Bit Error Rate Analysis Research Articles

BER analysis of a GMSK system using decision feedback

There are considerable literatures on the Bit Error Rate (BER) evaluation of Differential Detection of Gaussian Minimum Shift Keying (DDGMSK) system using Decision Feedback (DF), but most of them give the performance based on the Monte Carlo Error Counting (MCEC) technique. From the probability distribution of the phase angle between two vectors perturbed by Gaussian noises, the formulae of BER are derived for the performance analysis of DDGMSK system with DF in this letter. Considering the m-bit dock-tailed sequence, the new formulae of Gaussian Minimum Shift Keying (GMSK) modulated phase and the Time-Varying Signal to Noise Ratio (TVSNR) of the demodulated signal are presented, and it is proved that the relationship between the TVSNR of the demodulated signal and the size of eye opening is not inevitable. Simulation results show that the theoretical investigation gives analogous results with the MCEC technique. The formulae presented are useful for the performance analysis of systems using GMSK as modulating and demodulating method, for instance, the analysis of synchronous performance of frequency-hopping communication system.

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.

Interconnect Analysis for 80-Gbps Serial Link Design

This paper presents a case study of the modeling and simulation methods used to design the signal path for a proposed 80-Gbps serial data link between digital systems. This design includes flip-chip transitions from custom IBM 8HP integrated circuits to multilayer organic substrates, with coaxial-cable connections between substrates. Discussion topics include interconnect material selection, detailed 3-D electromagnetic modeling of the conductor transitions and signal paths, time-domain circuit simulation of the complete data path including the driver and receiver, and bit-error rate analysis of the complete link. Simulated data are presented.

BER analysis of MPSK space-time code with differential detection over correlated block-fading Rayleigh channel

MIMO technology proposed in recent years can effectively combat the multipath fading of wireless channel and can considerably enlarge the channel capacity, which has been investigated widely by researchers. However, its performance analysis over correlated block-fading Rayleigh channel is still an open and challenging objective. In this article, an analytic expression of bit error rate (BER) is presented for multiple phase shift keying (MPSK) space-time code, with differential detection over correlated block-fading Rayleigh channel. Through theoretical analysis of BER, it can be found that the differential space-time scheme without the need for channel state information (CSI) at receiver achieves distinct performance gain compared with the traditional nonspace-time system. And then, the system simulation is complimented to verify the above result, showing that the diversity system based on the differential space-time block coding (DSTBC) outperforms the traditional nonspace- time system with diversity gain in terms of BER. Furthermore, the numerical results also demonstrate that the error floor of the differential space-time system is much lower than that of the differential nonspace-time system.

Performance Analysis of a Maximum-Likelihood FFH/MFSK Receiver with Partial-Band-Noise Jamming over Frequency-Selective Fading Channels

A maximum-likelihood (ML) receiver is proposed for a fast frequency-hopping M-ary frequency-shift-keying system. The effects of frequency-selective Rayleigh-fading channels, partial-band-noise jamming, and additive white Gaussian noise are considered. It is shown that side information on the noise variance, the jamming variance, as well as the power levels of the correlated paths, is required to implement the ML receiver. Analytical bit-error rate expressions are derived for the ML receiver. Our analysis also shows that there exists an optimum diversity order under certain channel conditions.

Synchronization and Integration Region Optimization for UWB Signals with Non-coherent Detection and Auto-correlation Detection

Non-coherent detection and auto-correlation detection are promising techniques for low complexity, low cost and low data rate ultra-wideband communication applications. For both schemes, the integration region of a receiver integrator significantly affects the bit error rate (BER) performance. In this paper, a method of synchronization and estimating the optimal integration region, i.e., the initial point and the length of the integration, is presented. Following a theoretical BER analysis, a data-aided estimation method using the idea of inter-symbol correlation is proposed. It is shown that using noise corrupted received signals, the proposed method is not only practically applicable, but also enhances the performance compared to non-optimal timing methods.

