the derivation of a closed-form cumulative distribution function (cdf) for the decision statistic. As a result, a closed-form BEP expression in the form of an infinite series of elementary functions is developed, which is general and unifies previous published BEP results for 2/4 DPSK and NCFSK for multichannel reception in Rician fading. Specialization to some important cases are discussed and, as a byproduct, a new and general finite-series expression for the BEP in arbitrarily correlated Rayleigh fading is obtained. The theory is applied to study 2/4 DPSK and NCFSK performance for independent and correlated Rician fading channels; and some interesting findings are presented.

Optimizing the transmit power for slow fading channels

We consider the design of power-adaptive systems for minimizing the average bit-error rate over flat fading channels. Channel state information, obtained through estimation at the receiver, is sent to the transmitter over a feedback channel, where it is used to optimally adapt the transmit power. We consider finite-state optimal policies to reflect the limitations of the feedback channel. We develop an iterative algorithm that determines the optimal finite-state power control policy given the probability density function (PDF) of the fading. Next, we present a discretized formulation of the problem and obtain a suboptimal solution via standard dynamic programming techniques. The discretization of the problem enables us to obtain a suboptimal policy for arbitrary fading channels for which the analytic expression of the fading probability density function is not available. Simulation results are used to draw conclusions regarding the effects of limited feedback channel capacity, delay and number of states on the bit-error rate performance of the proposed policies under slow and moderate fading conditions.