Pairwise Error Probability Research Articles

Fully Improved Quadrature Spatial Modulation

In this paper, novel space modulation techniques (SMT), which we called fully improved quadrature spatial modulation (FIQSM) and fully improved quadrature space shift keying (FIQSSK), are presented for multiple-input–multiple-output (MIMO) communication systems. In these techniques, the improved structure that allows the use of an arbitrary number of Tx antennas is implemented. Unlike other SMT schemes, the spectral efficiency (SE) of proposed techniques increases linearly with the increase in the number of Tx antennas and a twofold increase in the number of spatially modulated bits is achieved with the aid of quadrature spatial structure. The bit error rate (BER) performance of the proposed techniques is investigated over Rayleigh fading channels for several MIMO designs. The average BER performances are also obtained analytically with the help of pairwise error probability and union-bound techniques in order to validate the simulation results. In addition, SE values achieved for varying SNR at a BER of $$10^{-3}$$ are obtained for both correlated and uncorrelated Rayleigh channels. In these figures, spatial multiplexing is considered as a benchmark as well as SMTs. As a result, the proposed modulation schemes outperform the benchmarks (e.g., spatial modulation, generalized spatial modulation, quadrature spatial modulation) in terms of BER at different spectral efficiencies. Additionally, the receiver complexity of the FIQSM scheme is equal to the benchmarks at the same spectral efficiency and the receiver complexity of the FIQSSK is lower than the others.

Large Intelligent Surface-Assisted Nonorthogonal Multiple Access for 6G Networks: Performance Analysis

Large intelligent surface (LIS) has recently emerged as a potential enabling technology for 6G networks, offering extended coverage and enhanced energy and spectral efficiency. In this work, motivated by its promising potentials, we investigate the error rate performance of LIS-assisted nonorthogonal multiple access (NOMA) networks. Specifically, we consider a downlink NOMA system, in which data transmission between a base station (BS) and L NOMA users is assisted by an LIS comprising M reflective elements (REs). First, we derive the probability density function (PDF) of the end-to-end wireless fading channels between the BS and NOMA users. Then, by leveraging the obtained results, we derive an approximate expression for the pairwise error probability (PEP) of NOMA users under the assumption of imperfect successive interference cancellation. Furthermore, accurate expressions for the PEP for M = 1 and large M values ( M > 10) are presented in closed-form. To gain further insights into the system performance, an asymptotic expression for PEP in high signal-to-noise ratio regime, asymptotic diversity order, and tight union bound on the bit error rate are provided. Finally, numerical and simulation results are presented to validate the derived mathematical results.

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.

Decoupled Transmit and Receive Antenna Selection for Precoding-Aided Spatial Modulation

This paper proposes an optimal joint transmit and receive antenna subsets (TRASs) selection scheme for linear precoding-aided spatial modulation (PSM) systems. The optimal joint TRASs selection is performed by exhaustively searching, so that it is difficult to analyze an achievable diversity gain and it has a huge complexity. To tackle this problem, we propose a decoupled TRAS selection method which selects receive antenna subset (RAS) and transmit antenna subset (TAS) in a two-step serial manner. By computing a lower bound on the pairwise error probability and conducting extensive simulations, it is shown that the zero-forcing (ZF)-based PSM system with $N_{T} $ transmit antennas, $N_{S} $ selected transmit antennas, $N_{R} $ receive antennas, and $N_{D} $ selected receive antennas achieves diversity order of $(N_{T} -N_{D} +1)(N_{R} -N_{D} +1)$ even with TAS selection. Furthermore, decreasing the number of active transmit antennas by TAS selection after RAS selection is analytically shown to always degrade the bit error rate performance. The analysis results are validated by simulations. These analytical and simulation results can be regarded as natural extensions of earlier works on receive antenna selection and transmit antenna selection for the PSM systems. In addition, we study and compare two efficient algorithms for TRAS selection. First, incremental and decremental algorithms are employed for separable RAS and TAS successive selection, respectively, which have an excellent performance. It is analytically shown that the computational complexity of the first proposed decoupled suboptimal TRAS selection scheme is enormously reduced compared to the joint optimal and decoupled optimal algorithms. Second, an incremental TAS selection approach replaces the decremental strategy in the first TRAS selection algorithm to further reduce the complexity.

