Asymptotic Performance Analysis Research Articles

Asymptotic Mutual Information Analysis for Double-Scattering MIMO Channels: A New Approach by Gaussian Tools

The asymptotic mutual information (MI) analysis for multiple-input multiple-output (MIMO) systems over double-scattering channels has achieved engaging results, but the convergence rates of the mean, variance, and the distribution of the MI are not yet available in the literature. In this paper, by utilizing the large random matrix theory (RMT), we give a central limit theory (CLT) for the MI and derive the closed-form approximation for the mean and the variance by a new approach—Gaussian tools. The convergence rates of the mean, variance, and the characteristic function are proved to be <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (1/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ) for the first time, where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the number of receive antennas. Furthermore, the impact of the number of effective scatterers on the mean and variance was investigated in the moderate-to-high SNR regime with some interesting physical insights. The proposed evaluation framework can be utilized for the asymptotic performance analysis of other systems over double-scattering channels.

Utilizing double-shadowed Rician fading over energy detector-based spectrum sensing with diversity reception

This study explores the capabilities of an Energy Detector (ED)-based Cognitive Radio (CR) device in a double shadowed (DS) Rician distribution environment for spectrum sensing. The effectiveness of the ED is evaluated using metrics such as average probability of detection (PD) and average area under the receiver operating characteristics curve (AUC). The investigation extends to single-input-multiple-output (SIMO) channel conditions, considering maximal ratio combining (MRC) and square-law selection (SLS) diversity techniques. To provide a comprehensive understanding of the system, the study also includes the asymptotic performance analysis of diversity techniques, including MRC, equal gain combining (EGC), and selection combining (SC). The findings indicated a notable enhancement in detection performance through the application of diversity combining techniques. Among the evaluated schemes, MRC demonstrated the most favorable results, followed EGC, while SC yielded comparatively weaker outcomes. To further minimize error probability, the detection threshold is optimized, resulting in improved energy detection statistics, even in scenarios involving diversity. The formulations are additionally applied to cooperative spectrum sensing (CSS). It further noted that fading parameter directly influence the array gain, while diversity gain only depends on the number of diversity branches. The accuracy and validity of the proposed results are confirmed through Monte-Carlo simulation.

Novel Mode Selection Schemes for Buffer-Aided Cooperative NOMA System

This paper investigates a cooperative non-orthogonal multiple access (C-NOMA) system, where the NOMA and buffer-aided cooperative transmission modes between the users are integrated. Two novel mode selection schemes are proposed, which adaptively select the NOMA and cooperative modes according to different buffer states and communication environments. These two proposed schemes are termed single-core state (SCS) and dual-core state (DCS) schemes since they correspond to single and dual-core buffer states. These core states are carefully chosen, which ensure not only a sufficient amount of available transmission modes or links but also a small number of stored packets at each buffer. The closed-form expressions of the outage probabilities and average delays of the proposed schemes are derived and verified by simulation results. Asymptotic performance analysis is also performed, revealing that both proposed schemes achieve the full diversity within the minimum required buffer size of two. Analytical and simulation results show that the proposed SCS and DCS schemes ensure favourable outage performance and the lowest delay, respectively.

Exploiting Unit Circle Roots for Improved Radar Moving Target Detection in Low Rank Clutter With Limited Secondary Data

Measured radar clutter often exhibits a low-rank structure that can be exploited for designing adaptive moving target detectors to reduce the amount of secondary data necessary for desirable detection performance. It has been shown recently that for symmetrically spaced pulse trains significant performance improvements can be achieved by constraining the roots of the Adaptive Matched Filter (AMF) polynomial onto the unit circle (UC) that satisfies a theoretical property of the known-covariance AMF. In this paper, the UC-roots approach is extended to develop a generalized likelihood ratio test (GLRT) for radar moving target detection in low-rank clutter with limited secondary data. The proposed unit circle GLRT (UC-GLRT) uses the properties of orthogonal projection matrices to enforce the UC roots constraint. The asymptotic performance analysis of the proposed UC-GLRT conducted in this paper is verified by simulation. Simulation studies with limited secondary data demonstrate the superior performance of the UC-GLRT approach over several existing detectors. Clutter rank and target velocity mismatch issues are also studied.

