Closed-form Bit Error Rate Research Articles

BER Analysis for Equal Gain Transmission in Downlink Multiuser MIMO Systems

In this letter, we derive the bit error rate (BER) performance of a multiuser multiple-input multiple-output (MU-MIMO) system using equal gain transmission (EGT) precoding. Considering binary phase shift keying (BPSK) modulation, we analyze and propose a statistical model based on the Nakagami distribution for the interference terms involved in the received signals. The precision of our model is compared with the common Gaussian approximation and validated through simulation results. A closed-form BER expression is derived as a function of the number of transmit antennas for arbitrary $E_b/N_0$ .

A MPR optimization algorithm for FSO communication system with star topology

In this paper, we introduce the multi-packet reception (MPR) technology to the outdoor free space optical (FSO) communication system to provide excellent throughput gain. Hence, we address two challenges: how to realize the MPR technology in the varying atmospheric turbulence channel and how to adjust the MPR capability to support as many devices transmitting simultaneously as possible in the system with bit error rate (BER) constraints. Firstly, we explore the reliability ordering with minimum mean square error successive interference cancellation (RO-MMSE-SIC) algorithm to realize the MPR technology in the FSO communication system and derive the closed-form BER expression of the RO-MMSE-SIC algorithm. Then, based on the derived BER expression, we propose the adaptive MPR capability optimization algorithm so that the MPR capability is adapted to different turbulence channel states. Consequently, the excellent throughput gain is obtained in the varying atmospheric channel. The simulation results show that our RO-MMSE-SIC algorithm outperforms the conventional MMSE-SIC algorithm. And the derived exact BER expression is verified by Monte Carlo simulations. The validity and the indispensability of the proposed adaptive MPR capability optimization algorithm are verified as well.

General closed-form bit-error rate expressions for coded M-distributed atmospheric optical communications.

In this Letter, general closed-form expressions for the average bit error rate in atmospheric optical links employing rate-adaptive channel coding are derived. To characterize the irradiance fluctuations caused by atmospheric turbulence, the Málaga or M distribution is employed. The proposed expressions allow us to evaluate the performance of atmospheric optical links employing channel coding schemes such as OOK-GSc, OOK-GScc, HHH(1,13), or vw-MPPM with different coding rates and under all regimes of turbulence strength. A hyper-exponential fitting technique applied to the conditional bit error rate is used in all cases. The proposed closed-form expressions are validated by Monte-Carlo simulations.

Impact of Channel Estimation Error on the Performance of Relay Selection in Cognitive Radio Networks

Channel estimation error, which adversely affects the performance of any wireless communication system, is inevitably available in receivers. However, its impact on the bit error rate (BER) performance of relay selection in underlay cognitive networks has not been investigated analytically. This paper fills in this literature gap by firstly proposing an exact single-integral form BER formula for general network topology. Based on this proposal, we further analyze the diversity gain to have insights into asymptotic performance and system design. Secondly, we derive a closed-form approximate BER formula, which has been shown highly accurate, for a typical network topology where relays are closely positioned for reduced simulation time. Various results demonstrate that the channel estimation error significantly degrades the performance of the relay selection in underlay cognitive networks and completely destroys its diversity gain. In addition, increasing the number of involved relays drastically remedies its impact.