Evaluation of coherent homodyne and heterodyne optical CDMA structures

This paper evaluates the coherent optical code-division multiple-access (OCDMA) techniques and examines the overall system performance in terms of signal-to-noise ratio (SNR) penalty as a function of simultaneous users accommodated to maintain an appropriate value of the bit-error rate (BER) for homodyne and heterodyne detections. As spreading codes, the proposed structures are utilizing a recently introduced prime code family hereby referred to as double-padded modified prime code (DPMPC). As a coherent modulation, binary phase-shift keying (BPSK) format is deployed. In homodyne detection, two different phase modulations are studied including either an external phase-modulator or injection-locking methods. The phase limitation and the performance for two methods plus multiple-access interferences (MAI) and receiver noise in a shot-noise limited regime are investigated. In heterodyne detection, BER analysis of the system based on only external phase modulator is examined. It is found that by maintaining BER = 10−9, this system can accommodate an increased number of simultaneous users to compare with systems which employ conventional bipolar codes.

Orthogonal Multi-Carrier DS-CDMA with Frequency-Domain Equalization

Orthogonal multi-carrier direct sequence code division multiple access (orthogonal MC DS-CDMA) is a combination of orthogonal frequency division multiplexing (OFDM) and time-domain spreading, while multi-carrier code division multiple access (MC-CDMA) is a combination of OFDM and frequency-domain spreading. In MC-CDMA, a good bit error rate (BER) performance can be achieved by using frequency-domain equalization (FDE), since the frequency diversity gain is obtained. On the other hand, the conventional orthogonal MC DS-CDMA fails to achieve any frequency diversity gain. In this paper, we propose a new orthogonal MC DS-CDMA that can obtain the frequency diversity gain by applying FDE. The conditional BER analysis is presented. The theoretical average BER performance in a frequency-selective Rayleigh fading channel is evaluated by the Monte-Carlo numerical computation method using the derived conditional BER and is confirmed by computer simulation of the orthogonal MC DS-CDMA signal transmission.

BER Analysis of M-QAM with Packet Combining Over Space-Time Block Coded MIMO Fading Channels

We analyze the bit error rate (BER) performance of M-ary quadrature amplitude modulation (M-QAM) when using space-time block coding (STBC) along with packet combining triggered by automatic repeat request (ARQ) retransmission over multiple-input multiple-output (MIMO) fading channels. Specifically, adopting a log-likelihood ratio (LLR) based approach and considering the 16-QAM case of study, we provide an exact formulation for the aggregate LLR distribution in the case the STBC codeword can be transmitted twice, and derive the resulting BER. For higher number of retransmissions, an approximation of the error function is used to derive the LLR distributions and the system's ensuing BER. Considering different values of combined transmissions and M-QAM with possible constellation rearrangement (CoRe), validation of the proposed BER analytical model through simulations and assessment of the advantages of packet combining are provided for transmissions over additive white Gaussian noise (AWGN) channel and orthogonalized MIMO Rayleigh fading channels with different STBC mappings.

Exact bit error rate analysis of direct sequence ultra-wide band multiple access systems in lognormal multipath fading channels

Exact BER analysis is carried out using the characteristic function (CF) method for direct sequence ultra-wide band (DS-UWB) systems in lognormal multipath fading channels. Unlike the Gaussian approximation (GA) method, the CF method deals with exact probability density function (PDF) of the total noise [including multiple access interference, self interference and additive white gaussian noise (AWGN)] instead of making approximation on PDF of the total noise. Exact bit error rate (BER) formula is derived and verified by simulation results. It is shown that the CF method is more accurate than the GA method in BER calculation when SNR is large. Based on the BER formula, the performance of the DS pulse amplitude modulation UWB and DS pulse position modulation UWB systems is accurately compared. Discussions based on CFs provide further insight into the numerical results.

Joint Tomlinson-Harashima Precoding and Frequency-Domain Equalization for Broadband Single-Carrier Transmission

The performance of single-carrier (SC) transmission in a frequency-selective fading channel degrades due to a severe inter-symbol interference (ISI). Using frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can improve the bit error rate (BER) performance of SC transmission. However, the residual ISI after FDE limits the performance improvement. In this paper, we propose a joint use of Tomlinson-Harashima precoding (THP) and FDE to remove the residual ISI. An approximate conditional BER analysis is presented for the given channel condition. The achievable average BER performance is evaluated by Monte-Carlo numerical computation method using the derived conditional BER. The BER analysis is confirmed by computer simulation of the signal transmission.

