Average Pairwise Error Probability Research Articles

Error Probability Analysis of Intelligent Reflecting Surface-Enabled Non-Orthogonal Multiple Access Systems

We analyze the error performance of intelligent reflecting surface (IRS)-aided non-orthogonal multiple access (NOMA) systems. We deduce novel approximate analytical expressions for average symbol error probability (SEP) for PAM and QAM. We also analyze the multi-user scenario by deriving the novel approximate analytical expressions for (i) the average SEP for multicast transmission and (ii) the average pairwise error probability (PEP) for unicast transmission. We consider Rayleigh fading direct path and independently Rician fading reflected paths from access point to users via IRS. We also formulate and solve a constrained optimization problem to determine the fraction of elements to be activated at any IRS in order to guarantee near-identical SEP performance for both the users. We present results to elucidate that adding few extra IRS elements yields SNR gain for both users, requires allocation of lower power to weaker user and supports communication with higher-order constellation without significant increase in SEP/PEP. Furthermore, a 3-bit programmable IRS yields near-identical performance as an IRS with infinite precision phase-shift. Impact of estimation error on average SEP is also investigated.

Bit-Interleaved Coded Energy-Based Modulation With Iterative Decoding

This paper develops a low-complexity suboptimal non-coherent receiver for a multi-level energy-based coded modulation system. Inspired by the turbo processing principle, we incorporate the fundamentals of bit-interleaved coded modulation with iterative decoding (BICM-ID) into the proposed receiver design. The resulting system is called bit-interleaved coded energy-based modulation with iterative decoding (BICEM-ID) and its error performance is analytically studied. Specifically, we derive upper bounds on the average pairwise error probability (PEP) of the non-coherent BICEM-ID system in the feedback-free (FF) and error-free feedback (EFF) scenarios. It is revealed that the definition of the nearest neighbors, which is important in the performance analysis in the FF scenario, is very different from that in the coherent BICM-ID counterpart. The analysis also reveals how the mapping from coded bits to energy levels influences the diversity order and coding gain of the BICEM-ID systems. A design criterion for good mappings is then formulated, and an algorithm is proposed to find a set of best mappings for BICEM-ID. Finally, simulation results corroborate the main analytical findings.

Performance Analysis of STBC-Based MIMO PLC System in Cyclostationary Noise Environment

The paper proposes a multiple-input multiple-output-based power line communication (PLC) system subject to Rayleigh fading and corrupted by additive cyclostationary Gaussian noise. The proposed coherent receiver structure employs a block reception rule at the reception unit for detecting the space-time block-coded transmitted data symbols. A closed-form expression for the pairwise error probability (PEP) is derived using a characteristic function approach. Exact and asymptotic expressions for the average PEP are obtained for the special case of Alamouti code transmission which show that the PLC system under consideration offers full diversity. Numerical results depict the improvement in the system performance with increase in the number of receive diversity branches and the average signal-to-noise ratio per branch and decrease in the correlation value between the noise samples.

An Investigation of the MIMO Space Time Block Code Based Selective Decode and Forward Relaying Network over n-u Fading Channel Conditions

In this paper, we examine the end-to-end average pairwise error probability (PEP) and output probability (OP) performance of the maximum ratio combining (MRC) based selective decode and forward (S-DF) system over an η–µ scattering environment considering additive white Gaussian noise (AWGN). The probability distribution function (PDF) and cumulative distribution function (CDF) expressions have been derived for the received signal-to-noise (SNR) ratio and the moment generating function (MGF) technique is used to derive the novel closed-form (CF) average PEP and OP expressions. The analytical results have been further simplified and are presented in terms of the Lauricella function for coherent complex modulation schemes. The asymptotic PEP expressions are also derived in terms of the Lauricella function, and a convex optimization (CO) framework has been developed for obtaining optimal power allocation (OPA) factors. Through simulations, it is also proven that, depending on the number of multi-path clusters and the modulation scheme used, the optimized power allocation system was essentially independent of the power relation scattered waves from the source node (SN) to the destination node (DN). The graphs show that asymptotic and accurate formulations are closely matched for moderate and high SNR regimes. PEP performance significantly improves with an increase in the value of η for a fixed value of µ. The analytical and simulation curves are in close agreement for medium-to-high SNR values.