A Novel Solution for OFDM Based Relay Systems

In this paper we propose a novel solution for performance enhancement of dual-hop orthogonal frequency division multiplexing (OFDM) based decode-and-forward (DF) relay system, which assumes that relay station uses more than one antenna for downlink communications and implements transmit antenna selection (TAS) on subcarrier basis jointly with ordered subcarrier mapping (SCM). Ordered SCM is technique where subcarriers from the first hop are mapped to corresponding subcarriers on the second hop in accordance to their instantaneous signal-to-noise ratios (SNRs). It is proven to be a mapping scheme that maximizes the achievable ergodic capacity in OFDM based relay systems, while enabling bit error rate (BER) improvement at the same time. In order to assess the level of BER performance improvement in the system proposed in this paper, we analytically derive closed form BER expression of binary phase shift keying modulated OFDM DF relay system with TAS and SCM, assuming a scenario with Rayleigh fading statistics on both hops. Additionally, for further BER reduction, we analyze the combination of TAS with a modified SCM scheme, in which the subcarriers having the lowest SNRs on both hops are omitted. All derived analytical results are completely verified through simulations, showing that significant BER performance improvements are achieved with the novel proposed OFDM relay system, compared to the systems implementing only SCM, or only TAS, which approves that it can be considered as an interesting solution for the next generation of mobile cellular systems.

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 Improvement of Dual-Hop OFDM Decode-and-Forward Relay System

Ergodic capacity of dual-hop orthogonal frequency division multiplexing (OFDM) based decode-and-forward (DF) relay system may be significantly enhanced if ordered subcarrier mapping (SCM) is implemented at relay station (R). We proved earlier that this SCM scheme also brings certain bit error rate (BER) performance improvement to assumed system. However, the level of the achieved BER reduction is very small, with no reduction at all for the high signal-to-noise ratios (SNRs) on both hops. Therefore, in this paper we propose a modification of the SCM scheme where one or more subcarriers with the lowest SNRs from both hops are omitted before ordered SCM is performed at the relay station of an OFDM DF relay system. For the scenario with Rayleigh fading statistics on both hops, and no direct communication between the source of information (S) and destination (D), we derived a closed form BER relation of the assumed uncoded BPSK modulated relay system. The analytically obtained BER results, which are verified through simulations, show that the proposed modified SCM scheme brings significant BER performance improvements for all SNR values on both hops. Additionally, in order to provide analytical tool for the assessment of ergodic capacity enhancement achieved through ordered SCM, we derived ergodic capacity expression of the dual-hop OFDM DF relay system with ordered SCM.

On the performance of the zero‐forcing‐space‐time block coding multiple‐input–multiple‐output receiver with channel estimation error and error propagation

Multi-user multiple-input–multiple-output (MU-MIMO) systems are a promising technology for increasing spectral efficiency and diversity gain in the up-link channel. Space-time block coding (STBC) or the spatial-multiplexing (SM) scheme may selectively be used by each user. The simple techniques, zero-forcing (ZF), STBC and successive interference cancellation are jointly applied to separate and detect all streams at the ZF-STBC MIMO receiver. Unfortunately the channel estimation error (CEE) and error propagation (EP) are usually presented in practical multi-layers detection. In this study, the author investigates the effect of CEE and EP on the bit error rate (BER) performance of the ZF-STBC MIMO receiver over Rayleigh flat fading channels. They derive a nearly exact closed-form BER for general phase shift keying/quadrature-amplitude modulation with CEE and EP for arbitrary number of users. Finally, simulation results demonstrate the validity of the author's analysis.

Novel OFDM Based on C-Transform for Improving Multipath Transmission

In this paper, a new orthogonal-frequency-division multiplexing using the C-transform (C-OFDM) is introduced. An exact closed-form bit-error rate (BER) is derived for the proposed C-OFDM system over multipath channels and different kinds of modulation formats. The BER performance of the proposed C-OFDM is evaluated by mathematics and simulation for different channel models, modulation formats, under zero-padding (ZP) and minimum mean-square-error (MMSE) detection. The results are then compared with those of the discrete cosine transform (DCT) and discrete Fourier transform (DFT)-based OFDM, showing that over multipath channel, the new C-OFDM has better BER performance than both the DCT-OFDM and the DFT-OFDM. The proposed scheme is also found to achieve some reduction in the peak-to-average power ratio (PAPR) in comparison with the aforementioned OFDM schemes as the block-diagonal-structure (BDS) property of the C-transform minimizes the input signal superposition. The proposed system has the merits of being resilience to multipath channel dispersion and relatively has lower PAPR.