Practical Design Model of DnPSK Systems using direct BER Counting and Rigorous BER Modeling

Summary We present a design model for practical 100 Gb/s transmission DnPSK systems which accounts for imperfections in system components i.e. fiber attenuation, dispersion and non-linear effects, electrical drive circuitry for optical modulators, optical amplifiers including amplified spontaneous emission ASE noise and a realistic Rx description with non-ideal Low Pass Filtering (LPF). The model uses direct error-counting combined with an analytical rigorous BER model. An example 50 Gs/s DQPSK transmission system with 240 km transmission is considered for a specified 6 2 PRBS symbolsequence as well as for a 14 2 PRBS symbol-sequence where a selected 6 2 symbol-sequence is used in the theoretical results. We demonstrate excellent agreement between the two methods over two orders of magnitude for the Bit-Error-Rate (BER) in a system regime where the signal interaction with ASE noise during fiber transmission is not significant. The analytical BERresults are extended over ten orders of magnitude.

Analysis of Narrowband Communication Systems Impaired by MB-OFDM UWB Interference

In this paper, we investigate the effect of multi-band orthogonal frequency division multiplexing (MB-OFDM) ultra-wideband (UWB) interference on narrowband (NB) receivers. For this purpose, we first derive the exact moment generating function of MB-OFDM UWB interference. Based on this result, we develop analytical expressions for the amplitude probability distribution (APD) and the bit error rate (BER) of a binary phase-shift keying NB receiver. These expressions can be efficiently numerically evaluated and the presented analysis is general enough to encompass non-fading and various fading NB channels. We show that for NB signals with, respectively, much smaller and much larger bandwidths than the MB-OFDM sub-carrier spacing a Gaussian approximation (GA) and an impulsive GA (IGA) of the MB-OFDM UWB interference lead to accurate performance predictions. However, for most NB channel models and signal bandwidths the exact BER analysis has to be used to obtain meaningful results. An exception is the Rayleigh fading NB channel where both GA and IGA yield tight approximations of the exact BER regardless of the NB signal bandwidth.

BER Analysis of OFDM Systems Impaired by DC Offset and Carrier Frequency Offset in Multipath Fading Channels

We perform bit-error-rate (BER) analysis of orthogonal frequency division multiplexing (OFDM) systems impaired by both direct current (DC) offset and carrier frequency offset (CFO) in multipath Rayleigh fading channels. Since the performance of OFDM systems is sensitive to the CFO, it is necessary to estimate and correct the CFO at the receiver. The existence of DC offset degrades the performance of CFO estimator and results in large residual CFO after compensation. Moreover, the process of CFO compensation spreads the DC offset energy and causes DC offset interference to all subcarriers. By deriving the BER formula for OFDM systems employing binary phase-shift keying modulation, the dependency of BER on the DC offset, CFO, and estimated CFO is accurately quantified. Simulation results validate the correctness of our theoretical analysis.

BER analysis of coherent optical CDMA communication systems with transfer function matrix

We analyze the bit error rate (BER) of coherent optical code-division multiple-access (CDMA) communication systems with a transfer function matrix (TFM). The coherent optical CDMA is a promising system for an access network due to its advantages of asynchronous transmission, information security, multiple-access capability. TFM is defined as the Fourier transform of the impulse response of an optical fiber, which interconnects each CDMA system. TFM has parameters such as the state of polarization (SOP), phase difference, power distribution between two orthogonal modes over an optical frequency range. We first analyze the statistic of a received signal via an optical fiber with TFM, and then apply the statistic to the BER analysis. The analytical results show that BER increases with the bandwidth of a signal, and that selecting a proper center frequency leads to the BER reduction.

