Pairwise Error Probability Research Articles

Performance analysis of polar-coded FSO systems using turbulence-oriented rotational probabilistic shaping.

Free-space optical (FSO) communications can provide high speed and large capacity, yet atmospheric turbulence poses a challenge. We propose a novel turbulence-oriented rotated probabilistic shaping (TRPS) scheme to achieve joint gains in coding, shaping, and signal space diversity for FSO systems. Our approach significantly enhances achievable rates in high signal-to-noise ratio (SNR) regions as turbulence intensity increases by optimizing probabilities and rotation angles. For instance, the achievable rate can be increased by 0.08 to 0.23 b/s from weak to strong turbulence compared to non-rotated uniform 16-ary quadrature amplitude modulation (16QAM) with a rate of 3.0 bits per symbol (b/s). Accordingly, the non-equivalent pairwise error probability as an upper bound on the average symbol error rate (ASER) is derived and verified, theoretically validating the superiority of TRPS in FSO systems. Furthermore, simulation results on ASER, and post-forward error correction bit error rate (BER) using polar codes demonstrate the potential of the proposed scheme. Compared to the uniform transmission without rotation, TRPS achieves joint gains of over 11.5 dB and 3 dB in ASER and BER for both 16QAM and 32QAM with a shaping depth of 0.05 in strong turbulence conditions.

Enhancing wireless communication systems through large intelligent surfaces: a performance analysis of LIS-assisted NOMA networks

The integration of large intelligent surfaces (LIS) with non-orthogonal multiple access (NOMA) networks has emerged as a promising solution to enhance the capacity and coverage of wireless communication systems. In this study, we analyse the performance of a NOMA network with the assistance of LIS. We propose a system model where a base station (BS) equipped with a LIS serves multiple users. The LIS consists of many passive elements that can influence the wireless channel by adjusting the reflection coefficients. We consider a downlink scenario where the BS transmits to multiple users simultaneously using NOMA, and the LIS helps to improve the signal quality and coverage. We additionally evaluate the efficiency of the suggested LIS-assisted NOMA network. In addition, we evaluate the efficiency of the LIS-assisted NOMA network in comparison to conventional NOMA systems that do not utilize LISs. The findings indicate that the LIS has a notable impact on enhancing the system's performance in terms of diversity gain, probability of error, and pairwise error probability (PEP). Moreover, the suggested LIS-assisted NOMA network is shown to be superior to conventional NOMA systems through comparison. These findings offer useful insights into the performance analysis of LIS-assisted NOMA networks. They also serve as inspiration and motivation for future research and development in this new subject, with the potential to revolutionize wireless communication systems.

Spectral efficiency improvement in cooperative RIS aided OFDM-IM system with hybrid indexing

Increasing demand for wireless communication leads to significant challenges in achieving high spectral efficiency (SE) and energy efficiency (EE). Orthogonal Frequency Division Multiplexing with Index Modulation (OFDM-IM) is one of the considerations, although it has the inherent disadvantage of a trade-off between SE and EE. In this work, frequency-dependent control on reconfigurable intelligent surfaces (RIS) and indexing to activate or deactivate the elements of RIS have been proposed to improve the SE of OFDM-IM systems. The Upper bound pairwise error probability has been derived and confirmed by simulation. The proposed work enhances the SE and EE compared to the conventional OFDM-IM systems. For instance, SE loss of 0.5bpcu in an OFDM-IM system with quadrature phase shift keying (QPSK) compared to an OFDM system has been compensated by the proposed work by maintaining EE.

Concatenated Nanopore DNA Codes.

