Approximate Symbol Error Rate Research Articles

RIS-Assisted NOMA With Interference-Cancellation and Interference-Alignment Scheme

Reconfigurable intelligent surface (RIS) is a cost-effective method to enhance the end-to-end wireless channel. Meanwhile, Non-Orthogonal Multiple Access (NOMA) improves the overall spectral efficiency, connectivity and latency by allowing different users to utilize the same resource blocks. Combining these two technologies has been the main focus of recent research. In this letter, we propose a RIS-assisted NOMA with an interference-cancellation scheme, wherein a group of phase shift elements is assigned to mitigate interference to other users not being supported. We also propose an interference-alignment scheme when RIS is supporting all the NOMA users. In this particular scheme, we align the RIS-amplified signal of each user to the interference for better reception. We analyze the symbol error rate (SER) performance of these schemes in a downlink <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}$ </tex-math></inline-formula> -QAM NOMA system. We adopt a simple model where we derive approximate SER expressions and bounds, and simulate them to validate the results.

Theoretical Performance of LoRa System in Multipath and Interference Channels

This paper presents a semi-analytical approximation of Symbol Error Rate (SER) for the well known LoRa Internet of Things (IoT) modulation scheme in the following two scenarios: 1) in multi-path frequency selective fading channel with Additive White Gaussian Noise (AW GN) and 2) in the presence of a second interfering LoRa user in flat-fading AW GN channel. Performances for both coherent and non-coherent cases are derived by considering the common Discrete Fourier transform (DF T) based detector on the received LoRa waveform. By considering these two scenarios, the detector exhibits parasitic peaks that severely degrade the performance of the LoRa receiver. We propose in that sense a theoretical expression for this result, from which a unified framework based on peak detection probabilities allows us to derive SER, which is validated by Monte Carlo simulations. Fast computation of the derived closedform SER allows to carry out deep performance analysis for these two scenarios.

Circularly Symmetric Companding Quantization-Inspired Hybrid Constellation Shaping for APSK Modulation to Increase Power Efficiency in Gaussian-Noise-Limited Channel

In this paper we address hybrid probabilistic-geometric constellation shaping (HCS) of amplitude phase shift keying (APSK) constellation based on the reversed model of optimal companding quantization for circularly symmetric sources with the goal to increase the constellation power efficiency in Gaussian-noise-limited channel. To empirically optimize the proposed APSK constellation such that a symbol-error rate (SER) reaches its minimum under given constraints with respect to signal-to-noise ratio (SNR) and the prior probabilities of constellation points, for various settings of constellation parameters, we investigate SER dependence on SNR and determine the constellation parameters achieving minimum SER. The SER dependence on SNR we estimate theoretically by deriving approximate formula for SER of uncoded APSK constellation in Gaussian-noise-limited channel and practically by performing simulation. The obtained results are well-matched verifying the accuracy of approximate SER formula. The results also show that our APSK constellation outperforms some previous APSK and M-ary QAM constellations in terms of power efficiency. Thus, for SER equal to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> the gain in power efficiency amounts up to 2.35 dB, 2.23dB and 1.64 dB compared with the maximum mutual information-optimized 4+12-APSK, 4+12+16-APSK and 4+12+20+28-APSK constellations, respectively. This means that by employing APSK constellation we propose instead the traditional APSK constellations the transmitted signal power can be reduced by a third enabling lower power consumption. The improved power efficiency of our APSK constellation makes it suitable for application in power-limited communications such as fiber-optic communications, satellite communications, power-line communications, and multiple-input multiple-output wireless transmissions.

Flexible Generalized Spatial Modulation for Visible Light Communications

Adaptive spatial modulation (ASM) varies the modulation size across the transmit light-emitting diodes (LEDs) to improve the overall spectral efficiency of visible light communication (VLC) systems. This article proposes a novel ASM scheme, referred to as flexible generalized spatial modulation (FGSM), for VLC systems. The proposed FGSM system changes the modulation sizes over the LEDs and the number of active LEDs, to improve the average symbol error rate (SER) and spectral efficiency compared to ASM with a fixed overall number of LEDs. The modulation sizes are selected in order to optimize the average SER under a predefined spectral efficiency value. A closed-form expression of approximate SER is derived along with decoding complexity calculations for the proposed system. Numerical results are provided to confirm the superiority of the proposed system and to support theoretical derivations.

