Approximate Bit Error Rate Expressions Research Articles

Reconfigurable-Intelligent-Surface-Aided Number Modulation for Symbiotic Active/Passive Transmission

Reconfigurable intelligent surface (RIS)-aided symbiotic active/passive transmission is a promising communication paradigm, which is able to improve the propagation environment while transmitting additional information. In this paper, a novel scheme, termed RIS-aided number modulation (RIS-NM), is proposed for symbiotic active/passive communications. In RIS-NM, the RIS elements are divided into in-phase (I-) and quadrature (Q-) subsets depending on their phase shift configurations, and the number of elements in the I-subset (or Q-subset, equivalently) is used to convey the RIS’s private information. A low-complexity yet near-optimal detector is designed for RIS-NM by shrinking the search space of constellation points. We then investigate a special case of RIS-NM, termed RIS-aided number shift keying (RIS-NSK), in which the radio-frequency source transmits unmodulated carrier signals. Statistic channel state information (CSI)-based maximum-likelihood (ML) detection is developed for RIS-NSK. We analyze the bit error rate (BER) performance of RIS-NM/NSK over Rician fading channels. BER upper bounds are derived in closed-form for RIS-NM by assuming instantaneous CSI-based ML detection, while an approximate BER expression is obtained for RIS-NSK by assuming statistic CSI-based ML detection. Furthermore, we extend RIS-NM to multiple-input multiple-output scenarios. Our simulation results in terms of BER corroborate the performance analysis and the superiority of RIS-NM over the state-of-the-art RIS-aided symbiotic active/passive transmission scheme.

Approximate expressions for BER performance in downlink mmWave MU‐MIMO hybrid systems with different data detection approaches

Millimetre-wave (mmWave) communications have been regarded as a key technology for the next-generation cellular systems since the huge available bandwidth can potentially provide the rates of multiple gigabits per second. Conventional precoding and combining techniques are impractical at mmWave scenarios due to manufacturing costs and power consumption. Hybrid alternatives have been considered as a promising technology to provide a compromise between hardware complexity and system performance. This study examines, using a semi-analytic approach, the downlink performance of massive MU-MIMO mmWave systems in terms of the bit error rate (BER). Also, a general expression is derived to estimate an upper bound/approximation to the BER performance via the Monte Carlo method, which can be used for any hybrid precoder/combiner, modulation and different data detectors. Numerical results evidence that the approximate BER expressions provide values very close to the ones obtained through simulation using only two statistical moments related to parameters of the system, mean and variance.

Optimal Detection for Ambient Backscatter Communication Systems With Multiantenna Reader Under Complex Gaussian Illuminator

This article addresses the issue of symbol detection in ambient backscatter communication systems with the multiantenna reader. Focusing on the ON-OFF keying modulation, the optimal detector minimizing the bit error rate (BER) is devised based on the maximum a posteriori principle. We then analyze the exact closed-form BER expression for the optimal detector. Moreover, simple approximate BER expressions are derived in certain asymptotic regimes. Furthermore, a simple energy detector is analyzed as a benchmark scheme, and the asymptotic BER is devised in a closed form. The findings of this article suggest that implementing multiple antennas at the reader is an effective means to enhance the BER performance and extend the tag-reader communication range. Also, the optimal detector always outperforms the energy detector. In particular, the optimal detector can avoid the error floor phenomenon, which is inevitable for the energy detector in the high SNR regime.

Bit error probability analysis of IR-UWB ED-OOK system using cooperative dual-hop DTF strategy

The Bit Error Rate (BER) of a single user cooperative Impulse Radio (IR)-Ultrawideband (UWB) communication system employing Energy Detector (ED) receiver with On-Off Keying (OOK) in IEEE 802.15.4a UWB multipath environment is investigated in this paper. Analytical evaluation based on Energy detection principle is performed to derive approximate BER Expressions for various diversity combining cases, namely optimum combining, linear combining and selective combining using cooperative dual-hop Detect and Forward (DTF) relay protocol in presence and absence of Inter-symbol interference (ISI). Numerical results reveal that there is a significant improvement in BER, with increase in number of relay diversity paths and decrease in number of frames Nf. The accuracy and perfection in approximation used in investigation of BER is confirmed with the validation of the analytical BER expressions with that of the simulation results. The analytical and simulation results confirm that among the diversity combining schemes, the performance of optimum combining is better compared with linear combining, which in turn performs better than selective combining.