Impact of IQ Imbalance on RIS-Assisted SISO Communication Systems

Reconfigurable intelligent surface (RIS) for wireless networks has emerged as a promising future transmission technique to create smart radio environments that improve the system performance by turning the wireless channel into an adjustable system block. However, transceivers come with various hardware impairments, such as phase noise and in-phase/quadrature-phase imbalance (IQI). Hence, for robust configuration of RIS-based communication under practical conditions, assuming the identical performance analysis when subject to IQI, will lead to inaccurate analysis. In this paper, the implementation of this novel transmission technique is thoroughly investigated under intensive realistic circumstances. For this purpose, based on the maximum likelihood (ML) detector, a novel analytical expression of average pairwise error probability under IQI is proposed and compared to the standard ML detector. Further, the proposed analytical approaches are confirmed by numerical simulations.

Sum Rate Analysis of Generalized Space Shift Keying-Aided MIMO-NOMA Systems

We investigate the sum rate performance of a generalized space shift keying (GSSK)-aided, non-orthogonal multiple access (NOMA) network. In particular, we consider a multiple-input multiple-output (MIMO) NOMA downlink channel, where the base station employs GSSK modulation to transmit additional information to the NOMA users. We present a novel energy-based maximum likelihood (ML) detection strategy at the NOMA users to decode the active antenna indices. We derive a closed-form expression for the average pairwise error probability of the energy-based ML strategy to find a union bound on the bit error probability. Further, we derive the expression for the overall sum rate of the proposed GSSK-aided MIMO-NOMA system. Through numerical evaluations, we show that the proposed system outperforms the conventional MIMO-NOMA system, in terms of spectral efficiency.

Optimal Diversity and Coding Gains for Millimeter-Wave Communication

We consider a millimeter-wave communication system where the fading channel follows the Nakagami-m distribution. We derive performance limits of such a system in terms of the diversity and coding gains. First, we argue that although traditional design criteria for space-time codes (STCs) are optimal for Rayleigh and Rician fading channels, they fail to capture the optimal diversity and coding gains for Nakagami-m fading channels. Then, we derive a tight upper bound on the average pair-wise error probability at high signal-to-noise ratios. From such a bound, we obtain upper and lower bounds on the diversity and coding gains of any STC over the Nakagami-m fading channel. We then identify necessary and sufficient conditions for STCs to achieve the upper bounds, leading to a fundamental trade-off between maximizing the diversity and coding gains. We also investigate the effect of blockage using stochastic geometry. We show that the diversity and coding gains are limited by the non-line-of-sight link. Numerical simulations assuming different fading scenarios further illustrate that STCs that satisfy the new design achieve full diversity. Whereas, STCs that are otherwise optimal for Rayleigh and Rician channels do not. Furthermore, in a typical indoor environment, blockage reduces the coding gain by 1.5 dB for BERs less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> .

Effect of Generalized Improper Gaussian Noise and In-Phase/Quadrature-Phase Imbalance on Quadrature Spatial Modulation

Quadrature spatial modulation (QSM) isa recently proposed multiple-input multiple-output (MIMO) wireless transmission paradigm that has garnered considerable research interest owing to its relatively high spectral efficiency. QSM essentially enhances the spatial multiplexing gain while maintaining all the inherent advantages of spatial modulation (SM). This work studies the effects of in-phase/quadrature-phase (I/Q) imbalance and improper Gaussian noise (IGN) on the performance of QSM. Considering a scenario where both receiver and transmitter operate under the effects of I/Q imbalance, we propose a novel receiver design that optimizes the system bit error rate (BER) when there is IGN at the receiver. Closed forms of the average pairwise error probability (APEP) and upper bound of the average BER formulas are derived. These formulas are derived considering the Beckmann fading channel model, where most well-known fading channel models can be considered special cases. The proposed designs demonstrate solid performance despite the effects of I/Q imbalance. In fact, these effects can be entirely eliminated if they exist at the receiver and significantly reduced at the transmitter. All analytical results were verified by computer simulations.

PEP and OP examination of relaying network over time-selective fading channel

In this paper, we consider the selective decode and forward cooperative communication system and investigate its performance over time-selective fading in the presence of nodes’ mobility and channel estimation errors. Closed-form expressions for the outage probability (OP) and per-block average pairwise error probability (PEP) are derived, considering constraints at the relay, source, and destination nodes. We assume that both dual and multiple hops are subject to independent but non-identically distributed time-selective Nakagami-m fading channel. It has been observed that with an increase in the value of shape parameter and link strength of the relay-to-destination (RD) fading link gain, the per-block average PEP performance improves. Also increasing RD link gain is more significant than increasing the shape parameter of the RD link. The OP performance for optimal power allocation factors is better than its performance for equal power allocation factors. It is demonstrated that the OP decreases with increasing the value of distance-dependent power transfer factors (PTFs). Further, it has been observed that due to the mobility of nodes and imperfect channel state information, the PEP performance of the system experiences degradation, especially for high values of signal-to-noise ratio. Furthermore, when all the nodes are static and the estimation processes are perfect, the asymptotic error floors vanish, i.e., the nodes' mobility impact is removed. Monte Carlo simulation results confirm the accuracy of the analytical results.