SER Analysis for SWIPT-Enabled Differential Decode-and-Forward Relay Networks

In this article, we analyze the symbol error rate (SER) performance of the simultaneous wireless information and power transfer (SWIPT) enabled three-node differential decode-and-forward (DDF) relay networks, which adopt the power splitting (PS) protocol at the relay. The use of non-coherent differential modulation eliminates the need for sending training symbols to estimate the instantaneous channel state information (CSI) at all network nodes, and therefore improves the power efficiency, as compared with the coherent modulation. However, performance analysis results are not yet available for the state-of-the-art detectors such as the maximum-likelihood detector (MLD) and approximate MLD. Existing works rely on the Monte-Carlo simulation method to show the existence of an optimal PS ratio that minimizes the overall SER. In this work, we propose a near-optimal detector with linear complexity with respect to the modulation size. We derive an approximate SER expression and prove that the proposed detector achieves the full diversity order. Based on our expression, the optimal PS ratio can be accurately estimated without requiring any Monte-Carlo simulation. We also extend the proposed detector and its SER analysis for adopting the time switching (TS) protocol at the relay. Simulation results verify the effectiveness of our proposed detector and the accuracy of our SER results in various network scenarios for both PS and TS protocols.

Product of Squared SR Random Variables: Application to Satellite Communication

We investigate the problem associated with the statistics of the product of two squared Shadowed Rician (SR) random variables (RVs). Both SR RVs are independent and nonidentically distributed. The distribution of the product of two squared SR RVs is very important from the satellite communication perspective. We derive approximate expressions of the probability density function (p.d.f.), the moment generating function (m.g.f.), and the cumulative distribution function (c.d.f.) in terms of Meijer-G functions. Furthermore, exact closed-form expressions for higher order moments, channel quality estimation index, and amount of fading are derived. The outage probability is also discussed by utilizing the expression of the c.d.f. An approximate closed-form expression of channel capacity is also derived with the help of the p.d.f. expression. Furthermore, the performance of satellite communication system is discussed in terms of the approximate symbol error rate by using the derived results. Specifically, the derived expression of the p.d.f. is used to develop an approximate closed-form expression of the m.g.f. for an amplify-and-forward-based satellite communication system.

Particle swarm optimization–based power allocation for Alamouti amplify and forward relaying protocol

SummaryThe performance of wireless communication systems is improved over flat fading channel by using Alamouti coding scheme, which provides the quality of diversity gain. In this paper, performance analysis of symbol error rate (SER) and particle swarm optimization (PSO)–based power allocation (PA) for Alamouti amplify and forward (AF) relaying protocol using maximum ratio combining (MRC) technique is presented. Analytical expression of SER upper bound and SER approximation is derived for Alamouti AF relaying protocol with quadrature phase shift keying (QPSK) modulation over Rayleigh fading channel and Rician fading channel. In addition, PSO‐based optimum PA factor is calculated on the basis of the minimum SER of proposed method. PSO‐based optimum PA gives 0.5 dB of improved signal‐to‐noise ratio (SNR) compared with the equal power allocation (EPA). The theoretical approximate SER result is compared with the simulated SER. The proposed protocol provides full diversity gain and reduces SER compared with the existing AF and decode and forward (DF) relaying protocols over Rayleigh fading channel and Rician fading channel.

Analysis of Optimal Combining in Rician Fading With Co-Channel Interference

Approximate symbol error rate (SER), outage probability, and rate expressions are derived for receive diversity system employing optimum combining when both the desired and the interfering signals are subjected to Rician fading, for the cases of equal power uncorrelated interferers, unequal power interferers, and interferer correlation. The derived expressions are applicable for an arbitrary number of receive antennas and interferers and for any quadrature amplitude modulation constellation. Furthermore, we derive a simple closed-form expression for SER in the interference-limited regime, for the special case of Rayleigh faded interferers. A close match is observed between the SER, outage probability, and rate results obtained through the derived analytical expressions and the ones obtained from Monte Carlo simulations.