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.

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.

An Error Rate Comparison of Power Domain Non-Orthogonal Multiple Access and Sparse Code Multiple Access

Non-orthogonal Multiple Access (NOMA) has been envisioned as one of the key enabling techniques to fulfill the requirements of future wireless networks. The primary benefit of NOMA is higher spectrum efficiency compared to Orthogonal Multiple Access (OMA). This paper presents an error rate comparison of two distinct NOMA schemes, i.e., power domain NOMA (PD-NOMA) and Sparse Code Multiple Access (SCMA). In a typical PD-NOMA system, successive interference cancellation (SIC) is utilized at the receiver, which however may lead to error propagation. In comparison, message passing decoding is employed in SCMA. To attain the best error rate performance of PD-NOMA, we optimize the power allocation with the aid of pairwise error probability and then carry out the decoding using generalized sphere decoder (GSD). Our extensive simulation results show that SCMA system with “ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5\times 10$ </tex-math></inline-formula> ” setting (i.e., ten users communicate over five subcarriers, each active over two subcarriers) achieves better uncoded BER and coded BER performance than both typical “ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\times 2$ </tex-math></inline-formula> ” and “ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times 4$ </tex-math></inline-formula> ” PD-NOMA systems in uplink Rayleigh fading channel. Finally, the impacts of channel estimation error on SCMA, SIC and GSD based PD-NOMA and the complexity of multiuser detection schemes are also discussed.

Non-Orthogonal Multiple Access in the Presence of Additive Generalized Gaussian Noise

In this letter, we investigate the performance of non-orthogonal multiple access (NOMA), under the assumption of generalized Gaussian noise (GGN), over Rayleigh fading channels. Specifically, we consider a NOMA system with $L$ users, each of which is equipped with a single antenna, and derive an exact expression for the pairwise error probability (PEP). The derived PEP expression is subsequently utilized to derive a union bound on the bit error rate (BER) and to quantify the diversity orders realized by NOMA users in the presence of additive white (AW) GGN. Capitalizing on the derived PEP expression and the union bound, the error rate performance of NOMA users is further evaluated for different special cases of AWGGN. The derived analytical results, corroborated by simulation results, show that the shaping parameter of the GGN $(\alpha)$ has negligible effect on the diversity gains of NOMA users, particularly for large $\alpha $ values. Accordingly, as in the case of additive white Gaussian noise (AWGN), the maximum achievable diversity order is determined by the user’s order.

Optimal Open-Loop MIMO Precoder Design

Multiple-input multiple-output (MIMO) is a favorable technique that can improve system capacity and performance through spatial multiplexing. However, the performance gets degraded over the correlated wireless channels. In this letter, we consider a point-to-point MIMO system and jointly optimize both the precoding matrix and the difference between two transmit vectors to resist transmit correlation. The simulation results demonstrate that the proposed method can get average 75% gain comparing with the existing method in terms of the minimum pairwise error probability.

A Generalized Dimming Control Scheme for Visible Light Communications

A novel dimming control scheme, termed as generalized dimming control (GDC), is proposed for visible light communication (VLC) systems. The basic idea of GDC is to exploit adaptively time, spatial and signal domain resources for enhancing communication performance under practical illumination constraints. In particular, to satisfy the illumination constraints, an incremental algorithm for index mapping is first proposed to achieve target optical power and uniform illumination. Next, GDC having the optimal activation pattern is investigated to improve the bit-error rate (BER) performance of VLC. In particular, the BER performance of GDC is analyzed using the union bound technique. Based on the analytical BER bound, the optimal activation pattern of GDC scheme having the minimum BER criterion (GDC-MBER) is obtained by exhaustively searching all conditional pairwise error probabilities. However, since GDC-MBER requires high search complexity, two low-complexity GDC schemes having the maximum free distance criterion (GDC-MFD) are proposed. The first low-complexity GDC-MFD scheme, termed as GDC-MFD1, is derived by a lower bound of the free distance using the Rayleigh-Ritz theorem. The second low-complexity GDC-MFD scheme, termed as GDC-MFD2, is proposed to reduce further the computation by exploiting the time-invariance characteristics of the VLC channel. Simulation and numerical results show that GDC-MBER, GDC-MFD1 and GDC-MFD2 have similar BER performance, and they can achieve more than 3 dB SNR gains compared with conventional dimming control schemes for a BER of ${10^{ - 4}}$ and a dimming level of 50%.