In nanopore sequencers, single-stranded DNA molecules (or k-mers) enter a small opening in a membrane called a nanopore and modulate the ionic current through the pore, producing a channel output in the form of a noisy piecewise constant signal. An important problem in DNA-based data storage is finding a set of k-mers, i.e. a DNA code, that is robust against noisy sample duplication introduced by nanopore sequencers. Good DNA codes should contain as many k-mers as possible that produce distinguishable current signals (squiggles) as measured by the sequencer. The dissimilarity between squiggles can be estimated using a bound on their pairwise error probability, which is used as a metric for code design. Unfortunately, code construction using the union bound is limited to small k's due to the difficulty of finding maximum cliques in large graphs. In this paper, we construct large codes by concatenating codewords from a base code, thereby packing more information in a single strand while retaining the storage efficiency of the base code. To facilitate decoding, we include a circumfix in the base code to reduce the effect of the nanopore channel memory. We show that the decoding complexity scales as [Formula: see text], where m is the number of concatenated k-mers. Simulations show that the base code error rate is stable as m increases.

A Simple Design of Reconfigurable Intelligent Surface-Assisted Index Modulation: Generalized Reflected Phase Modulation

As a potential member of next generation wireless communications, the reconfigurable intelligent surface (RIS) can control the reflected elements to adjust the phase of the transmitted signal with less energy consumption. A novel RIS-assisted index modulation scheme is proposed in this paper, which is named the generalized reflected phase modulation (GRPM). In the GRPM, the transmitted bits are mapped into the reflected phase combination which is conveyed through the reflected elements on the RIS, and detected by the maximum likelihood (ML) detector. The performance analysis of the GRPM with the ML detector is presented, in which the closed form expression of pairwise error probability is derived. The simulation results show the bit error rate (BER) performance of GRPM by comparing with various RIS-assisted index modulation schemes in the conditions of various spectral efficiency and number of antennas.

A Design of Low-Projection SCMA Codebooks for Ultra-Low Decoding Complexity in Downlink IoT Networks

This paper conceives a novel sparse code multiple access (SCMA) codebook design which is motivated by the strong need for providing ultra-low decoding complexity and good error performance in downlink Internet-of-things (IoT) networks, in which a massive number of low-end and low-cost IoT communication devices are served. By focusing on the typical Rician fading channels, we analyze the pair-wise error probability of superimposed SCMA codewords and then deduce the design metrics for multi-dimensional constellation construction and sparse codebook optimization. For significant reduction of the decoding complexity, we advocate the key idea of projecting the multi-dimensional constellation elements to a few overlapped complex numbers in each dimension, called low projection (LP). An emerging modulation scheme, called golden angle modulation (GAM), is considered for multi-stage LP optimization, where the resultant multi-dimensional constellation is called LP-GAM. Our analysis and simulation results show the superiority of the proposed LP codebooks (LPCBs) including one-shot decoding convergence and excellent error rate performance. In particular, the proposed LPCBs lead to decoding complexity reduction by at least 97% compared to that of the conventional codebooks, whilst owning large minimum Euclidean distance. Some examples of the proposed LPCBs are available at https://github.com/ethanlq/SCMA-codebook.

Co-Efficient Vector Based Differential Distributed Quasi-Orthogonal Space Time Frequency Coding.

Distributed space time frequency coding (DSTFC) schemes address problems of performance degradation encountered by cooperative broadband networks operating in highly mobile environments. Channel state information (CSI) acquisition is, however, impractical in such highly mobile environments. Therefore, to address this problem, designers focus on incorporating differential designs with DSTFC for signal recovery in environments where neither the relay nodes nor destination have CSI. Traditionally, unitary matrix-based differential designs have been used to generate the differentially encoded symbols and codeword matrices. Unitary based designs are suitable for cooperative networks that utilize the amplify-and-forward protocol where the relay nodes are typically required to forego differential decoding. In considering other scenarios where relay nodes are compelled to differentially decode and re-transmit information signals, we propose a novel co-efficient vector differential distributed quasi-orthogonal space time frequency coding (DQSTFC) scheme for decode-and-forward cooperative networks. Our proposed space time frequency coding scheme relaxes the need for constant channel gain in the temporal and frequency dimensions over long symbol periods; thus, performance degradation is reduced in frequency-selective and time-selective fading environments. Simulation results illustrate the performance of our proposed co-efficient vector differential DQSTFC scheme under different channel conditions. Through pair-wise error probability analysis, we derive the full diversity design criteria for our code.