Exact error rate analysis of two-hop AF Rayleigh fading cooperative systems with variable amplification gain

A careful exploration of literature confirms that exact symbol-error-rate (SER) performance of amplify-and-forward (AF) wireless cooperative communication systems with variable amplification gain has not been analyzed before; even for simple models with single relay (i.e, two-hop systems) and Rayleigh fading channels. The main source of this mathematical intractability is the appearance of the modified Bessel function of the second type Kν(·) in the statistics of these systems end-to-end SNR. Here, however, we aim at filling this literature gap by proposing a novel theoretical method that helps in examining, for the first time, the exact SER performance of two-hop AF systems, where, as a case study, we assume Rayleigh quasi-static fading environment with perfect channel estimation. Specifically, we derive two new exact expressions for the system’s SER performance, which involve rapidly convergent infinite summation(s) and efficiently computable special functions. Furthermore, for the same system, we obtain new approximate closed-form SER expression, which outperforms its literature counterpart. The obtained analytical results are useful to gain insight about the actual error performance of variable gain AF systems. The presented methodologies can form a generic framework for exact SER performance evaluation of other variable gain AF cooperative system models.

Space-Time Network Coding With Multiple AF Relays Over Nakagami- $m$ Fading Channels

This paper first analyzes the symbol error rate (SER) performance of the space-time network coding (STNC) over independent but not necessarily identically distributed (i.n.i.d) Nakagami- $m$ fading channels, where multiple sources transmit information symbols to a destination through multiple helping amplify-and-forward (AF) relays. The exact expressions of the overall end-to-end received signal-to-noise ratio (SNR) via multiple STNC-AF relays and its moment generating function (MGF) are derived. Based on these results, the closed-form expression of STNC-AF for the SER with $M$ -ary phase-shift keying and $M$ -ary quadrature-amplitude modulation (QAM) modulations are then presented by adopting the unified MGF method. Furthermore, an approximate SER expression with low computational complexity is also given. In order to observe the performance limit, the diversity order and the nonorthogonality of STNC codes are discussed. Simulation results demonstrate our analytical results and it is illustrated that the diversity order of the STNC with multiple AF relay nodes is a sum function of the fading index of the direct link and the minimal fading indices of the multiple two-hop links.

Comparative study of signalling methods for high-speed backplane transceiver

ABSTRACTA combined analysis of transient simulation and statistical method is proposed for comparative study of signalling methods applied to high-speed backplane transceivers. This method enables fast and accurate signal-to-noise ratio and symbol error rate estimation of a serial link based on a four-dimension design space, including channel characteristics, noise scenarios, equalisation schemes, and signalling methods. The proposed combined analysis method chooses an efficient sampling size for performance evaluation. A comparative study of non-return-to-zero (NRZ), PAM-4, and four-phase shifted sinusoid symbol (PSS-4) using parameterised behaviour-level simulation shows PAM-4 and PSS-4 has substantial advantages over conventional NRZ in most of the cases. A comparison between PAM-4 and PSS-4 shows PAM-4 gets significant bit error rate degradation when noise level is enhanced.

Average symbol error rate and outage probability of DS-CDMA systems with AF relaying over asymmetric fading channels

In this paper, approximate outage probability (OP) and average symbol error rate (SER) of cooperative direct-sequence code-division multiple access (DS-CDMA) systems with amplify-and-forward (AF) relaying are evaluated over asymmetric fading channels. Practically, the channels between source (S), relay (R) and destination (D) nodes in a DS-CDMA system can be subject to different fading due to the nature of wireless medium. Motivated by this reality, the S–D path is assumed to be Nakagami-m distributed which is a general fading model for different types of channel conditions while S–R and R–D paths are considered to experience Rician fading in order to include line of sight conditions. First, closed-form solutions are obtained for both the cumulative distribution function and the probability density function of S–R–D paths. Then, a closed-form total moment generating function (MGF) of the considered system is derived. The lower bound of the OP is calculated with the help of the inverse Laplace transform of the derived MGF expression while average SER is analyzed by evaluating the integral over the derived MGF. Finally, an asymptotic MGF expression is proposed for high signal-to-noise ratio (SNR) analysis of AF DS-CDMA systems. The simulation results are provided to verify the correctness of the analytical derivations. It is shown that the approximate OP and average SER results are in well agreement with the simulations and the asymptotic results are tight from medium to high SNR regime.