Performance Analysis and Constellation Design for the Parallel Quadrature Spatial Modulation.

Spatial modulation (SM) is a multiple-input multiple-output (MIMO) technique that achieves a MIMO capacity by conveying information through antenna indices, while keeping the transmitter as simple as that of a single-input system. Quadrature SM (QSM) expands the spatial dimension of the SM into in-phase and quadrature dimensions, which are used to transmit the real and imaginary parts of a signal symbol, respectively. A parallel QSM (PQSM) was recently proposed to achieve more gain in the spectral efficiency. In PQSM, transmit antennas are split into parallel groups, where QSM is performed independently in each group using the same signal symbol. In this paper, we analytically model the asymptotic pairwise error probability of the PQSM. Accordingly, the constellation design for the PQSM is formulated as an optimization problem of the sum of multivariate functions. We provide the proposed constellations for several values of constellation size, number of transmit antennas, and number of receive antennas. The simulation results show that the proposed constellation outperforms the phase-shift keying (PSK) constellation by more than 10 dB and outperforms the quadrature-amplitude modulation (QAM) schemes by approximately 5 dB for large constellations and number of transmit antennas.

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.

Generalized OFDM-IM With Noncoherent Detection

This paper generalizes the conventional noncoherent OFDM-IM systems by allowing selection of different numbers of active subcarriers for message representation. We then present the maximum-likelihood (ML) detection rule for frequency-selective block fading channels. The performance of the ML receiver is analyzed in terms of pairwise-error probability as well as diversity order. Asymptotic analysis of the proposed system reveals the role of partial Hamming distance in designing diversity-exploiting activation patterns. Practical issues including low-complexity receiver, and code (activation pattern) design techniques are discussed. Furthermore, the effect of inter-carrier interference in fast fading scenarios, and generalization of the technique to multiple-antenna scenarios are studied. Finally, we present simulation results to illustrate performance benefits of the generalized OFDM-IM systems over the conventional noncoherent OFDM-IM systems.

Spatial-Modulation-Based Techniques for Backscatter Communication Systems

A vision of a digital and connected world is now a global strategy for 5G Internet of Things (IoT), targeting for high-speed communication services with more capacity, lower latency, increased reliability, and availability. In this article, we assess the added value of backscatter communication in 5G IoT technology, by studying spatial modulation (SM)-based techniques, applied over a traditional multiple antenna backscatter communication system. Particularly, with backscatter, we fulfill the need for wireless self-powered devices, as one of the main characteristics of 5G IoT. Furthermore, with the use of multiple antennas, we apply sophisticated techniques that enhance the overall efficiency of the backscatter communication system. Initially, we study generalized SM (GSM) and its special case of SM, exploiting the antenna index as an additional source of information. With this technique, enhanced performance in terms of symbol error rate (SER) and spectral efficiency, is provided. In addition, we expand GSM in the time domain, by applying the Alamouti coding scheme (GSMA) in two out of the multiple available antennas. In this way, we further enhance the performance and succeed transmit diversity. Finally, analytical expressions regarding the pairwise error probability are derived and presented, while a diversity analysis is carried out for the proposed techniques. The simulation results along with theoretical bounds are provided, validating the enhanced performance of our study.

Down-Link NOMA Networks in the Presence of IQI and Imperfect SIC: Receiver Design and Performance Analysis

This article addresses the practical aspects that may affect the performance of down-link non-orthogonal multiple access (NOMA) systems. The system performance of two down-link NOMA users, where both users suffer from the effects of in-phase/quadrature-phase imbalance (IQI), while the first user also experiences imperfect successive interference cancellation (SIC) is examined. In order to mitigate the effects of IQI, an optimal maximum likelihood (ML) receiver is designed and analyzed, and the performance of the proposed receiver is compared with the traditional ML one. Moreover, closed-form mathematical expressions of the conditional pairwise error probability (PEP) for each user are derived. The simulation results validate the analysis and demonstrate that the proposed receiver outperforms the traditional one, with the ability to reduce the effects of IQI for both users.

