BER Analysis of OFDM Systems Impaired by Phase Noise in Frequency-Selective Fading Channels

In this paper, we study the effect of finite-power, phase-locked loop based phase noise on the bit-error-rate (BER) performance of orthogonal frequency division multiplexing (OFDM) systems in frequency-selective fading channels. It is well known the impact of phase noise on the performance of an OFDM system can be divided into a multiplicative term called common phase error (CPE) and an additive term called intercarrier interference (ICI). Based on the conditional Gaussian approximation technique, we first derive the BER formulas for BPSK, QPSK, 16-QAM, and 64-QAM modulated OFDM signals in frequency-selective Rayleigh fading channels. To further quantify the individual influence of the CPE and the ICI on system performance for different phase noise spectra, we derive the BER expressions for perfect CPE compensation cases. The analytical results obtained for frequency-selective Rayleigh fading channels are then generalized to frequency-selective Rician fading channels. Simulation results not only validate the accuracy of our analysis but also show the dependency of BERs on the shapes of phase noise spectra.     

Performance of GMSK in a land mobile radio channel

Discriminator detection of Gaussian minimum shift keying (GMSK) in a cellular mobile-communication channel is analyzed. The channel is modeled as a frequency-selective fast Rayleigh fading channel corrupted by additive white Gaussian noise (AWGN) and co-channel interference (CCI). A closed-form expression for the probability of error is derived. Numerical computation is used to obtain the GMSK bit error rate (BER) performance for various combinations of channel parameters. These results show that GMSK gives slightly better performance compared to that for π/4-quadrature phase shift keying (QPSK) previously reported in the literature     

Interference suppression for space-time coded CDMA via decision-feedback equalization

A single-user receiver structure is proposed for space-time coded code-division multiple-access (CDMA) downlink in a multiuser frequency-selective channel. This structure is a two-dimensional (2-D) decision-feedback equalizer (2D-DFE) whose filters are optimized based on the MMSE criterion to mitigate noise, intersymbol interference (ISI), and multiuser interference (MUI) with a moderate complexity. By modeling the spreading codes of the interfering users as random sequences, system performance was evaluated using the Gaussian approximation. Two models for the desired user's spreading sequence have been considered and compared. Our numerical results show that in both cases the 2D-DFE exhibits significant performance improvement over the standard space-time coded RAKE, especially in interference-limited conditions. It is also observed that the gain obtained by using DFE in a MISO channel is less that in a SISO channel and this problem can be solved by providing diversity at the receiver.     

Performance of BICM-SC and BICM-OFDM systems with diversity reception in non-gaussian noise and interference

In this paper, we present a general mathematical framework for performance analysis of single?carrier (SC) and orthogonal frequency division multiplexing (OFDM) systems employing popular bit?interleaved coded modulation (BICM) and multiple receive antennas. The proposed analysis is applicable to BICM systems impaired by general types of fading (including Rayleigh, Ricean, Nakagami-m, Nakagami-q, and Weibull fading) and general types of noise and interference with finite moments such as additive white Gaussian noise (AWGN), additive correlated Gaussian noise, Gaussian mixture noise, co-channel interference, narrowband interference, and ultra-wideband interference. We present an approximate upper bound for the bit error rate (BER) and an accurate closed-form approximation for the asymptotic BER at high signal-to-noise ratios for Viterbi decoding with the standard Euclidean distance branch metric. For the standard rate-1/2 convolutional code the proposed approximate upper bound and the asymptotic approximation become tight at BERs of 10-6 and 10-12, respectively. However, if the code is punctured to higher rates (e.g. 2/3 or 3/4), the asymptotic approximation also becomes tight at a BER of 10-6. Exploiting the asymptotic BER approximation we show that the diversity gain of BICM systems only depends on the free distance of the code, the type of fading, and the number of receive antennas but not on the type of noise. In contrast their coding gain strongly depends on the noise moments. Our asymptotic analysis shows that as long as the standard Euclidean distance branch metric is used for Viterbi decoding, BICM systems optimized for AWGN are also optimum for any other type of noise and interference with finite moments.     