Enhanced quadrature signaling-based cooperative transmission with full rate and full diversity

Quadrature signaling-based cooperative transmission is an efficient and simple scheme to obtain spatial diversity. However, this scheme causes date rate loss compared with direct transmission. In this work, our focus is on recovering from the data rate loss while simultaneously achieving spatial diversity. Particularly, an enhanced quadrature signaling-based cooperative scheme was designed, which can realize full-rate transmission by using the signal space diversity (SSD) technique. Then, accurate bit error rate (BER) expression for the full-rate scheme was derived over independent and non-identically distributed (INID) Rayleigh fading channels. Specifically, a closed-form BER expression is obtained, which is quite tight over the whole SNR range, and thus allows for rapid and efficient evaluation of system performance under various channel conditions. Moreover, an asymptotic approximation of the BER was derived to show that the full-rate scheme can achieve full diversity. Simulation results verify the tightness of the analysis and show that the full-rate scheme significantly outperforms the traditional quadrature signaling-based scheme by about 2 dB with the same complexity order.

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.

On the Closed-Form Performance Analysis of Maximal Ratio Combining in Shadowed-Rician Fading LMS Channels

In this paper, the maximal ratio combining (MRC) scheme in Shadowed-Rician (SR) fading land mobile satellite (LMS) channels is studied. The MRC scheme for SR fading LMS channels has been studied in existing literature; however, most of the existing analytical results are in the form of infinite power series, which are not in closed-form. In this paper, we derive approximate closed-form expressions of the probability density function and cumulative distribution function of the received signal-to-noise ratio of the MRC based receiver in SR fading LMS channels. Then we provide approximate closed-form expressions of the bit error rate (BER), outage probability, and capacity of the considered scheme. One of the derived closed-form BER expressions is found useful for obtaining the analytical diversity order and coding gain of the considered MRC scheme.

Implications of I/Q Imbalance, Phase Noise and Noise Figure for SNR and BER of FSK Receivers

In energy-constrained applications like Body Area Networks (BAN) receiver performance is traded for lower power consumption. The limited receiver performance will deteriorate the output signal-to-noise-ratio (SNR) and bit-error-rate (BER) of the receiver. In this paper we present closed-form output SNR and BER models of a non-ideal receiver front-end with limiter-discriminator demodulator for binary FSK. The presented model is very useful in defining the minimally required receiver specifications. Moreover, the models are useful for gaining insight into the influences of the receiver impairments on its performance. In the models, the gain and phase imbalances between the in-phase and quadrature-phase paths as well as the receiver generated noise and the phase noise produced by the local frequency reference are taken into account. This paper shows that the gain and phase imbalances shift the FM threshold to higher carrier-to-noise-ratios (CNR) and only have small influence on the SNR above threshold. On the other hand, receiver generated noise reduces the output SNR both below and above the FM threshold, and phase noise limits the maximum output SNR. Additionally, a trade-off between the FSK frequency deviation and phase noise robustness is derived.

Performance analysis and power allocation for full‐rate and full‐diversity signal space cooperative communications

Signal space cooperative (SSC) system is bandwidth and energy efficient, which can achieve full-rate and full-diversity simultaneously. In this study, the authors first derive accurate bit error rate (BER) of the SSC system with maximum-likelihood detection (MLD), low-complexity linear detection (LD) and combined MLD and LD (MLD&LD). Specifically, closed-form BER expressions for the three detection schemes are derived. Also, asymptotic approximation analysis is performed to show clearly the diversity and coding gains of the three detection schemes. Through the analysis, the authors find out that MLD is optimal in diversity but has a high complexity, whereas LD is of low complexity but only achieves diversity order one. Interestingly, MLD&LD has almost the same BER as the BER-optimal MLD over the whole SNR range when equal power allocation (EPA) is adopted, whereas having lower complexity than MLD at low-to-medium SNR. Then, optimum power allocation for MLD&LD is developed, however, the largest power gain over EPA is proven to be only 0.37 dB. In view of the BER performance of MLD&LD and implementation simplicity of EPA, they conclude that MLD&LD with EPA is a wise choice for the SSC system. Finally, outage probability of MLD&LD with EPA is analysed to characterise the transmission reliability.