Performance Analysis for Spatial Modulation With AF Relaying Over Spatially Correlated Rayleigh Channels

As a low-complexity and energy-efficient multiple input multiple output (MIMO) technique, spatial modulation (SM) has received much interest recently. Combining SM with cooperative relaying, the performance of SM systems can be significantly improved. Considering joint transmit-receive-correlated Rayleigh channels, the error performance and power allocation (PA) of the amplify-and-forward (AF) relaying aided cooperative SM system are presented in this paper. Based on the moment generating function (MGF), the probability density function (PDF) of effective signal-to-noise ratio (SNR) is derived. With this PDF, a closed-form expression of the pairwise error probability (PEP) is obtained. Utilizing the obtained PEP and the union bound of bit error rate (BER), the approximate average BER expression is further derived, which will benefit the performance analysis of the system in spatially correlated channels. According to the asymptotical performance analysis at high SNR, an asymptotic BER expression is also derived. By minimizing this asymptotic BER, a suboptimal power allocation scheme is developed, and the closed-form PA coefficients are attained. Besides, the diversity order of system is also analyzed and derived for the performance evaluation. Numerical results show that our theoretical analysis is valid, and can match the corresponding simulation well. Moreover, the proposed PA scheme can achieve superior BER performance over the conventional equal PA scheme since the powers are well allocated in terms of channel information.

Error Performance Analysis of Diffusive Molecular Communication Systems With On-Off Keying Modulation

In this paper, we analyze the bit error rate (BER) of the diffusive molecular communication (DMC) systems employing on-off keying (OOK) modulation. We also analyze the BER of the OOK-modulated DMC systems with inter-symbol interference cancellation (ISIC). Our main motivation is to introduce alternative tools for analyzing and efficiently computing the BER of the DMC systems without or with ISIC. Specifically, for the OOK-modulated DMC systems without ISIC, we first derive an exact BER expression based on the Poisson modeling of DMC systems. Then, the Gaussianand Gammaapproximation approaches are introduced to approximate the discrete Poisson distribution, and based on the approximation approaches, the corresponding BER expressions are derived. Furthermore, in order to reduce the computation complexity imposed by long inter-symbol interference, we propose the Monte-Carlo, simplified Poisson, simplified Gaussian, and the simplified Gamma approaches for BER computation. In the context of the OOK-modulated DMC systems with ISIC, we consider both the Poisson and Gaussian-approximation approaches for BER analysis. Again, exact and approximate BER expressions are derived under the Poisson, Gaussian-approximation, simplified Poisson, and simplified Gaussian approaches. Finally, the considered approaches are compared and validated by a range of performance results obtained from evaluation of the derived expressions or by simulations. Our studies show that the alternative approaches are in general effective for providing near-accurate BER estimation.

Effect of Correlation on BER Performance of the FSO-MISO System With Repetition Coding Over Gamma–Gamma Turbulence

In free space optical (FSO) communication systems, atmospheric turbulence is the major cause of bit error rate (BER) performance degradation. The error performance of the system can be significantly improved with the help of spatial diversity by employing multiple transmit or receive apertures. However, correlation of channels under turbulence in the case of small separation between transmit apertures can substantially reduce the benefits of spatial diversity. Still, a thorough analysis of the system performance in terms of diversity order and coding gain for the FSO multiple-input single-output (MISO) system under turbulence influenced correlated channels has not been studied when the repetition coding is used to achieve improved BER performance. In this paper, we provide unique results of the BER performance analysis of the considered correlated FSO-MISO system over Gamma–Gamma distributed turbulence channel. Using the joint moment generating function of received signal-to-noise ratio (SNR), a novel generalized approximate BER expression is derived, followed by convergence test of the power series based BER expression using the Cauchy's ratio test. Then, an asymptotic analysis at high SNR is performed to obtain a novel closed-form expression for BER of FSO-MISO system. We also derive expressions for coding gain, diversity gain, and coding gain loss due to correlation in channels. Although the effect of correlation in channels on the BER performance of the system is analyzed under different scenarios, while it is observed that it does not affect the diversity order; it significantly degrades the coding gain of the considered system.