Blind turbo multiuser detection for long-code multipath CDMA

We consider the problem of demodulating and decoding multiuser information symbols in an uplink asynchronous coded code-division multiple-access (CDMA) system employing long (aperiodic) spreading sequences, in the presence of unknown multipath channels, out-cell multiple-access interference (OMAI), and narrow-band interference (NBI). A blind turbo multiuser receiver, consisting of a novel blind Bayesian multiuser detector and a bank of MAP decoders, is developed for such a system. The effect of OMAI and NBI is modeled as colored Gaussian noise with some unknown covariance matrix. The main contribution of this paper is to develop blind Bayesian multiuser detectors for long-code multipath CDMA systems under both white and colored Gaussian noise. Such detectors are based on the Bayesian inference of all unknown quantities. The Gibbs sampler, a Markov chain Monte Carlo procedure, is then used to calculate the Bayesian estimates of the unknowns. The blind Bayesian multiuser detector computes the a posteriori probabilities of the channel coded symbols, which are differentially encoded before being sent to the channel. Being soft-input soft-output in nature, the proposed blind Bayesian multiuser detectors and the MAP decoders can iteratively exchange the extrinsic information to successively refine the performance, leading to the so-called blind turbo multiuser receiver     

On turbo code decoder performance in optical-fiber communication systems with dominating ASE noise

In this paper, we study the effects of different ASE noise models on the performance of turbo code (TC) decoders. A soft-decoding algorithm, the Bahl, Cocke, Jelinek, and Raviv (BCJR) decoding algorithm, is generally used in TC decoders. The BCJR algorithm is a maximum a posteriori probability (MAP) algorithm, and is very sensitive to noise statistics. The Gaussian approximation of ASE noise is widely used in the study of optical-fiber communication systems, and there exist standard TCs for additive white Gaussian noise (AWGN) channels. We show that using a MAP decoding algorithm based on the Gaussian noise assumptions, however, may significantly degrade the TC decoder performance in an optical-fiber channel with non-Gaussian ASE noise. To take full advantage of TC, accurate noise statistics in optical-fiber transmissions should be used in the MAP decoding algorithm.     

具有低复杂度的 LDPC 已编码非相干酉空时调制系统设计简

提出一种克服无线信道瑞利衰落和高斯白噪声干扰的非相干编码调制MIMO系统方案。纠错码采用IEEE 802.16e中的非规则QC-LDPC码,非相干调制采用基于三角函数的酉空时调制(SC-USTM)。在接收端,推导出SC-USTM的最大后验概率（MAP）解调算法;为了降低复杂度,构造了SC-USTM的双解调器方案;为了改善双解调的性能,在置信传播（BP）迭代解码器和MAP解调器之间引入了迭代反馈机制。仿真实验表明LDPC已编码SC-USTM的MIMO系统比未编码USTM的MIMO系统在 误码率时,性能改善15~17 dB,并且整个系统具有较低的计算复杂度。     

Bit error rate performance for edge-detected CMI data transmission

A single edge detector for coded mark inversion, data transmission is proposed. Its detection performance depends mainly on the false transition probability if the bandwidth of the receiver low-pass filter is reasonably large, say equal to twice the data rate. An approximate expression for the bit error rate (BER) performance of this detector operating in white Gaussian noise is derived by considering the level crossing probability of the noise process. Measurements show that this approximation is closer to the actual BER performance than results obtained from a previously established theoretical approach in some cases     