On the Asymptotic Performance Analysis of the k-th Best Link Selection Over Non-Identical Non-Central Chi-Square Fading Channels

This paper derives the asymptotic distribution of the normalized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -th maximum order statistics of a sequence of non-central chi-square random variables with non-identical non-centrality parameters. We demonstrate the utility of these results in characterizing the signal-to-noise ratio in three different applications in wireless communication systems where the statistics of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -th maximum channel power over Rician fading links are of interest. Furthermore, we derive simple expressions for the asymptotic outage probability, average throughput, achievable throughput, and average bit error probability. The proposed results are validated via extensive Monte Carlo simulations.

Performance of subspace-based algorithms associated with the sample sign covariance matrix

Complex-valued data in statistical signal processing applications have many advantages over their real-valued counterparts. It allows us to use the complete statistical information of the signal thanks to its statistical property of non-circularity. This paper presents a general framework for developing asymptotic theoretical results on the distribution-free sample sign covariance matrix (SSCM) under circular complex-valued elliptically symmetric (C-CES) and non-circular CES (NC-CES) multidimensional distributed data. It extends some partial asymptotic results on SSCM derived for real elliptically symmetric (RES) distributed data. In particular closed-form expressions of the first and second-order of the SSCM are derived for arbitrary spectra of eigenvalues for C-CES and NC-CES distributed data which facilitates the derivation of numerous statistical properties. Then, the asymptotic distributions of associated projectors are deduced, which are applied in the study of asymptotic performance analysis of SSCM-based subspace algorithms, followed by a comparison to the asymptotic results derived using Tyler's M estimate. However, a more in-depth analytical analysis of the efficiency of the SSCM relative to Tyler's M estimate is performed, yielding that the performances of the SSCM and Tyler's M estimate are close for a high-dimensional data and not too small dimension of the principal component space. We conclude therefore that, although the SSCM is inefficient relative to Tyler's M estimate, it is of great interest from the point of view of its lower computational complexity for high-dimensional data. Finally, numerical results illustrating the theoretical analysis are presented through the direction-of-arrival (DOA) estimation CES data models.

Asymptotic Performance Analysis of Distributed Non-Bayesian Quickest Change Detection With Energy Harvesting Sensors

This article focuses on the distributed non-Bayesian quickest change detection based on the cumulative sum (CUSUM) algorithm in an energy harvesting wireless sensor network, where the distributions before and after the change point are assumed to be known. Each sensor is powered by randomly available harvested energy from the surroundings. It samples the observation signal and computes the log-likelihood ratios (LLRs) of the aforementioned two distributions if enough energy is available in its battery for sensing and processing the sample ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$E_{s}$</tex-math></inline-formula> ). Otherwise, the sensor decides to abstain from the sensing process during that time slot and waits until it accumulates enough energy to perform the sensing and processing of a sample. This LLR is used for performing the CUSUM test to arrive at local decisions about the change point, which are then combined at the fusion center (FC) by a predecided fusion rule to arrive at a global decision. In this article, we derive the asymptotic expressions (as the average time to a false alarm goes to infinity) for the expected detection delay and the expected time to a false alarm at the FC for three common fusion rules, namely, <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">or</small> , <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</small> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$r$</tex-math></inline-formula> out of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> majority rule, respectively, by considering the scenario, where the average harvested energy at each sensor is greater than the energy required for sensing and processing a sample <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$E_{s}$</tex-math></inline-formula> . To this end, we use the theory of order statistics and the asymptotic distribution of the first passage times of the local decisions. Numerical results are also provided to support the theoretical claims.

Performance of a hybrid dual-hop and multi-hop network based on NOMA

ABSTRACT In this work, a novel network is proposed, which supports simultaneous dual-hop and multi-hop transmissions using the key concept of non-orthogonal multiple access (NOMA). The proposed network is designed in such a way that the existing infrastructure of a multi-hop network can be utilised efficiently for concurrent dual-hop transmissions. While one source transmits its signal to a remote destination via relay nodes in time slots, a maximum of another sources may transmit their information to the corresponding destinations using dual-hop transmissions via the same relay nodes over time slots. The performance of this hybrid dual-hop/multi-hop network is analysed and the impact of number of hops, transmit signal-to-noise ratio (SNR) and imperfection of successive interference cancellation (SIC) on the outage performance of each source is evaluated. Novel closed-form expressions for outage probability and ergodic capacity have been developed to assess the performance of the proposed network. In addition, an asymptotic performance analysis has also been also carried out for both outage probability and ergodic capacity of the proposed network.