An Approximation for BER of Optical Wireless System under Weak Atmospheric Turbulence using Point Estimate

Abstract Obtaining analytically closed-form expression for bit error rate (BER) of an optical wireless communication (OWC) system under weak atmospheric turbulence is extremely difficult and intractable. In this paper, a simple closed-form approximate expression for average BER of OWC system under weak turbulence condition is obtained using point estimate method. The proposed expression is used to compute the BER for on-off keying (OOK) and sub carrier intensity modulated (SIM) binary phase shift keying (BPSK) modulation schemes. Results obtained using proposed expression are compared with those obtained using Gauss-Hermite quadrature approximation and Monte-Carlo simulations.

Power imbalance induced BER performance loss under limited-feedback CoMP techniques

Coordinated multipoint (CoMP) technology utilizes simultaneous transmission/reception from/to different access points, and it is considered as an important feature to exploit and/or mitigate intercell interference in fourth-generation mobile networks. Yet, channel power imbalance at the receiver is experienced in CoMP systems due to, e.g., spatially distributed transmissions. Traditional co-located multi-antenna systems may also experience power imbalance among antenna branches due to inaccurate antenna calibration. This paper presents a bit error rate (BER) analysis and derives asymptotic and approximate BER expressions for some practical CoMP transmission techniques under channel power imbalance. Besides the analytical results, numerical analysis is made to thoroughly capture the performance impact of channel power imbalance on the performance gain of the CoMP methods. The results demonstrate that power imbalance considerably affects BER performance and applying long-term amplitude information with fast phase feedback has insignificant benefit to effectively compensate the detrimental effect of large channel power imbalance when base stations use a single antenna. In this case, exploiting both short-term amplitude and phase information is a very good choice. On the contrary, for a large number of diversity antennas in base stations, using long-term amplitude information with a sparsely quantized phase shows BER performance close to the case where full channel state information is applied.

Bit error rate performance of IR‐UWB ED‐PPM system using cooperative dual‐hop AF strategy

This study presents a novel analytical approach for evaluation of bit error rate (BER) performance of an impulse radio-ultra-wideband (IR-UWB) energy detector-pulse position modulation (ED-PPM) system, using dual-hop cooperative amplify and forward (AF) relaying strategy with optimum diversity combining, over IEEE 802.15.4a UWB channel. An approximate expression for BER has been derived based on energy detection principle. The analytical BER expression thus derived is validated with computer simulations, which confirm the accuracy in approximation used in investigation of BER. Furthermore, it is observed that the BER performance of IR-UWB ED-PPM system, improves substantially using dual-hop cooperative AF scheme, compared with non-cooperative scheme. Despite its poor BER performance, ED systems are preferred over AC systems, because of simplicity and low complexity.

Average BER performance of FSO SIM-QAM systems in the presence of atmospheric turbulence and pointing errors

This paper presents the exact average bit error rate (BER) analysis of the free-space optical system employing subcarrier intensity modulation (SIM) with Gray-coded quadrature amplitude modulation (QAM). The intensity fluctuations of the received optical signal are caused by the path loss, atmospheric turbulence and pointing errors. The exact closed-form analytical expressions for the average BER are derived assuming the SIM-QAM with arbitrary constellation size in the presence of the Gamma–Gamma scintillation. The simple approximate average BER expressions are also provided, considering only the dominant term in the finite summations of obtained expressions. Derived expressions are reduced to the special case when optical signal transmission is affected only by the atmospheric turbulence. Numerical results are presented in order to illustrate usefulness of the derived expressions and also to give insights into the effects of different modulation, channel and receiver parameters on the average BER performance. The results show that the misalignment between the transmitter laser and receiver detector has the strong effect on the average BER value, especially in the range of the high values of the average electrical signal-to-noise ratio.