Near-capacity coding in multicarrier modulation systems

We apply irregular low-density parity-check (LDPC) codes to the design of multilevel coded quadrature amplitude modulation (QAM) schemes for application in discrete multitone systems in frequency-selective channels. A combined Gray/Ungerboeck scheme is used to label each QAM constellation. The Gray-labeled bits are protected using an irregular LDPC code with iterative soft-decision decoding, while other bits are protected using a high-rate Reed-Solomon code with hard-decision decoding (or are left uncoded). The rate of the LDPC code is selected by analyzing the capacity of the channel seen by the Gray-labeled bits and is made adaptive by selective concatenation with an inner repetition code. Using a practical bit-loading algorithm, we apply this coding scheme to an ensemble of frequency-selective channels with Gaussian noise. Over a large number of channel realizations, this coding scheme provides an average effective coding gain of more than 7.5 dB at a bit-error rate of 10/sup -7/ and a block length of approximately 10/sup 5/ b. This represents a gap of approximately 2.3 dB from the Shannon limit of the additive white Gaussian noise channel, which could be closed to within 0.8-1.2 dB using constellation shaping.     

A comparison of long versus short spreading sequences in codedasynchronous DS-CDMA systems

The performance of turbo-coded asynchronous direct sequence code division multiple access (DS-CDMA) using long and short spreading sequences is compared by both analysis and simulation. For coded systems with a conventional matched filter (MF) receiver, three analytical methods with different complexity are compared: the standard Gaussian approximation, the improved Gaussian approximation (IGA), and the density function approach. It is shown that while the standard Gaussian approximation is fairly accurate for the long sequences, it is too optimistic for the short sequences. For the short-sequence systems, the IGA gives an accurate estimate for the performance with much less complexity than the density function approach. The analysis shows that for either the additive white Gaussian noise (AWGN) channel or the flat Rayleigh fading channel and a MF receiver, there is a degradation in the average performance of the turbo-coded short-sequence systems compared to the long-sequence systems due to the fact that the cross-correlations are not time-varying. However, the short-sequence systems are amenable to the use of an interference suppression technique designed to minimize the mean square error. Such a minimum mean square error (MMSE) receiver in the turbo-coded system is shown to outperform the long-sequence system with the MF receiver, especially when there is a near-far problem, as previously observed in a convolutionally-coded system. Finally, similar results are obtained by computer simulations for the turbo-coded CDMA systems on a frequency-selective Rayleigh fading channel     

Particle Filters for Joint Blind Equalization and Decoding in Frequency-Selective Channels

This paper introduces new algorithms for joint blind equalization and decoding of convolutionally coded communication systems operating on frequency-selective channels. The proposed method is based on particle filters (PF), recursively approximating maximum a posteriori (MAP) estimates of the transmitted data without explicitly determining channel parameters. Further elaborating on previous works, we assume that both the channel order and the noise variance are unknown random variables, and develop a new formulation for PF weight propagation which allows these quantities to be analytically integrated out. We verify via numerical simulations that the proposed methods lead to near optimal performance, closely approximating that of algorithms that require exact knowledge of all channel parameters.     

Phase-noise effects on turbo trellis-coded over M-ary coherent channels

The effect of the phase noise on the performance of bandwidth-efficient coded modulation is studied. To this end, the average mutual information (AMI) for specific constellations such as 8-phase-shift keying and 16-quadrature amplitude modulation is calculated in the presence of carrier phase error caused by imperfect carrier tracking over an additive white Gaussian noise channel. The AMI not only quantifies the effect of the phase noise from an information-theoretic viewpoint, but also serves as an estimate for a permissible amount of the phase noise for a given signal-to-noise ratio. The bit-error rate (BER) performance of a near-optimal turbo trellis-coded modulation scheme is then investigated over such a channel. For this purpose, an optimal branch metric which best fits the channel characteristics is derived. Furthermore, simple branch metrics (referred to as suboptimal, simplified, and Gaussian metrics) are derived, which may offer the tradeoff between BER performance and computational complexity. Numerical analysis shows that a near-optimal coded-modulation scheme renders a transmission system more robust against phase noise than is the case with a conventional trellis-coded modulation scheme.     