Performance of Dual-Hop Relaying for OWC System Over Foggy Channel With Pointing Errors and Atmospheric Turbulence

Optical wireless communication (OWC) over atmospheric turbulence and pointing errors is a well-studied topic. Still, there is limited research on signal fading due to random fog in an outdoor environment for terrestrial wireless communications. In this paper, we analyze the performance of a decode-and-forward (DF) relaying under the combined effect of random fog, pointing errors, and atmospheric turbulence with a negligible line-of-sight (LOS) direct link. We consider a generalized model for the end-to-end channel with independent and not identically distributed (i.ni.d.) pointing errors, random fog with Gamma distributed attenuation coefficient, double generalized gamma (DGG) atmospheric turbulence, and asymmetrical distance between the source and destination. We develop density and distribution functions of signal-to-noise ratio (SNR) under the combined effect of random fog, pointing errors, and atmospheric turbulence (FPT) channel and distribution function for the combined channel with random fog and pointing errors (FP). Using the derived statistical results, we present analytical expressions of the outage probability, average SNR, ergodic rate, and average bit error rate (BER) for both FP and FPT channels in terms of OWC system parameters. We also develop simplified and asymptotic performance analysis to provide insight on the system behavior analytically under various practically relevant scenarios. We demonstrate the mutual effects of channel impairments and pointing errors on the OWC performance, and show that the relaying system provides significant performance improvement compared with the direct transmissions, especially when pointing errors and fog becomes more pronounced.

Asymptotic Performance Analysis of MMSE Receivers in Multicell MU-MIMO Systems

For large-scale antenna array multiple-input multiple-output (MIMO) systems, a typical solution often put forward for uplink detection consists in applying low-complexity linear receivers such as zero-forcing (ZF) and minimum mean-square error (MMSE) combiners. In this paper, the performance of uplink MMSE detection has been analyzed in the context of a multi-cell multiuser MIMO system. An approximate expression for the signal-to-interference-plus-noise ratio (SINR) is proposed, which is in simple form and becomes exact in the low SNR regime. This approximate SINR applies to systems where the base station (BS) has the statistical information of the out-of-cell interfering signals, and systems where the BS ignores the presence of such interfering signals. This approximate SINR is tight for arbitrary user powers, arbitrary number of antennas at the base station, and arbitrary channel correlation matrix associated with any particular user. Approximate expressions for capacity and bit-error rate/symbol-error rate have also been derived. Particularly, it can be proven that, when the MMSE receiver ignores the presence of out-of-cell interfering signals, the performance gap between ZF and MMSE vanishes in the high SNR regime.

Comparison of two polynomial approaches in performance analysis for periodic piecewise polynomial systems

In this paper, the theory and effectiveness of two polynomial approaches are compared in the analysis of L2-L∞ and H∞ performance for a type of periodic piecewise polynomial systems, where the time-varying subsystems can be characterized in Bernstein polynomials. Using the Bernstein polynomial-based lemma and the existing lemma concerning the negativity/positivity of matrix polynomial functions, sufficient conditions are established in tractable forms aimed at the global asymptotic stability and performance analysis. Four cases of optimization constraints are considered based on the proposed conditions. The performance indices obtained via the four cases are compared through a numerical example, and the lower conservatism achieved by the proposed Bernstein polynomial approach is demonstrated.

Energy Harvesting Irregular Repetition ALOHA With Replica Concatenation

In this paper, we consider an asynchronous random access scheme called irregular repetition ALOHA (IRA) as a generalization of contention resolution ALOHA (CRA) with varying repetitions. We present an asymptotic performance analysis of CRA and IRA on the collision channel for regular and irregular repetition rates. We also propose an improvement by merging the clean parts of packet replicas in partial collisions, and extend our analysis to this scenario as well. Specific designs of repetition distributions based on the new analysis show that the optimized solutions of irregular repetition slotted ALOHA (IRSA) perform well in both IRA and the enhanced scheme, and they considerably outperform the regular repetition distributions. We also introduce energy harvesting (EH) to both schemes as a practical and sustainable adaptation, where users are able to harvest energy and store it in their finite-capacity batteries. We model the battery state by a discrete-time Markov chain and derive an optimal transmission policy to maximize the asymptotic performance of the system. We provide comprehensive numerical results for both practical and asymptotic scenarios to verify the validity of the proposed analyses, and illustrate the benefits of the proposed systems.