Constrained Riemannian Noncoherent Constellations for the MIMO Multiple Access Channel

We consider the design of multiuser constellations for a multiple access channel (MAC) with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> users, with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> antennas each, that transmit simultaneously to a receiver equipped with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> antennas through a Rayleigh block-fading channel when no channel state information (CSI) is available to either the transmitter or the receiver. In full-diversity scenarios where the coherence time is at least <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ≥ ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> + 1) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> , the proposed constellation design criterion is based on the asymptotic expression of the multiuser pairwise error probability (PEP) derived by Brehler and Varanasi (2001). In non-full diversity scenarios, for which the previous PEP expression is no longer valid, the proposed design criteria are based on proxies of the PEP recently proposed by Ngo and Yang (2021). Although both the PEP expression and its bounds or proxies were previously considered intractable for optimization, in this work we derive their respective unconstrained gradients. These gradients are in turn used in the optimization of the proposed cost functions in different Riemannian manifolds representing different power constraints. In particular, in addition to the standard unitary space-time modulation (USTM) leading to optimization on the Grassmann manifold, we consider a more relaxed percodeword power constraint leading to optimization on the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">oblique manifold</i> , and an average power constraint leading to optimization on the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">trace manifold</i> . Equipped with these theoretical tools, we design multiuser constellations for the MIMO MAC in full-diversity and non-full-diversity scenarios with state-of-the-art performance in terms of symbol error rate (SER).

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.

A unified bit-to-symbol mapping for generalized constellation modulation

Gray mapping is a well-known way to improve the performance of regular constellation modulation, but it is challenging to be applied directly for irregular alternative. To address this issue, in this paper, a unified bit-to-symbol mapping method is designed for generalized constellation modulation (i.e., regular and irregular shaping). The objective of the proposed approach is to minimize the average bit error probability by reducing the hamming distance (HD) of symbols with larger values of pairwise error probability. Simulation results show that the conventional constellation modulation(i.e., phase shift keying and quadrature amplitude modulation (QAM) with the proposed mapping rule yield the same performance as that of classical gray mapping. Moreover, the recently developed golden angle modulation (GAM) with the proposed mapping method is capable of providing around 1 dB gain over the conventional mapping counterpart and offers comparable performance to QAM with Gray mapping.

A Flexible Design Strategy for Three-Element Non-Uniform Linear Arrays

This paper illustrates a flexible design strategy for a three-element non-uniform linear array (NULA) aimed at estimating the direction of arrival (DoA) of a source of interest. Thanks to the spatial diversity resulting from non-uniform sensor spacings, satisfactory DoA estimation accuracies can be achieved by employing a very limited number of receiving elements. This makes NULA configurations particularly attractive for low-cost passive location applications. To estimate the DoA of the source of interest, we resort to the maximum likelihood estimator, and the proposed design strategy is obtained by constraining the maximum pairwise error probability to control the errors occurring due to outliers. In fact, it is well known that the accuracy of the maximum likelihood estimator is often degraded by outliers, especially when the signal-to-noise power ratio does not belong to the so-called asymptotic region. The imposed constraint allows for the defining of an admissible region in which the array should be selected. This region can be further modified to incorporate practical design constraints concerning the antenna element size and the positioning accuracy. The best admissible array is then compared to the one obtained with a conventional NULA design approach, where only antenna spacings multiple of λ/2 are considered, showing improved performance, which is also confirmed by the experimental results.