Multichannel MLSE equalizer with parametric FIR channelidentification

We propose a parametric finite impulse response (FIR) channel identification algorithm, apply the algorithm to a multichannel maximum likelihood sequential estimation (MLSE) equalizer using multiple antennas, and investigate the improvement in the overall bit error rate (BER) performance. By exploring the structure of the specular multipath channels, we are able to reduce the number of channel parameters to provide a better channel estimate for the MLSE equalizer. The analytic BER lower bounds of the proposed algorithm as well as those of several other conventional MLSE algorithms in the specular multipath Rayleigh-fading channels are derived. In the derivation, we consider the channel mismatch caused by the additive Gaussian noise and the finite-length channel approximation error. A handy-to-use simplified BER lower bound is also derived. Simulation results that illustrate the BER performance of the proposed algorithm in the global system for mobile communications (GSM) system are presented and compared to the analytic lower bounds     

Analysis of low-density parity-check codes based on EXIT functions

We exploit extrinsic information transfer functions of single parity-check and repetition codes over the binary input additive white Gaussian noise (biAWGN) channel, derived by the authors, for asymptotic performance analysis of belief propagation decoding of low-density parity-check codes. The approach is based on a Gaussian approximation (GA) of the density evolution algorithm using the mutual information measure. We show that this method allows more accurate prediction of the decoding threshold in the biAWGN channel than the earlier known GA methods.     

Error Rate Analysis for Coded Multicarrier Systems Over Quasi-Static Fading Channels

Several standards such as IEEE 802.11a/g, IEEE 802.16, and the European Computer Manufacturers Association (ECMA) multiband orthogonal frequency division multiplexing (MB-OFDM) for high data-rate ultra-wideband employ bit-interleaved convolutionally coded multicarrier modulation over quasi-static fading channels. Motivated by the lack of appropriate error rate analysis techniques for this popular type of system and channel model, we present two novel analytical methods for bit error rate (BER) estimation of coded multicarrier systems operating over frequency-selective quasi-static channels with nonideal interleaving. In the first method, the approximate performance of the system is calculated for each realization of the channel, which is suitable for obtaining the outage BER performance (a common performance measure for, e.g., MB-OFDM systems). The second method assumes Rayleigh distributed frequency-domain subcarrier channel gains and knowledge of their correlation matrix, and can be used to directly obtain the average BER performance. Both methods are applicable to convolutionally coded interleaved multicarrier systems employing quadrature amplitude modulation, and are also able to account for narrowband interference (modeled as a sum of tone interferers). To illustrate the application of the proposed analysis, both methods are used to study the performance of a tone-interference-impaired MB-OFDM system.     

Bit error rate performance of π/4-DQPSK in a frequency-selectivefast Rayleigh fading channel

The bit error rate (BER) performance of π/4-differential quadrature phase shift keying (DQPSK) modems in cellular mobile communication systems is derived and analyzed. The system is modeled as a frequency-selective fast Rayleigh fading channel corrupted by additive white Gaussian noise (AWGN) and co-channel interference (CCI). The probability density function of the phase difference between two consecutive symbols of M-ary differential phase shift keying (DPSK) signals is first derived. In M-ary DPSK systems, the information is completely contained in this phase difference. For π/4-DQPSK, the BER is derived in a closed form and calculated directly. Numerical results show that for the 24 kBd (48 kb/s) π/4-DQPSK operated at a carrier frequency of 850 MHz and C/I<20 dB, the BER will be dominated by CCI if the vehicular speed is below 100 mi/h. In this derivation, frequency-selective fading is modeled by two independent Rayleigh signal paths. Only one co-channel is assumed in this derivation. The results obtained are also shown to be valid for discriminator detection of M-ary DPSK signals     

Sequence detection and adaptive channel estimation for ISI channels under class-a impulsive noise