Joint Impact of I/Q Imbalance and Imperfect CSI on SM-MIMO Systems Over Generalized Beckmann Fading Channels: Optimal Detection and Cramer-Rao Bound

Spatial modulation (SM) has been shown to be a promising low-complexity alternative to the state-of-art multiple-input multiple-output (MIMO) schemes due to its novel transmission approach. This paper investigates the performance of SM-MIMO systems in the presence of two practical undesirable effects, namely in-phase (I) and quadrature-phase (Q) imbalance (IQI) and imperfect channel state information (ICSI). An optimum maximum likelihood detection (MLD) method is proposed to tackle the effects of self-interference and signal distortion caused by IQI impairment by adapting the traditional MLD technique in accordance with the asymmetric characteristics of the IQI. More particularly, upper-bounds of the closed-form average pairwise error probability (APEP) and the average bit error rate (ABER) are derived for generalized Beckmann fading channels. As erroneously interpreted channel coefficients at the receiver (Rx) cause the error rate to increase and the detection to fall short, Cramer-Rao bound, which is a lower bound on the variance of the channel estimator, is utilized to assess the estimation accuracy. The system performance is evaluated by analytical derivations that are corroborated with computer simulations. The obtained results show that ICSI and IQI should be seriously considered while designing the future SM-based wireless communication systems.

Investigation of multiple hop cooperative communication system over time-selective Nakagami-m fading channel

Real-time communication is affected by practical constraints such as node mobility and imperfect channel state information. Most technical contributions in the area of cooperative communication neglect these practical constraints, thus, assumes ideal propagation scenarios. Such approximations make sense in low-rate systems, but can lead to very false results when examining future high data rate systems. In this work, closed-form expression of pairwise error probability (PEP) is derived for dual hop and multiple hop selective decode-and-forward relaying network over time-selective Nakagami-m fading links. Space–time block code is used in combination with multiple-input multiple-output to achieve the diversity gain along with cooperative diversity. To obtain the optimal source-relay power allocation factors, a mathematical framework has been proposed to improve the performance of the system in the power-constraint situation. Simulation results have been presented for various values of fading severity parameter and channel variance. Results for different node-mobility scenarios are also provided. Results show that the system performance improves by increasing the fading severity parameter and relay-to-destination (RD) channel gain. It is noted that the relaying network’s diversity order (DO) is the same as the non-cooperative network’s DO in a scenario when both source node (SN) and destination nodes (DNs) are static, and relay node (RN) is mobile. Also, if the RN and DN are static and the SN is mobile, DO will be equivalent to zero. At high signal-to-noise ratio (SNR), system performance with equal and optimal energy distribution can be seen approaching an asymptotic floor limit, because system performance independent of the power of the noise components. The effect of mobility of the DN on the average per-block PEP output is less important compared to the mobility of the SN. The scheme is restricted by an asymptotic error floor with a greater SNR regime for other node-mobility situations. The analytical results are verified by Monte Carlo simulations for M-ary signaling maximal ratio combiner cooperative system.

On the Joint Impact of Hardware and Channel Imperfections on Cognitive Spatial Modulation MIMO Systems: Cramer–Rao Bound Approach

This paper investigates the performance of spatial modulation for multiple-input multiple-output underlay spectrum-sharing systems in the presence of three practical deleterious effects: 1) transceiver hardware impairments, 2) outdated channel state information (CSI), and 3) imperfect CSI. In particular, for Rayleigh fading channels, a closed-form expression of the average pairwise error probability and a tight upper bound of the average bit error rate (ABER) are derived. In addition, asymptotic and yet simple approximate expressions are obtained, and consequently insightful discussions are manifested on the impacts of channel and hardware imperfections and on the diversity order. Moreover, explicit exact and approximate expressions for the Cramer–Rao bound are computed for assessing the channel estimation accuracy. Numerical results, which are validated through simulations, show that nonzero bounds of the ABER occur in the high power domain because of the effects of channel and hardware impairments.