A Novel Maximum Distance Separable Coded OFDM-RIS for 6G Wireless Communications

The vision of the sixth generation mobile communication (6G) calls for extremely reliable data transmission over complex and diverse wireless channels. By combining the maximum distance separable (MDS) codes with the classic orthogonal frequency division multiplexing (OFDM), we present a new paradigm with the assistance of the reconfigurable intelligent surfaces (RIS). In our design, the RIS with limited phase shifts are adopted and the pairwise error probability (PEP) of the proposed system is first derived. Then, in order to further minimize the bit error rate (BER), we provide a novel method based on phase alignment to obtain the optimal solution for the discrete phase shifts. Our simulation results show that the proposed scheme provides considerable BER performance improvements compared to conventional OFDM systems. Moreover, the proposed discrete phase optimization algorithm is capable of achieving performance similar to that of the system with continuous phase shifts.

Union Bound Minimization Approach for Designing Grassmannian Constellations

In this paper, we propose an algorithm for designing unstructured Grassmannian constellations for noncoherent multiple-input multiple-output (MIMO) communications over Rayleigh block-fading channels. Unlike the majority of existing unitary space-time or Grassmannian constellations, which are typically designed to maximize the minimum distance between codewords, in this work we employ the asymptotic pairwise error probability (PEP) union bound (UB) of the constellation as the design criterion. In addition, the proposed criterion allows the design of MIMO Grassmannian constellations specifically optimized for a given number of receiving antennas. A rigorous derivation of the gradient of the asymptotic UB on a Cartesian product of Grassmann manifolds, is the main technical ingredient of the proposed gradient descent algorithm. A simple modification of the proposed cost function, which weighs each pairwise error term in the UB according to the Hamming distance between the binary labels assigned to the respective codewords, allows us to jointly solve the constellation design and the bit labeling problem. Our simulation results show that the constellations designed with the proposed method outperform other structured and unstructured Grassmannian designs in terms of symbol error rate (SER) and bit error rate (BER), for a wide range of scenarios.

Performance Analysis and Power Allocation for Spatial Modulation-Aided MIMO-LDM With Finite Alphabet Inputs

In this paper, we study a spatial modulation (SM) aided multiple-input multiple-output (MIMO) layered division multiplexing (LDM) system for broadcast/multicast service delivery in future broadcast/multicast systems. Comprehensive performance analysis and the injection level (IL) optimization are investigated for the SM-aided MIMO-LDM system over correlated Rayleigh fading channels. First, the symbol detection pairwise error probability (PEP) and the average symbol error rate (SER) union bound under joint maximum-likelihood (ML) detection are derived. Second, the spectral efficiency (SE) of the SM-aided MIMO-LDM system with finite alphabet inputs is analyzed. Since the theoretical SE lacks closed-form expression and involves prohibitive computational complexity, we then derive the closed-form lower bounds and tight approximations for the theoretical SE, in which the computational complexity is relieved by several orders of magnitude compared to direct calculation of the theoretical SE. Third, based on the SE analysis, a weighted sum (WS) SE maximization problem with quality of service (QoS) constraints is formulated to optimize IL for the SM-aided MIMO-LDM system. We first demonstrate that WS SE is a unimodal function of IL, and then develop an efficient golden section search (GSS) based algorithm. Simulation results are provided to validate the theoretical analysis. It is shown that our derived SER union bound well matches the simulated SER in the high SNR region. The tightness of the derived closed-form lower bounds and approximations for theoretical SE and the effectiveness of the developed IL optimization algorithm are also verified by simulation results.

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.

SCMA Codebook for Uplink Rician Fading Channels

In this letter, the codebook design criteria for uplink Rician fading channels are explored. The probability distribution of the weighted sums of the Rician random variables from each frequency resource is derived based on the independent non-central circular complex Gaussian random variable. Then, considering the pairwise error probability, the key performance indicators of multidimensional constellations for uplink Rician channels are explored. A sub-optimal optimization approach is deployed to generate an enhanced codebook for various Rician scenarios. Finally, numerical results are provided to verify the key performance indicators in the uplink Rician fading channels.

