Closed-form Expressions For Bit Error Rate Research Articles

Exact and Closed-Form Error Performance Analysis for Hard MMSE-SIC Detection in MIMO Systems

We investigate the exact error performance of hard minimum mean-squared error (MMSE) detection possibly with successive interference cancellation (SIC) in multiple-input multiple-output (MIMO) systems. To facilitate the analysis, we start with an exact bit-error rate (BER) analysis for a general system with decision statistic, z=ax+u, where a>;0, x is the transmitted signal, and u is an arbitrarily distributed noise component which is possibly dependent on the signal component x. For this general system, we derive the exact and closed-form BER expressions for M-ary pulse amplitude modulation (PAM) and arbitrary rectangular quadrature amplitude modulation (QAM), which include the well-known BER result of as a special case. Furthermore, by formulating the MIMO MMSE decision statistics in the same form as z in the general system, we derive the exact and closed-form instantaneous BER and symbol-error rate (SER) expressions for MIMO hard MMSE detection with/without SIC employing PAM and QAM. Finally, the validity of our derived error probability expressions is verified through extensive Monte Carlo simulations and the results reported in the literature.

Performance analysis of free-space optical links with transmit laser selection diversity over strong turbulence channels

Transmit laser selection (TLS) diversity scheme has been proposed recently for free-space optical communication systems and its bit error rate (BER) performance has been investigated over K-distributed turbulence channels based on lengthy simulations. Moreover, for a limiting case of strong turbulence conditions that have been modelled by negative exponential distribution, a closed-form expression for the average BER has been presented in the open technical literature. In this study, first a novel approximate analytical expression is derived for the probability density function (PDF) of the resulting channel irradiance corresponding to a TLS diversity scheme over the K channel. The approximated PDF accurately estimates the statistics of the channel irradiance over a wide range of channel conditions. Then, based on the derived PDF, an analytical closed-form expression is presented for the average BER, which can be used to estimates the BER of the system very accurately over K-distributed turbulence channels without resorting to lengthy simulations. Additionally, based on the derived analytical results, the effect of using laser pulse shape with increased peak-to-average optical power ratio on the system performance is investigated. Numerical results are further demonstrated to confirm the analytical results.

BER Performance Analysis of Cooperative DaF Relay Networks and a New Optimal DaF Strategy

An analytical bit error rate (BER) performance study of three detect-and-forward (DaF) policies under a common framework is presented in this paper. More specifically, the direct, thresholded and link-adaptive schemes are studied, which differ in the way the decision on the transmitted symbol is forwarded from the relay to the destination. The analysis is carried out for a single relay DaF transmission protocol and takes into account the symbol decision errors that may occur at the relay. Simple closed-form analytical BER expressions are derived for all three schemes, which are completely verified by simulations. Moreover, by minimizing a properly selected conditional BER expression, a novel optimal DaF strategy is proposed, which outperforms all previously known related methods.

Bit Error Rate Analysis for an OFDM System with Channel Estimation in a Nonlinear and Frequency-Selective Fading Channel

Orthogonal frequency division multiplexing (OFDM) is an effective technique for high-speed digital transmission over time-dispersive channels. However, for coherent detection, a reliable channel estimation (CE) is required. OFDM is characterized by its high peak-to-average power ratio (PAPR), which makes it very sensitive to nonlinear distortions that may affect the channel estimation accuracy leading to a bit error rate (BER) performance degradation. In this paper, we present closed-form BER expression for OFDM with a pilot-assisted CE in a nonlinear and frequency-selective fading channel. We discuss how, and to what extent, the nonlinear degradation affects the BER performance with the CE based on a time/frequency division-multiplexed (TDM/FDM) pilot. The analysis is based on a Gaussian approximation of the nonlinear noise due to both HPA amplitude limitation and quantization. We also evaluate the estimator's mean square error (MSE) with both TDM and FDM pilots. Our results show that pilot-assisted CE using FDM pilot is more sensitive to nonlinear distortions than the CE using a TDM pilot, since its pilot subcarriers are affected by nonlinear noise due to both the HPA and the quantization.