Cognitive Networks in the Presence of I/Q Imbalance and Imperfect CSI: Receiver Design and Performance Analysis

Future wireless communication systems, including fifth-generation (5G) networks and the Internet of Things (IoT), require a massive number of inexpensive transceivers. These transceivers come with various hardware impairments, such as phase noise and in-phase/quadrature phase (I/Q) imbalance. This piece of work studies the performance of underlay cognitive radio (CR) networks, considering the joint effect of I/Q imbalance and imperfect channel-state information (CSI) at the secondary user. In order to mitigate the effect of I/Q imbalance, an optimal maximum likelihood (ML) receiver design is proposed and analyzed. Specifically, a closed-form expression of the average pairwise error probability (APEP) and a tight upper bound of the average bit error rate (ABER) are derived. In addition, a widely linear equalization (WLE) receiver that has performance close to the optimal receiver with a computational complexity close to the traditional blind receiver is proposed. In particular, the exact PEP of this WLE receiver is obtained and its APEP is calculated numerically. Moreover, an exact expression is derived for Cramer-Rao lower bound (CRLB) of the secondary system receiver channel estimation error in the presence of I/Q imbalance at the secondary transmitter/receiver (STx/SRx) sides. Computer simulations prove the analytical results of the proposed receivers. The obtained results show that the optimal receiver has the best performance and the WLE receiver outperforms the traditional ML receiver in most cases. In addition, the analysis shows that the best estimator that reaches the CRLB is not affected by the I/Q imbalance at STx/SRx.

Joint Spatial Division and Diversity for Massive MIMO Systems

We propose a downlink beamforming scheme that combines spatial division and orthogonal space-time block coding (OSTBC) in multi-user massive MIMO systems. The beamformer is divided into two parts: a pre-beamforming matrix to separate the users into different beams with no interference between each other, which is designed based on the low rank covariance matrix of the downlink channel, and a linear precoding matrix using partial or even no channel state information (CSI) concatenated by an OSTBC. To construct the pre-beamforming matrix, a simple method that selects columns from DFT matrix is presented. To design the linear precoding matrix with partial CSI of the effective channel after the pre-beamforming, we solve an optimization problem to minimize the pairwise error probability (PEP) of the users under an individual power or sum power constraint, respectively. For the individual power constraint, a semi-definite relaxing (SDR) method with a sufficient condition achieving the globally optimal solution is proposed to provide a performance benchmark. In addition, an efficient iterative successive convex approximation (SCA) method is provided to achieve a suboptimal solution. Furthermore, closed form solutions are derived under some special cases. For the sum power constraint, we consider two different designs, i.e., minimizing the average PEP and minimizing the maximum PEP of all users. We find that both non-convex problems have a similar structure, and proposed a unified SCA-Alternating Direction Method of Multipliers (ADMM) algorithm to handle them. The SCA-ADMM method can be implemented in a parallel manner, and thus is with great efficiency. Simulation results show the efficiency of our proposed JSDD scheme and the optimization method.

Average Worst-Case PEP Optimality of Repetition Coding Among Rate-1 DC-Offset STBCs for MIMO Optical Intensity Channels

An optical wireless intensity-modulation direct-detection multiple-input multiple-output communication system is considered. The performance of $M$ -PAM rate-1 direct current offset space-time block codes is studied in terms of average worst-case pairwise error probability (WC-PEP) in quasi-static channels. It is shown that within this code class, the average WC-PEP is minimized by repetition coding (RC) under both electrical and optical individual power constraints, irrespective of channel statistics. This agrees with previously published results related to ON–OFF keying RC. This is further extended to sum power constraints, where it is shown that spatial beamforming minimizes the average WC-PEP within this code class, which simplifies to RC if the channel matrix has independent and indentically distributed columns and a sum electrical power constraint. Under a sum optical power constraint, this also holds true at high signal-to-noise ratio (SNR), but not at low SNR. Generally, the time dimension of this code class is redundant from an average WC-PEP perspective. Numerical results are provided to support the theoretical findings and to show that the average WC-PEP leads to a good approximation of the actual error probability at high SNR.

Performance Analysis of Media-Based Modulation With Imperfect Channel State Information

Media-based modulation (MBM) is an attractive modulation scheme where information bits are conveyed by digitally controlling the on/off status of radio frequency mirrors (which are parasitic elements) placed near the transmit antenna. The MBM alphabet (which is the set of channel fade coefficients corresponding to all possible mirror on/off status vectors) is estimated at the receiver through pilot transmissions. In this paper, we analyze the effect of imperfect channel estimation on the bit error performance of MBM. We present the analysis for generalized spatial modulation MBM (GSM-MBM). We analyze the performance for two types of detectors, namely the commonly studied mismatched detector, and the true maximum-likelihood (ML) detector that maximizes the likelihood by taking the statistics of the channel estimate into account. First, we derive an exact average pairwise error probability (PEP) expression for the mismatched detector using characteristic function approach, and obtain a union bound based upper bound on the average bit error probability (BEP). Next, given the estimate of the MBM alphabet, we derive the true ML detector for GSM-MBM, and derive an exact average PEP expression (by averaging the conditional PEP over the statistics of the channel estimate) and an upper bound on the average BEP. The exactness of the average PEP and the tightness of the average BEP upper bounds of the detectors are validated through simulations.