In this paper, sequence detection and channel estimation for frequency-selective, intersymbol interference (ISI)-producing channels under Class-A impulsive noise are considered. We introduce a novel suboptimum sequence detection (SSD) scheme and show that although SSD employs a simplified metric, it achieves practically the same performance as maximum-likelihood sequence detection (MLSD). For both SSD and MLSD, a lower bound on the achievable performance is derived, which is similar to the classical matched-filter bound for frequency-selective (fading) channels under Gaussian noise. For channel estimation, we adopt a minimum entropy criterion and derive efficient least-mean-entropy and recursive least-entropy algorithms. For both adaptive algorithms, we analyze the steady-state channel-estimation error variance. Theoretical considerations and simulation results show that in Class-A impulsive noise, the proposed sequence detection and adaptive channel-estimation schemes yield significant performance gains over their respective conventional counterparts (designed for Gaussian noise). Although the novel algorithms require knowledge of the Class-A noise-model parameters, their computational complexity is comparable to that of the corresponding conventional algorithms.     

Turbo processing in transmit antenna diversity systems

We consider turbo-trellis-coded transmission over fading multiple-input-multiple-output (M1M0) channels with transmit diversity using space-time block codes. We give a new view on space-time block codes as a transformation of the fading MIMO channel towards a Gaussian single-input-single-output (siso) channel and provide analytical results on the BER of space-time block codes. Furthermore, we describe the concatenation of Turbo-TCM with a space-time block code and show that in addition to the transmit diversity substantial benefits can be obtained by turbo iterations as long as the channel is time-varying during transmission of a coded block or frequency hopping is applied. Finally, a double iterative scheme for turbo equalization and turbo decoding of the concatenation of Turbo-TCM and space-time block code in frequency-selective MIMO channels is described.     

A New Method for the Computation of the Error Probability of Differentially Detected Modulation Formats in Mobile Radio Channels – The Case of Minimum Shift Keying

We show a new approach to analytically compute the error probability BER in mobile radio channels. The method is applicable to a variety of differentially detected modulation formats; here we use minimum shift keying (MSK) as an example. We include the following effects: (i) fading and (ii) time dispersion of the mobile radio channel (iii) noise, and (iv) filtering both of the data sequence and the received signal. Sampling is at a fixed but arbitrary instant. We develop a new mathematical formalism, which we call the two-path equivalent-matrix (TPEM) method. In this method, we reduce the general channel (including noise) exactly to a two-path fading channel without noise, whose BER can be easily computed. With this method, we can find analytically the BER for both filtered and unfiltered (G)MSK if the BER is small; for large BER a single well-behaved integral must be solved numerically. Asymptotic equations for unfiltered MSK and small BERs are also given. To a first approximation, the BER is 0.5· [(S/T)²+1/SNR] for pure MSK, where S/T is the delay spread normalized to the bit duration and SNR is the signal-to-noise ratio. The BER is increased by less than 50% for Gaussian filtering of the data sequence and receiver filtering with a time-bandwidth product larger than 0.3.     

Error rate analysis of MDPSK/CPSK with diversity reception undervery slow Rayleigh fading and cochannel interference

The distribution of the phase noise due to additive white Gaussian noise (AWGN) and cochannel interference (CCI) is analyzed for differential phase detection (DPD) and coherent phase detection (CPD) in a very slow nonfrequency selective Rayleigh fading environment. The effects of modulation timing offset between the desired signal and the CCI and of the overall channel filter response are considered. Simple closed-form expressions are derived for ideal selection diversity reception. The derived phase noise distributions are used for evaluating the bit error rate (BER) performance of 2-16DPSK/CPSK assuming square-root raised cosine Nyquist transmit/receive filters. It is found that the BER performance of CPSK is less sensitive to CCI modulation timing offset than DPSK, and that increasing the filter rolloff factor can improve the BER performance due to CCI. Finally, the accuracy of the BER approximation that uses the symbol error rate is discussed