Decode-to-cooperate: a sequential alamouti-coded cooperation strategy in dual-hop wireless relay networks

An optimal cooperation strategy, decode-to-cooperate, is proposed and investigated for performance improvements in dual-hop wireless relay networks. Based on decode-and-forward (DF) strategy with multiple relay selection, we design a novel scheme such that the source node keeps transmitting sequentially and the selected relays cooperate by transmitting the decoded signal using distributed Alamouti coding. We exploit the multipath propagation effect of the wireless channel to achieve lower probability of error and introduce optimum power allocation and relay positioning. We analyze the scenario when the source to destination direct link is not available and derive a closed form expression for symbol error rate (SER), its upper bound and an asymptotically tight approximation to exploit the performance gain by selecting the optimum relays in a multiple-relay cooperation scheme. Moreover, asymptotic optimum power allocation (based on the SER approximation) and optimal relay positioning are also considered to further improve the SER. The proposed relay selection scheme outperforms cooperative (DF) and non-cooperative schemes by more than 2 dB.

Achievable performance analysis of multiuser scheduling for different MIMO systems over Rayleigh fading channels

In this paper, a comprehensive performance analysis of downlink multiuser scheduling multiple-input multiple-output (MUS-MIMO) transceiving system under Rayleigh fading channels is presented. The attainable analysis is suitable for MIMO transceiving systems in which output signal-to-noise ratio (SNR) is specified as highest order statistic of chi-square distribution. Based on this framework, the closed-form expressions of average channel capacity, outage probability and average symbol error rate (SER) are evaluated for the MUS-MIMO exploiting selective transmission/selective combining (ST/SC), selective transmission/maximum ratio combining (ST/MRC) and space-time block codes (STBC). Thereafter the impact of antenna structures, antenna selection gains with significance on the consideration of MUS on the performance of the system has been observed. This paper also provides the upper bounds on the capacity, capacity in high & low SNR region as well as approximate SER performance. Numerical results illustrate that the MUS-MIMO transceiving schemes can achieve full diversity order and MUS-MIMO system with ST/MRC is outperformed compared to ST/SC and STBC due to relatively higher coding gain.

Correction of amplitude distortions for truncated Bessel beam and SER estimation for 4ASK

We apply amplitude corrections to a truncated Bessel beam that has propagated through turbulent atmosphere modelled by random phase screens. These corrections are realized via transmitting an unmodulated beam in parallel to the one carrying the 4 amplitude shift keying (ASK) modulated message signal. On the receiver side, the amplitude corrections are obtained by dividing the intensity of the unmodulated beam by its free space equivalence. The corrections are then used to restore the amplitude distortions of the beam carrying the 4ASK modulated message signal and in the determination of decision boundaries for the received 4ASK symbols. The success of the system is visually inspected by comparing the received intensity profiles before and after the application of corrections. Furthermore, simulation analysis of symbol error rate (SER) is made, where the proposed set-up is found to be quite insensitive to wavelength difference between the unmodulated and modulated beams. On the other hand, the difference in the structure constant values of these two beams seems to have profound effect on system performance.

Modified Cooperative Subchannel Allocation Algorithms and PSO Based Power Allocation for an Alamouti Decode and Forward Relaying Protocol in Multiuser OFDMA Systems

The present work is a discussion on the performance analysis of Modified Cooperative Subchannel Allocation (CSA) Algorithms which is used in Alamouti Decoded and Forward (Alamouti DF) Relaying Protocol for wireless multi-user Orthogonal Frequency Division Multiplexing Access (OFDMA) systems. In addition, the performance of approximate Symbol Error Rate (SER) for the Alamouti DF Relaying Protocol with the Cooperative Maximum Ratio Combining Technique (C-MRC) is analyzed and compared with SER upper bound. The approximate SER is asymptotically tight bound at higher Signal-to-Noise Ratio (SNR). From the asymptotic tight bound approximate SER, Particle Swarm Optimization (PSO) based Power Allocation (PA) is determined for the Alamouti DF Relaying Protocol. The simulation results suggested that the Modified Throughput based Subchannel Allocation Algorithm achieved an improved throughput of 6% to 33% compared to that of existing cooperative diversity protocol. Further, the Modified Fairness based Subchannel Allocation Algorithm rendered fairness of 7.2% to 17% among the multiuser against the existing cooperative diversity protocol.