Exact & Closed-Form BER Expressions Based on Error-Events at Relay Nodes for DF Relay Systems over Rayleigh Fading Channels

In this letter, we derive another exact bit error rate (BER) for decode-and-forward (DF) relay systems over Rayleigh fading channels. At first, our focus is on fixed-DF (FDF) relay schemes in which the probability density function (PDF) is derived based on error-events at relay nodes. Some insight into how erroneous detection and transmission at relay nodes affect both the combined signal-to-noise ratio (SNR) and the averaged BER is obtained, and cooperative diversity is observed from the closed-form BER expression. In addition, the developed analytical method is extended to adaptive-DF (ADF) schemes and the exact BER expressions are derived. Simulation results are finally presented to validate the analysis.

Unified BER and optimum threshold analysis of binary modulations in simple and cascaded Rayleigh fading channels with switched combining

Following a unified analytical framework, the bit error rate (BER) of several coherent and non-coherent binary modulation schemes is derived for a switched diversity system. The two variants of switched combining that have been investigated are switch and stay combining and switch and examine combining. For channel modelling, at first a simple slow flat fading channel is assumed, where the amplitude attenuation obeys the Rayleigh distribution. Later the BER calculations are repeated for cascaded Rayleigh fading channel case. Rayleigh fading is the most popular model for electromagnetic signal propagation in wireless media when both or either of the transmitter/receiver is fixed. On the other hand, when both the transmitter and the receiver are mobile, a cascaded (or double) Rayleigh fading model is better suited. The applicability of these two models, namely simple and cascaded Rayleigh model, has been indicated by several theoretical studies and their suitability is established by various field measurements. In our paper, simple closed-form BER expressions as a function of switching threshold have been found and optimum switching thresholds have been computed for both these models as well as for both types of diversity combining described earlier. The results presented in this paper can be very useful for communication system designers to analyze link quality of switched diversity assisted systems in various wireless environments. Copyright © 2010 John Wiley & Sons, Ltd.

Performance of a space-time block coded code division multiple access system over Nakagami-m fading channels

By introducing an orthogonal space-time coding scheme, multiuser code division multiple access (CDMA) systems with different space time codes are given, and corresponding system performance is investigated over a Nakagami-m fading channel. A low-complexity multiuser receiver scheme is developed for space-time block coded CDMA (STBC-CDMA) systems. The scheme can make full use of the complex orthogonality of space-time block coding to simplify the high decoding complexity of the existing scheme. Compared to the existing scheme with exponential decoding complexity, it has linear decoding complexity. Based on the performance analysis and mathematical calculation, the average bit error rate (BER) of the system is derived in detail for integer m and non-integer m, respectively. As a result, a tight closed-form BER expression is obtained for STBC-CDMA with an orthogonal spreading code, and an approximate closed-form BER expression is attained for STBC-CDMA with a quasi-orthogonal spreading code. Simulation results show that the proposed scheme can achieve almost the same performance as the existing scheme with low complexity. Moreover, the simulation results for average BER are consistent with the theoretical analysis.

Closed Form BER Expressions for BPSK OFDM Systems with Frequency Offset

This letter addresses the performance degradation caused by the presence of carrier frequency offset (CFO) in orthogonal frequency division multiplexing (OFDM) systems. Accurate closed form bit error rate (BER) expressions for BPSK-OFDM systems impaired by frequency offset are derived. The analysis is carried out for flat and frequency selective Rayleigh fading channels. Simulation results have been used to cross-check the accuracy of the theoretical analysis.

Performance Analysis of Space-Time Coded CDMA System Over Nakagami Fading Channels with Perfect and Imperfect CSI

In this paper, the performance of multiuser CDMA systems with different space time code schemes is investigated over Nakagami fading channel. Low-complexity multiuser receiver schemes are developed for space-time coded CDMA systems with perfect and imperfect channel state information (CSI). The schemes can make full use of the complex orthogonality of space-time coding to obtain the linear decoding complexity, and thus simplify the exponential decoding complexity of the existing scheme greatly. Moreover, it can achieve almost the same performance as the existing scheme. Based on the bit error rate (BER) analysis of the systems, the theoretical calculation expressions of average BER are derived in detail for both perfect CSI and imperfect CSI, respectively. As a result, tight closed-form BER expressions are obtained for space-time coded CDMA with orthogonal spreading code, and approximate closed-form BER expressions are attained for space-time coded CDMA with quasi-orthogonal spreading code. Computer simulation for BER shows that the theoretical analysis and simulation are in good agreement. The results show that the space-time coded CDMA systems have BER performance degradation for imperfect CSI.