Precise BER analysis of π/4-DQPSK OFDM with carrier frequency offset over frequency selective fast fading channels

An exact closed-form bit error rate (BER) expression is derived for an orthogonal frequency-division multiplexing system with π/4-shifted differentially encoded quadrature phase shift keying (π/4-DQPSK) in the presence of carrier frequency offset over frequency-selective fast Rayleigh fading channels. Different system configurations, including time domain differential modulation, frequency domain differential modulation, single channel reception, and multi-channel reception with maximal ratio combining diversity, are considered in the exact BER analysis. For a small number of subcarriers, the BER expression can be calculated directly. A Monte Carlo method is designed to evaluate the BER for a large number of subcarriers. The analytical expression can be used to investigate the effect of several channel parameters, including mean delay spread and maximum Doppler spread, on the system BER performance. Particularly, the effect of carrier frequency offset on the system performance, and the differences and opportunities to use frequency domain differential modulation or time domain differential modulation, can be studied in a quantitative way for a more realistic wireless channel environment model. By using the exact closed-form BER expression, an optimum number of subcarriers can be found, and the allowable carrier frequency offset, Doppler spread, and mean delay spread for given operating conditions can be determined.

A Unified Exact BER Performance Analysis of Asynchronous DS-CDMA Systems Using BPSK Modulation over Fading Channels

An asynchronous binary DS-CDMA system using random spreading sequences is considered when communicating over various fading channels. New closed-form expressions are derived for the conditional characteristic function (CF) of the multiple access interference. A unified analysis is provided for calculating the exact average bit error rate (BER) expressed in the form of a single numerical integration based on the CF approach. The numerical results obtained from our exact BER analysis are verified by our simulation results and are also compared to those obtained by the standard Gaussian approximation (SGA), confirming the accuracy of the SGA for most practical conditions, except for high signal-to-noise ratios (SNR) and for a low number of interferers.

Performance of BPSK Pre-detection MRC Systems over Two-Wave with Diffuse Power Fading Channels

The bit-error rate (BER) analysis for BPSK pre-detection maximal ratio combining (MRC) systems in two-wave with diffuse power (TWDP) fading is presented. In TWDP fading, the received signal is composed of two specular components in addition to the diffuse signal. The analysis shows that in TWDP fading, the BER of the MRC system is given by the weighted sum of the BERs of a number of MRC systems in Rician fading. The methodology used in the analysis is verified through simulation.

Simple Analysis for Average BER of Orthogonal Signals in Nonidentical Rician Channels with Improved-Gain Noncoherent Diversity Reception

This letter proposes a new noncoherent combiner, which we call the noncoherent weighted branches combiner (NC-WBC), to mitigate the disadvantages of the conventional noncoherent equal-gain combiner (NC-EGC) in nonidentically distributed Rician fading channels. It is shown that, unlike those of the NC-EGC, the NC-WBC results in simple closed-form expression for average bit error rate (BER) of the binary orthogonal signaling scheme. The results also show that the NC-WBC provides performance improvement, and alleviates the noncoherent combining loss of the NC-EGC. The theoretical development is verified by simulation results

Performance Analysis of Maximum-Likelihood Multiuser Detection in Space–Time-Coded CDMA With Imperfect Channel Estimation

In this paper, the performance of maximum-likelihood multiuser detection in space-time-coded code-division multiple-access (CDMA) systems with imperfect channel estimation is analyzed. A K-user synchronous CDMA system that employs orthogonal space-time block codes with M transmit antennas and N receive antennas is considered. A least-squares estimate of the channel matrix is obtained by sending a sequence of pilot bits from each user. The channel matrix is perturbed by an error matrix that depends on the thermal noise and the correlation between the signature waveforms of different users. Because of the linearity of the channel estimation technique, the characteristic function of the decision variable is used to obtain an exact expression for the pairwise error probability, and by using it, an upper bound on the bit error rate (BER) is obtained. The analytical BER bounds are compared with the BER obtained through simulations. The BER bounds are shown to be increasingly tight for large SNR values. It is shown that the degradation in BER performance due to imperfect channel estimation can be compensated by using a larger number of transmit/receive antennas