SER for Optimal Combining in the Presence of Multiple Correlated Co-Channel Interferers

Symbol error rate (SER) performance has been analyzed for a receive diversity system in the presence of multiple interferers and noise over fading channels. Both unequal power interferers and correlated interferers have been considered. The derived approximate SER expressions are easy to evaluate and are applicable to any QAM constellation and arbitrary number of receive antennas and interferers. Further, the impact of correlation between interferer channels is studied and it is shown that correlation behaves like partial interference alignment.

Performance Analysis of MIMO Systems with Antenna Selection over Generalized κ − μ Fading Channels

In this paper, we derive closed form expression for outage probability and infinite series expressions for exact and approximate symbol error rate (SER) and capacity of multiple input multiple output systems with transmit antenna selection (TAS) over generalized independent and identically distributed κ − μ fading channels. The results are applicable to systems employing maximal ratio combining or selection combining at the receiver. Furthermore, by taking special cases, we present closed form expressions for outage probability of TAS systems over Nakagami-m and Rayleigh fading channels. The closed form expressions of outage probability for Nakagami-m and Rayleigh fading are computationally efficient than the expressions reported in the existing literature. The expressions of SER and channel capacity are in the form of sum of fast converging infinite series for all values of fading parameters. The analytical results are validated by comparing them with Monte Carlo simulation results for different values of fading parameters. The results of channel capacity shows that increased strength of line of sight component and decreased severity of fading degrades the channel capacity.

MGF Based Approximate SER Calculation of SM MIMO Systems Over Generalized η − μ and κ − μ Fading Channels

Spatial modulation (SM) is a multiple input multiple output (MIMO) wireless communication system that gives better spectral efficiency without costing extra bandwith for the same signal constellation size. In an SM MIMO system with $$N_t$$Nt transmitting antennas, spectral efficiency increases by $$log_2(N_t)$$log2(Nt). The superior performance of SM systems over other MIMO systems like Alamouti Space-Time Block Codes and Vertical Bell Laboratories Layered Space-Time is already reported in the literature. In this paper, we analyzed the symbol error rate (SER) performance of an SM system in generalized $$\eta-\mu $$?-μ and $$\kappa - \mu $$?-μ fading channels for several modulation schemes. A closed form expression for approximate SER is derived using moment generating function (MGF) approach and the results are validated using Monte Carlo simulations. The approximate SER expression obtained in this communication is applicable for any fading channels whose MGF is known. The SER analysis over generalized fading channels can be easily deduced to various classical fading channels like Rayleigh, Rician, Nakagami-m and Nakagami-q fading channels by choosing appropriate values of $$\kappa $$?, $$\mu $$μ and $$\eta $$?.

Analysis of TAS/MRC based MIMO Systems over η − µ Fading Channels

ABSTRACTIn this paper, we derive expressions for exact, approximate, and asymptotic symbol error rate (SER) of transmit antenna selection with maximal ratio combining (TAS/MRC) multiple input multiple output (MIMO) systems for several modulation schemes. We have assumed independent and identically distributed η − µ fading channels. We use a moment generating function (MGF) based approach to derive the expressions of SER. The expression for approximate SER is derived by approximating Q Function as a sum of exponentials. The expressions of SER are in the form of sum of converging infinite series for all values of fading parameters. The analytical expressions derived in this paper are also applicable to the SER performance analysis of TAS with selection combining at receiver (TAS/SC) systems. The analytical results are validated by comparing them with the results of extensive Monte Carlo simulations for different values of fading parameters. Finally, the SER performance of TAS/MRC systems and TAS/SC systems has been compared and superiority of TAS/MRC systems over TAS/SC systems has been demonstrated.