Multi‐user uplink transmission with asymptotic full‐receiver‐diversity in massive MIMO systems

A scenario of uplink transmissions from multiple single-antenna users to a base-station with large number of antennas is considered in this letter. Based on the conditional statistic properties of the received signals, a maximum likelihood-based detector without prior channel state information is firstly presented. In order to estimate the whole transmitted symbols successfully, the optimal signal design can be equivalently converted to a max–min problem based on the conditional covariance matrix of the received signals. From the asymptotic performance analyses with the lower and upper bounds of the pairwise error probability, we show that the pairwise error probability decays exponentially with the number of receiver's antennas, which we define as the asymptotic full-receiver-diversity order in non-coherent massive MIMO systems. In addition, we present the numerical results and illustrate the comparisons with several non-coherent transmission schemes in the state-of-the-art to verify the performance of our proposed scheme.

Distributed Parameter Detection in Massive MIMO Wireless Sensor Networks Relying on Imperfect CSI

Distributed parameter detection is conceived for massive multiple-input multiple-output (MIMO) wireless sensor networks (WSNs), where multiple sensors collaborate to detect the presence/ absence of a spatially correlated parameter. Neyman-Pearson (NP) and generalized likelihood ratio test (GLRT)-based detectors are developed at the fusion center (FC) for known and unknown parameter detection scenarios, respectively. More explicitly, the GLRT detector also has to estimate the unknown parameter value. Closed-form expressions are derived for the probabilities of detection (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> ) and false alarm (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</sub> ) in order to characterize the performance of the proposed schemes. Furthermore, the optimal sensor transmit gains are determined for maximising the detection performance attained. An asymptotic performance analysis is carried out for determining the gain scaling laws for the massive MIMO WSN considered, when the number of antennas tends to infinity. The proposed framework is also extended to the realistic imperfect channel knowledge scenario at the FC, followed by the development of the associated fusion rules and analytical results to characterize the performance. Our simulation results closely tally the theoretical findings.

Finite-Length Performance Analysis of LDPC Coded Continuous Phase Modulation

Serial concatenation of LDPC codes and continuous phase modulation (CPM) has recently gained significant attention due to its capacity-approaching performance, efficient detection as well as owing to its constant-envelope nature. Most of the previous contributions on LDPC coded CPM were devoted to the design of LDPC codes and their asymptotic performance analysis. However, there is a paucity of work on the finite-length performance estimation of LDPC coded CPM, primarily because existing performance estimation techniques cannot be readily applied to the LDPC coded CPM. To fill this gap, we conceive an analytical bit error probability estimation technique for finite-length LDPC coded CPM in the waterfall region. Numerical results are provided both for regular and irregular LDPC codes having different codeword lengths, demonstrating that the estimated performances are closely matched by the simulated ones.

Asymptotic Performance Analysis of Successive Interference Cancellation With Dynamic User-Decoding Order

We address the evaluation of dynamic (estimation-based) user-decoding order in successive interference cancellation (SIC) in a proof-of-concept multiple access satellite setting in which many code-division multiple access users employ non-orthogonal spreading codes and the same encoder. We consider the practical setting where user symbol energies, unknown to the receiver, are estimated by preamble cross-correlations. Thereafter, SIC proceeds in non-increasing order of the former estimates. In contrast with small networks evaluated in the literature, we analyze the large-user regime and derive a simple system model to analyze the asymptotic network performance. Monte Carlo simulations validate our infinite-user analysis for hundreds of users and report the benefits of their application.