Performance analysis of LDPC codes with selection diversity combining over identical and non-identical rayleigh fading channels

Selection diversity combining employed in conjunction with low-density parity-check codes is able to mitigate the effects of fading. The closed-form bit-error rate expressions of this scheme over independent and non-identically distributed and independent and identically distributed flat Rayleigh fading channels are derived using the extrinsic information transfer chart and Gaussian approximation. The derived expressions are compared with simulation results as well as the Eb/N0 threshold using density evolution (DE). They are in good agreement with simulation results and have the advantage of reduced computational complexity over DE.

Performance of multiuser CDMA system with space-time block coding in MIMO Rayleigh fading channels

In this paper, by introducing orthogonal space-time coding scheme, the multiuser CDMA systems with different space time codes are given, and corresponding system performance is investigated over Rayleigh fading channel. A low-complexity multiuser receiver scheme is developed for space-time coded CDMA systems. The scheme can make full use of the complex orthogonality of space-time coding to simplify the high decoding complexity of the existing scheme. Compared to the existing scheme with exponential decoding complexity, it has linear decoding complexity. Based on the performance analysis and mathematical calculation, average bit error rate (BER) of the system is derived in detail, and tight closed-form approximation expressions of BER are attained. Simulation results on average BER are in agreement with the theory analysis. The results show that the proposed scheme can achieve almost the same performance as the existing scheme. Moreover, on the condition of same system throughput and concatenation of channel code, the given full-rate space-time coded CDMA system has lower BER than the full-diversity space-time coded CDMA systems.

An opportunistic cooperation scheme and its BER analysis

The cooperative communication technology proposed in recent years enables network nodes to share their antennas to achieve diversity gain. In this paper, an efficient variation scheme on opportunistic cooperation is proposed by using an outage criterion, in which the cooperation mode will be adopted only when the channel from source to relay does not occur outage event. We derive a closed-form BER (bit error rate) expression for the proposed scheme over Rayleigh fading channels, showing that the full diversity is achieved by the new scheme. Also, the BER performance of the known coded cooperation is presented for the purpose of comparison with our scheme. Numerical results illustrate the superiority of the proposed scheme over the coded cooperation in terms of BER performance. It is pointed out that the corresponding BER advantage of the proposed scheme comes at the expense of increasing system overhead since the new scheme needs some feedback from relay to both source and destination.

Average BER analysis for binary signallings in decode-and-forward dissimilar cooperative diversity networks

In this letter, the average bit-error rate (BER) performance is analyzed for uncoded decode-and-forward (DF) cooperative diversity networks. We consider two typical networks: a single-relay cooperative network with the direct source destination link and a two-relay cooperative network with the direct source-destination link, under dissimilar network settings, i.e., the fading channels of different relay branches may have different variances. We first derive a closed-form approximate average BER expression of binary signallings including noncoherent binary frequency shift keying (BFSK), coherent BFSK, and coherent binary phase shift keying (BPSK), for the single relay network. We then generalize our analysis to the two-relay network, and a closed-form approximate average BER expression for binary signallings is derived. We also show that our BER expressions can be considered as generalizations of previously reported results in the literature. Throughout our analysis, only one approximation, so-called the piecewise-linear approximation, is made. Simulation results are in excellent agreement with the theoretical analysis, which validates our proposed BER expressions.

Adaptive power loading with BER-constraint for OFDM systems

A novel adaptive power loading algorithm with the constraint of target overall bit error rate (BER) for orthogonal frequency division multiplexing (OFDM) systems is proposed in this article. The proposed algorithm aims to minimize the required transmit power with fixed data rate and uniform (nonadaptive) bit allocation, while guaranteeing the target overall BER. The power loading is based on the unequal-BER (UBER) strategy that allows unequal mean BERs on different subcarriers. The closed-form expressions for optimal BER and power distributions are derived in this article. Simulation results indicate the superiority of the proposed algorithm in terms of BER performance and algorithmic complexity.