Design of efficient full‐rate linear dispersion space‐time block codes over correlated fading channels

In this study, the authors present a method to design efficient full-rate linear dispersion space-time block codes (LD-STBCs) in correlated Rayleigh fading channels with simple detection at the receiver. The authors first derive a formula for the achievable capacity of an LD-STBC coded multi-input multiple-output (MIMO) system as a function of correlation at the transmitter and the receiver. Moreover, the authors compute closed-form bit-error rate equations for multiple phase shift keying (M-PSK) and multiple quadrature amplitude modulation (M-QAM) schemes. Then, the authors present a method to construct LD-STBCs over correlated Rayleigh fading MIMO channels. Finally, the authors design LD-STBCs for two and four transmit antennas. The designed LD-STBCs enjoy full-rate, minimum power fluctuation, simple structure, simple processing at the receiver. Moreover, the designed LD-STBCs for two transmit antennas provide better performance than Alamouti and LYC codes and the designed LD-STBCs for four transmit antennas provide better performance than TV codes at practical signal-to-noise ratios. Simulation results show that when the proposed LD-STBC for two transmit antennas is concatenated with an efficient outer channel encoder, it provides better performance than LYC code over correlated fading channels.

Error performance analysis for FSO systems with diversity reception and optical preamplification over gamma–gamma atmospheric turbulence channels

The error performance was investigated of free-space optical (FSO) systems that use optical preamplifiers and diversity reception in turbulent atmosphere with gamma–gamma distribution. More specifically, assuming that the dominant sources of the receiver noises are the background light and amplifier spontaneous emission noises, we develop an exact bit-error-rate (BER) expression for binary pulse position modulation (BPPM) by a moment-generating function (MGF) derivative-based method. To gain more insight, we also derive a closed-form asymptotic BER expression for BPPM at high received optical power, by which we obtain the diversity and coding gains of the considered systems. Our analytical results lead to the observations that the attained diversity gain only changes with the gamma-gamma distribution parameters and the number of spatial modes collected by the receiver, while independent on the number of temporal modes passed by the optical preamplifiers. We verify the analytical results by Monte Carlo simulations.

On the Exact BER of Bit-Wise Demodulators for One-Dimensional Constellations

The optimal bit-wise demodulator for M-ary pulse amplitude modulation (PAM) over the additive white Gaussian noise channel is analyzed in terms of uncoded bit-error rate (BER). New closed-form BER expressions for 4-PAM with any labeling are developed. Moreover, closed-form BER expressions for 11 out of 23 possible bit patterns for 8-PAM are presented, which enable us to obtain the BER for 8-PAM with some of the most popular labelings, including the binary reflected Gray code and the natural binary code. Numerical results show that, regardless of the labeling, there is no difference between the optimal demodulator and the symbol-wise demodulator for any BER of practical interest (below 0.1).

Performance of free-space optical communication systems using circle polarization shift keying with spatial diversity receivers

Corresponding author: yaoyong@hit.edu.cnReceived January 30, 2013; accepted March 10, 2013; posted online July 17, 2013A closed-form bit-error rate (BER) expression is derived for free-space optical (FSO) communicationsystems with circle polarization shift keying and spatial diversity receivers in the gamma-gamma (GG)distribution fading channel. This model can predict the performance without the need of lengthy simula-tion runs. The performance can be analyzed by some system parameters such as atmospheric conditions,link length, communication wavelength, receiver aperture size, and number of spatial diversity receivers.Numerical results demonstrate the influence of the above parameters on the FSO systems and show quan-titatively the differences in behavior among various different parameters.OCIS codes: 010.1300, 010.1330, 060.2605, 060.4080.doi: 10.3788/COL201311.S20101.

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.