Bit error rate of underlay decode-and-forward cognitive networks with best relay selection

This paper provides an analytic performance evaluation of the bit error rate (BER) of underlay decode-and-forward cognitive networks with best relay selection over Rayleigh multipath fading channels. A generalized BER expression valid for arbitrary operational parameters is firstly presented in the form of a single integral, which is then employed for determining the diversity order and coding gain for different best relay selection scenarios. Furthermore, a novel and highly accurate closed-form approximate BER expression is derived for the specific case where relays are located relatively close to each other. The presented results are rather convenient to handle both analytically and numerically, while they are shown to be in good agreement with results from respective computer simulations. In addition, it is shown that as in the case of conventional relaying networks, the behaviour of underlay relaying cognitive networks with best relay selection depends significantly on the number of involved relays.

Performance Analysis of Space-Shift Keying in Decode-and-Forward Multihop MIMO Networks

In this paper, space-shift keying (SSK) is considered for multihop multiple-input-multiple-output (MIMO) networks. In SSK, only one among $n_{s} = \hbox{2}^{m}$ available transmit antennas, chosen on the basis of $m$ information bits, is activated during transmission. We consider two different systems of multihop cooperation, where each node has multiple antennas and employs SSK. In system I, a multihop diversity relaying scheme is considered. In system II, a multihop multibranch relaying scheme is considered. In both systems, we adopt decode-and-forward (DF) relaying, where each relay forwards the signal only when it correctly decodes. We analyze the end-to-end bit error rate (BER) and diversity order of both the systems with SSK. For binary SSK $(n_{s} = \hbox{2})$ , our analytical BER expression is exact, and our numerical results show that the BERs evaluated through the analytical expression overlap with those obtained through Monte Carlo simulations. For nonbinary SSK $(n_{s} > \hbox{2})$ , we derive an approximate BER expression, where the analytically evaluated BER results closely follow the simulated BER results. We show the comparison of the BERs of SSK and conventional phase-shift keying (PSK) and also show the instances where SSK outperforms PSK. We also present the diversity analyses for SSK in systems I and II, which predict the achievable diversity orders as a function of system parameters.

BER of Subcarrier MPSK and MDPSK Systems in Atmospheric Turbulence

Bit-error rate (BER) performance of subcarrier $M$ -ary phase-shift keying (MPSK) and $M$ -ary differential PSK (MDPSK) is analyzed for optical wireless communications over Gamma–Gamma and lognormal turbulence channels. We study the relation between the exact BER and the approximate BER, which is obtained by dividing the symbol-error rate by the number of bits per symbol, for subcarrier MPSK and MDPSK modulations. The asymptotic BER performance gap between the exact and the approximate BERs is quantified analytically through our asymptotic analyses. The accuracy of the approximate BER of both MPSK and MDPSK depends on the channel conditions. Under weak turbulence conditions, the approximate BER expression can be used to predict the system performance with high accuracy, while under strong turbulence conditions the approximate BER becomes inaccurate and can only serve as a loose lower bound of the exact BER. The asymptotic BER performance loss of MDPSK with respect to MPSK is also quantified analytically.

BER performance of distributed antenna systems in Nakagami-m fading channel

The performance of distributed antenna systems (DASs) downlink is studied over MIMO Nakagami fading channel, and corresponding bit error rate (BER) analysis is presented. By means of the theoretical analysis, the probability density function and cumulative distribution function of the system effective signal to interference plus noise ratio (SINR) are attained. According to these results, we further derive average BER of DAS with MQAM and MPSK under fading environment. As a result, an accurate BER expression for DAS with MQAM and a tight BER approximation for DAS with MPSK are obtained. To simplify the calculation of the accurate BERs, approximate closed-form BER expressions are also derived, which are shown to match the accurate BERs well. With these expressions, the downlink performance is effectively assessed. Simulation results corroborate our theoretical analysis, and the approximate BER expressions are very close to the accurate ones but with lower computational complexity.