Energy Management for Energy Harvesting Wireless Sensors With Adaptive Retransmission

This paper analyzes the communication between two energy harvesting wireless sensor nodes. The nodes use automatic repeat request and forward error correction mechanism for the error control. The random nature of available energy and arrivals of harvested energy may induce interruption to the signal sampling and decoding operations. We propose a selective sampling scheme, where the length of the transmitted packet to be sampled depends on the available energy at the receiver. The receiver performs the decoding when complete samples of the packet are available. The selective sampling information bits are piggybacked on the automatic repeat request messages for the transmitter use. This way, the receiver node manages more efficiently its energy use. Besides, we present the partially observable Markov decision process formulation, which minimizes the long-term average pairwise error probability and optimizes the transmit power. Optimal and suboptimal power assignment strategies are introduced for retransmissions, which are adapted to the selective sampling and channel state information. With finite battery size and fixed power assignment policy, an analytical expression for the average packet drop probability is derived. Numerical simulations show the performance gain of the proposed scheme with power assignment strategy over the conventional scheme.

On the performance of wireless sensor networks with QSSK modulation in the presence of co-channel interference

This paper proposes the use of quadrature space shift keying (QSSK) modulation for wireless sensor networks (WSNs). QSSK is a multiple input multiple output communication protocol that attracted substantial interest due to several promised inherent advantages. It has been shown in literature that QSSK scheme achieves high spectral efficiency with low average error probability, high energy efficiency, and very simple transmitter and receiver architectures. Hence, its use in WSNs is very promising to ameliorate the major limitations of such networks. The performance of a WSN with QSSK modulation and in the presence of co-channel interference is studied in this paper. A closed form expression for the average pair wise error probability is derived and used to obtain a tight upper bound on the overall average bit error ratio. Obtained results verified the superiority of QSSK scheme as compared to traditional modulation techniques especially for high spectral efficiency.

On the SEP Analysis of OFDM Index Modulation With Hybrid Low Complexity Greedy Detection and Diversity Reception

In this work, we investigate the performance of multicarrier index keying (MCIK) orthogonal frequency division multiplexing (OFDM) proposing a hybrid low complexity detection and diversity reception. For performance analysis, we derive novel exact closed-form expressions for the average pairwise error probability (PEP) and symbol error probability (SEP) of three detection methods: a greedy detector (GD), and a GD with maximal ratio combining, or selection combining. Approximate and accurate expressions for the average PEP and SEP are also analyzed in closed-form. The derived expressions provide a useful insight into the error performance of MCIK-OFDM with the hybrid detector in low, moderate, and extreme rate of sparse sub-carrier indices activation. The effects of multiple antennas and sparse sub-carriers activation on the SEP are addressed in several extreme cases; decreasing the average SEP exponentially with proper choice of both subcarrier activation rate and number of antennas. In comparison with the benchmark detection, the numerical results and simulations clearly show that the proposed schemes can benefit from diversity gain, at substantially reduced complexity. The derived SEP expressions and analyses will be useful to evaluate various concepts of MCIK OFDM in low-power device applications.

MIMO Cooperative Cognitive Radio Relay Networks With Uniquely Factorable Signal Transmission

In this paper, we consider a cooperative cognitive radio relay network (CCRRN), in which there is a pair of primary transmitter (PT) and primary receiver (PR) with each having a single antenna, a secondary transmitter (ST) equipped with two antennas and a secondary receiver (SR) having a single antenna. We assume that ST operates in a half-duplex mode with an amplify-and-forward cooperative transmission scheme adopted. For such a system, a novel transmission scheme for CCRRN based on uniquely-factorable constellation pair is proposed, which enables ST to transmit its own information to SR without knowing its channel links to PR and SR while assisting PT transmission. It is shown that one of the significant advantages of our proposed new scheme is that, in a noise-free case, PR and SR are able to decode their own signals uniquely and that, in a Gaussian noise case, they are still able to reliably decode their own signals with full diversity. In addition, a tight upper bound of average pairwise error probability for the maximum-likelihood detector is derived, showing that full diversity is achieved. With this, an optimal power allocation strategy is proposed that minimizes the worst-case upper bound.