Adaptive power loading based on unequal-ber strategy for OFDM systems

An adaptive power loading algorithm with uniform (nonadaptive) bit allocation is proposed for constant data rate OFDM systems in this letter. This algorithm aims to minimize the transmit power while guaranteeing the target mean bit error rate (BER). The power loading is based on the unequal-BER (UBER) strategy which permits unequal mean BERs on different subcarriers. The closed-form expressions for optimal BER and power distributions are derived. Simulation results indicate the superiority of the proposed algorithm.

CDMA-SFBC Downlink Performance

In this paper a generic code division multiple access (CDMA)-space frequency block coded (SFBC) system for downlink transmission is proposed. Closed form expressions for the bit error rate (BER) performance of the proposed CDMA-SFBC downlink system are derived and numerically evaluated considering different scenarios. The closed form BER expressions are derived for both the M-ary phase shift keying (MPSK) and the M-ary quadrature amplitude modulation (MQAM) techniques considering different CDMA-SFBC configurations. The BER expressions are evaluated for a wide range of system parameters assuming Rayleigh fading. These parameters include M-ary size and channel estimation error variance. Such evaluations are crucial not only for system performance prediction, but also for network management, monitoring and future cross-layer design.

Closed-form BER expression for FSO links with transmit laser selection over exponential atmospheric turbulence channels

An exact closed-form expression for the average bit error rate (BER) of multiple-input-single-output free-space optical (FSO) communication systems with intensity modulation and direct detection using selection transmit diversity over strong atmospheric turbulence channels is derived. Assuming channel side information (CSI) at the transmitter and receiver, the transmit diversity technique based on the selection of the optical path with a greater value of scintillation has shown to be able to extract full diversity, outperforming other alternatives in which CSI at the transmitter is not considered.

Asymptotic Performance Analysis of Multihop Relayed Transmissions over Nakagami-m Fading Channels

This letter studies the asymptotic bit error rate (BER) performance of multihop communication systems with amplify-and-forward relaying over Nakagami-m fading channels. Since it is difficult to find the exact probability density function (PDF) of the output signal-to-noise ratio (SNR) at the destination, we resort to the series expansion of this PDF in the neighborhood of zero. Building upon this result, a closed-form expression for the average BER in the high SNR region is derived. Numeric results show that the derived asymptotic BER expression is accurate at medium and high SNR for both independent identically distributed (i.i.d.) and independent non-identically distributed (i.n.i.d.) channels.

Exact BER analysis for M-QAM modulation with transmit beamforming under channel prediction errors

Significant throughput improvements can be obtained in multiple-input multiple-output (MIMO) fading channels by merging beamforming at the transmitter and maximal ratio combining (MRC) at the receiver. In general, accurate channel state information (CSI) is required to achieve these performance gains. In this paper, we analyze the impact of channel prediction error on the bit error rate (BER) of combined beamforming and MRC in slow Rayleigh fading channels. Exact closed-form BER expressions are obtained in terms of elementary functions. Numerical results show that imperfect CSI causes little BER degradation using channel prediction of moderate complexity.

Average BER Analysis for $M$-ary FSK Signals in Nakagami-$q$ (Hoyt) Fading With Noncoherent Diversity Combining

This paper analyzes the average bit error rate (BER) of noncoherent M-ary frequency-shift keying (FSK) signals over multichannel nonidentically distributed Nakagami-q (Hoyt) fading employing diversity combining. The first part of the paper considers the conventional postdetection noncoherent equal-gain combiner (NC-EGC), in which a Fourier series inversion formula is employed to derive a simple and rapidly converging series-based expression for the system average BER. This expression is valid for arbitrary values of received average signal-to-noise ratios (SNRs) and fading parameters. The derived expression is then compared with some existing ones in the literature, and the results show a large reduction in computational complexity, particularly when M and/or the diversity order increases. In the second part, a new noncoherent combiner is proposed to achieve improvements over the conventional NC-EGC. It is also shown that this new combiner results in a simple closed-form expression for the system average BER that is given in terms of elementary functions; hence, it can be easily numerically evaluated with noticeable computation efficiency.