BER Performance of Distributed Antenna Systems in Nakagami-mFading Channel

The performance of distributed antenna systems (DASs) downlink is studied over MIMO Nakagami fading channel, and corresponding bit error rate (BER) analysis is presented. By means of the theoretical analysis, the probability density function and cumulative distribution function of the system effective signal to interference plus noise ratio (SINR) are attained. According to these results, we further derive average BER of DAS with MQAM and MPSK under fading environment. As a result, an accurate BER expression for DAS with MQAM and a tight BER approximation for DAS with MPSK are obtained. To simplify the calculation of the accurate BERs, approximate closed-form BER expressions are also derived, which are shown to match the accurate BERs well. With these expressions, the downlink performance is effectively assessed. Simulation results corroborate our theoretical analysis, and the approximate BER expressions are very close to the accurate ones but with lower computational complexity.

Multi-user receiver scheme and uplink performance of space–time-coded CDMA system in Rician fading channels

The uplink performance of multi-user space–time-coded code-division multiple access (STC-CDMA) system in Rician fading channel is presented. A simple and effective multi-user receiver scheme is developed for STC-CDMA system. The scheme has linear decoding complexity when compared to the existing scheme with exponential decoding complexity, and thus implements low-complexity decoding. Based on the bit error rate (BER) analysis and moment generation function, theoretical BER expressions are derived for STC-CDMA with orthogonal and quasi-orthogonal spreading code, respectively. It is shown that these expressions have more accuracy. Using these expressions and the approximation of error function, closed-form approximate BER expressions are obtained, which can simplify the calculation of the derived theoretical BER. Simulation results show that the developed low-complexity decoding scheme can achieve almost the same performance as the existing scheme. The theoretical BER are in good agreement with the corresponding simulated values. Moreover, the presented approximate expressions are also close to the simulated values due to the better approximation. Under the same system throughput and concatenation of channel code, the presented full-rate STC-CDMA system has lower BER than the corresponding full-diversity STC-CDMA systems.

BER Performance Analysis for Optical Communication using DPSK Modulation

In this paper we study and analyze Bit Error Rate (BER) performance for optical communication system using Differential Phase Shift Keying (DPSK) modulation scheme. Specifically, after developing an approximate form BER expression, we study the BER performance for different system parameters such as fiber length, gain and number of amplifier. With the aid of analysis and simulation results we demonstrate the influence of different system parameters on the BER performance of an optical system using differential modulation schemes.

Performance of orthogonal STBC-MIMO with variable-power adaptive modulation and delayed feedback in Nakagami fading channels

A variable-power (VP) adaptive modulation (AM) scheme with space-time block code (STBC) is developed in MIMO systems, and the corresponding performance is investigated in Nakagami fading channels. The optimum switching thresholds are derived so that the spectrum efficiency (SE) under an average power and a target bit error rate (BER) constraint is maximized. By the switching thresholds, average BER and SE are further derived. As a result, closed-form expressions are obtained. Besides, the exact and approximate BER expressions of VP AM and constant-power (CP) AM systems with delayed feedback are respectively derived. Simulation results show that the theoretical SE and BER can match the corresponding simulation well. The results indicate that VP-AM with STBC provide higher spectrum efficiency than the CP counterparts, and has slighter bite error rate performance degradation when the normalized delay is less than 0.01.

Performance Analysis of Space–Time Block-Coded MIMO Systems With Imperfect Channel Information Over Rician Fading Channels

The performance analysis of space-time block-coded multiple-input-multiple-output (STBC-MIMO) systems in Rician fading channels for perfect and imperfect channel state information (CSI) is presented in this paper. Accurate expressions of average bit error rate (BER) and symbol error rate (SER) of STBC-MIMO for multiple phase-shift keying (MPSK) and quadrature amplitude modulation (QAM) are derived. Based on asymptotic analysis and Nakagami approximation for Rician fading, closed-form expressions of approximate average BER and SER are obtained for low and high signal-to-noise ratios (SNRs). By combining the error rate expressions of low SNR and SNRs, approximate BER and SER expressions can be obtained for different SNRs. Computer simulation shows that the theoretical analysis is in good agreement with the simulation results, and the approximate expressions derived from the integration of high and low SNR asymptotic analyses are close to the accurate formulas for different SNRs. The asymptotic analysis at high SNR indicates that the coding gain is affected by the Rice factor, transmit and receive antenna numbers, code rate, and modulation, whereas the diversity gain is governed by the transmit and receive antenna numbers. However, the diversity gain will be zero at high SNR in the presence of estimation errors because of the error floor in the error probability curves.