Amplify-and-Forward Relaying With Maximal Ratio Combining Over Fluctuating Two-Ray Channel: Non-Asymptotic and Asymptotic Performance Analysis

Fluctuating two-ray (FTR) channel model was shown to effectively characterize millimeter wave (mmWave) communication channels. In this article, we adopt FTR to investigate amplify-and-Forward (AF) mmWave relaying system. Two communications scenarios are considered corresponding to the presence and absence of a direct link between the transmitter and receiver. Outage probability and symbol error rate (SER) are then analytically obtained as performance metrics. The results are further compared with the corresponding metrics obtained based on conventional channel models including Nakagami- ${m}$ and two-wave with diffuse power (TWDP). Especially, for the high-SNR regime, our analyses indicate that performance evaluations based on the conventional models significantly deviate from that of based on the FTR model. Our results provide quantitative insights on the importance of model selection in design and performance evaluations of relay-based mmWave systems. Moreover, for the high-SNR regime, we carry out asymptotic analysis and obtain a low-complexity expression for the achieved AF relaying gain. Such an expression provides a quantitative measure on whether or not AF relaying outperforms no-relaying in a given setting. Extensive numerical and simulation results are provided to confirm the accuracy of the analysis and investigate system performance in different settings.

Concatenated LDPC/2-D-Marker Codes and Non-Iterative Detection/Decoding for Recovering Position Errors in Racetrack Memories

Racetrack memories (RMs) are prone to alignment faults called position errors (PEs), which manifest as insertions and deletions of stored data bits. Conventional coding schemes for PEs demonstrate the promising results by employing low-density parity-check (LDPC) codes with an iterative detection and decoding algorithm. However, the computational complexity of detection is relatively high. In this article, for channels with PEs, we present a new coding scheme that can effectively decode corrupted data, even if the detection is executed only once (i.e., a non-iterative detection and decoding scenario). The proposed code consists of a concatenation of an inner 2-D marker code, which is specialized for PEs to mitigate the effect of insertion and deletion (ID) errors, and an outer irregular LDPC code. We also provide tractable design methodologies for these constituent codes. First, we identify the 2-D-marker code structures that offer higher achievable information rates in a non-iterative scenario and then optimize irregular LDPC codes to ensure good decoding properties. Through asymptotic-performance analysis and finite-length simulation, we confirm the effectiveness of the proposed coding scheme. Ultimately, the proposed coding scheme has the capability to reduce code rate loss and to provide excellent decoding performance under a non-iterative scenario, which also helps in understanding the reliability of RM when a low-complexity decoding algorithm is used to correct ID errors caused by PEs.

Diversity Gain Analysis of Distributed CDD Systems in Non-Identical Fading Channels

This paper investigates the diversity gain of a distributed cyclic delay diversity (dCDD) scheme for cyclic-prefixed single carrier systems in non-identical fading channels. Non-identical small-scale fading is assumed in the environment, in which non-identical line-of-sight and non-line-of-sight fading coexist. A condition for dCDD resulting in intersymbol interference free reception at the receiver, is extended to this new channel environment. For an overpopulated system setup, a generalized performance analysis, is not available from existing works, is conducted after developing closed-form expressions for the distribution of the signal-to-noise ratio (SNR) realized at the receiver. Since the order statistics are involved in the statistical properties of the SNR, the corresponding spacing statistics are utilized to derive feasible closed-form expressions. The finalized closed-form expressions are shown to provide very reliable outage probability and spectral efficiency of dCDD for underpopulated and overpopulated systems. An asymptotic performance analysis verifies the maximum achievable diversity of the dCDD even in the overpopulated case within the considered channel environment. Link-level simulations are conducted and these verify the maximum achievable diversity gain.

Outage-Optimal and Suboptimal Power Control for D2D Communications in SWIPT Cellular Networks With Local CSI

In this letter, we consider a downlink cellular network where a cellular user (CU) not only decodes information but also harvests energy. By reusing the spectrum resource of the CU, a device-to-device (D2D) transmitter sends its own signals to a D2D receiver. In order to protect the CU from the interference due to the D2D signals, we propose transmit power control schemes for the D2D transmission without increasing the outage probability of the CU. This is possible since the CU’s information loss due to the D2D signals can be compensated by the CU’s energy harvesting gain from the D2D signals. For asymptotic performance analysis, we provide a lower bound on the D2D outage probability. The numerical results show that the proposed schemes outperform the conventional scheme.