Coded Asymmetric Modulation Design for Block-Fading Channels With Nonlinear Energy Harvesting

In this letter, the design of coded modulation for simultaneous wireless information and power transfer (SWIPT) block-fading channels is proposed, for both power-splitting (PS) and time-switching (TS) nonlinear energy harvesting (EH). With PS, although the diversity-rate tradeoff is not affected, nonlinear EH requires asymmetric modulations design which leads to an information transfer (IT) performance penalty. We thus design an asymmetric circular quadrature amplitude modulation (ACQAM) scheme that provides large performance gains compared to conventional modulations. On the other hand, we show that TS negatively impacts the diversity-rate tradeoff of the coded modulation, while an optimal QAM can be employed in the IT phase. We next derive an upper bound on the average word error rate (WER) based on a pairwise error probability analysis for both EH methods. Finally, WER simulation results are shown together with the derived bounds.

Enhanced Signal Detection and Constellation Design for Massive SIMO Communications With 1-Bit ADCs

In this paper, we investigate a transmitter and receiver design for a single-user massive SIMO (single-input multiple-output) system with 1-bit analog-to-digital converters (ADCs) at the base station (BS), where the user adopts higher-order modulation, e.g., 16-quadrature amplitude modulation (16-QAM), for the data transmission. For the channel estimation and the signal detection, linear least-squares (LS) estimation and maximum ratio combining (MRC) are respectively employed. In this context, we first introduce closed-form formulas for the mean of the estimated symbols and for the correlation matrix between their real and imaginary parts considering the effect of 1-bit quantization. The study of the distribution of the estimated symbols indicates that, in presence of 1-bit ADCs, the conventional 16-QAM detector and the typical square 16-QAM modulation are not adequate. In light of this, we propose three novel symbol detectors and re-design the 16-QAM modulation in order to improve the symbol error rate (SER). Furthermore, the upper bound on the SER is analyzed based on the pair-wise error probability and the boundary equation between two regions is also studied. Through numerical results, the proposed framework, i.e., the symbol detector and the transmit constellation design, shows a significant enhancement in the SER performance against the conventional detector and the typical square 16-QAM modulation.

Performance analysis of signed quadrature spatial modulation system over Nakagami-m fading channels with spatial correlation

Novel performance analysis of the recently proposed signed quadrature spatial modulation (SQSM) multiple-input–multiple-output (MIMO) system is presented in this paper. This study covers the effects of Nakagami-m fading channels for different m values and the impact of spatial correlation impairment. The pairwise error probabilities (PEP) of SQSM over Nakagami-m fading channel with and without spatial correlation effects are computed. Moreover, a tight upper bound of average bit error ratio (ABEP) is derived. Monte Carlo simulation results for a wide range of signal to noise ratios (SNR) are introduced to corroborate the accuracy of the theoretical analyses. The performance of SQSM is compared with the quadrature spatial modulation (QSM) system.

Performance of Non-Orthogonal Multiple Access (NOMA) Systems Over $N$-Nakagami-m Multipath Fading Channels for 5G and Beyond

The new Fifth generation (5G) of wireless communications and beyond 5G (B5G) networks are required to provide connectivity for massive number of devices at high speed and low latency. Within this context, non-orthogonal multiple access (NOMA) has been involved and emerged in recent research since it is considered as an enabling technology for 5G and B5G networks. NOMA allows several users to share the same resources of time and frequency, making it an excellent candidate to provide impressively large connectivity with high spectral efficiency. In this paper, we study the performance of NOMA systems assuming independent but not necessarily to be identical <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> -Nakagami-m multipath fading channels. This channel model subsumes the double Nakagami-m, which was investigated in the context of intervehicular communications and keyhole multiple input multiple output systems, as special cases. To this end, we derive exact analytical and asymptotic expressions for the probability density function of the overall signal to noise ratio, system capacity, and the pairwise error probability (PEP) for each user. Numerical results are also provided herein to show the effects of fading parameters and number of users on the capacity and the PEP of each user.