SEP of the M-ary $$\theta $$-QAM signals under $$\eta -\mu $$ fading and AWGN noise in a communication system using spatial diversity

In this paper, an upper bound on the symbol error probability (SEP) of the M-ary $$\theta $$-quadrature amplitude modulation scheme, in a channel subject to additive white Gaussian noise (AWGN) and $$\eta -\mu $$ fading, is calculated by means of the union bound. In addition, an exact and closed-form expression for the pairwise error probability (PEP) of the system is derived. The PEP expression obtained is written in terms of the Beta function and the Lauricella hypergeometric function. Another expression for the PEP, written in terms of the Beta function and the Appell hypergeometric function, and two bounds for the PEP, one lower and one upper, are also presented. An exact expression for the optimum rotation angle for quadrature phase shift keying constellation, considering this channel model, is also determined. In addition, an analysis, in terms of PEP, of the modulation diversity system combined with a maximum ratio combining receiver in channels subject to $$\eta -\mu $$ fading and AWGN noise, is performed. PEP and SEP curves, as a function of signal-to-noise ratio, are plotted and corroborated by simulations performed with the Monte Carlo method under different parameters that characterize the channel mathematically. All the expressions determined in this article are closed and new.

NOMA-based downlink relaying with media-based modulation

In recent years, non-orthogonal multiple access (NOMA) has attracted considerable attention as a promising multi-access technique for next generation wireless communication systems. Media-based modulation (MBM), which is an emerging index modulation concept, is another technique that can be considered for next generation wireless communication systems due to its high spectral and energy efficiency. In this paper, we propose a NOMA-based decode-and-forward relaying system, where MBM is applied at the source to improve error performance at the relay. We consider a topology consisting of a single source with a single transmit antenna equipped with multiple radio frequency (RF) mirrors, one relay equipped with a single transmit and multiple receive antennas, and multiple users equipped with multiple receive antennas. Pairwise error probability expression for NOMA with multiple receive antennas is derived and the union bound on bit error rate (BER) for the overall system with imperfect successive interference cancellation (SIC) is obtained in closed-form. Analytical results are in agreement with the Monte Carlo simulation results. Moreover, two power allocation optimization problems are formulated in terms of user fairness and quality of service requirements of the users. BER performance of the proposed system is also investigated using the optimum coefficients according to the formulated problems. It is shown that the proposed system outperforms the conventional cooperative NOMA system in terms of error performance as the data rate increases.

Index and Constellation Order Lowering for OFDM With Index Modulation

Orthogonal frequency division multiplexing with index modulation (OFDM-IM) is a promising variant of OFDM where indices of symbol carrying sub-carriers also convey information bits besides the complex symbols themselves. Recently, a lower order modulation variant has been proposed for OFDM-IM, where the baseband constellation is lowered with appropriate rotations and index reuse, so as to lower the number of sub-blocks whose pairwise error probability is inversely related to the signal to noise ratio (SNR). In this work, we demonstrate that the number of symbol carrying sub-carriers and hence the number of used indices can also be lowered along with modulation order lowering. This reduces the aforementioned number of worst case sub-block pairs even further. The resulting unused sub-carriers can now be used to enhance the spectral efficiency as well. Numerical results reveal SNR gains up to 5dB for uncoded systems and 2dB for coded systems.

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.

Large-System Analysis of AF Full-Duplex Massive MIMO Two-Way MRC/MRT Relaying

The massive multiple-input multiple-output (MIMO) full-duplex two-way relaying (FD-TWR) literature has extensively investigated power scaling for rate guarantees by considering a fixed number of users. We investigate the pairwise error probability (PEP) and the per-user rate of a FD-TWR with $N_{r}$ relay antennas that employs maximal ratio combining/transmission to enable two-way communication between $K$ FD users. We propose novel relay and user powers scalings, with both $N_{r}$ and $K$ tending to infinity, and show that the PEP of each user converges almost surely to its AWGN counterpart. These power scalings are different from the existing ones, which are derived by fixing $K$ and by assuming that only $N_{r}$ tends to large values. We show that the analysis developed herein applies to both Gaussian and non-Gaussian complex channels with finite number of moments. We numerically show that when both $K$ and $N_{r}$ increase concurrently to large values, the proposed power scaling schemes not only have better per-user PEP and rate than the existing schemes, but they are also robust to the FD self loop-interference power.