New Approach for Error Compensation in Coded V-BLAST OFDM Systems

In this paper, we investigate coded layered space-time architectures for frequency-selective fading multiple-input multiple-output orthogonal frequency-division multiplexing (OFDM) channels. By computing outage capacity formulas, we will show that the capacity of the vertical Bell Labs layered space-time (V-BLAST) architecture can closely approach the Shannon capacity in the frequency-selective OFDM environment. Motivated by the capacity analysis, we propose pragmatic approaches which preserve the optimality of the layered space-time concept. We present methods to prevent the error propagation from catastrophically affecting the signal detection in subsequent layers. First, we start with a comprehensive signal modeling which includes error propagation. We derive an improved signal detector and describe the optimal soft-bit log-likelihood ratio value-computation method by taking decision errors into account for soft-input channel decoding. Then, to further enhance the V-BLAST performance, we show that cancellation using decoded decisions from previous layers makes the decision errors almost completely disappear, so that the layered space-time architecture can approach the attainable channel capacity. Finally, simulations confirm that the proposed schemes show a significant performance improvement over the conventional methods     

Union Bounds on the Bit Error Probability of Coded MRC in Nakagami-m Fading

In this letter new union bounds are derived for coded maximal ratio combining (MRC) over Nakagami-m fading channels. The union bounds are expressed in the product form, which makes them easily, evaluated using the transfer function of the code. The bounds are general to any diversity order and coding scheme with a known transfer function. Results show that the new bounds are tight to simulation results for wide ranges of diversity orders and Nakagami parameters     

Union Bound on the Bit Error Rate for MIMO-GFDM Systems

Wireless Personal Communications - In this paper, a union bound on the bit error rate (BER) for multiple input multiple output generalized frequency division multiplexing (MIMO-GFDM) systems is...     

A Tightened Upper Bound on the Error Probability of Binary Convolutional Codes with Viterbi Decoding

Tighter upper bounds on the error event and the bit error probabilities, respectively, for maximum-likelihood decoding of binary convolutional codes on the binary symmetric channel are derived from upper bounds previously published by Viterbi [1]. The measured bit error rateP_bfor a constraint length 3 decoder has been plotted versus the channel transition probabilitypand shows close agreement with the improved bound on the bit error probability.     

A Comment on "Probability of Error in PN-Modulated Spread Spectrum Binary Communication Systems"

Examination of the interference power of spread spectrum PN systems gives a result approximately twice as large as that reported by Hopkins and Simpson [1]. The additional factor is due to a correlation between intersymbol interferences at different chip times. A corrected characteristic function for the interference is given here.     

An Exact Error Probability Analysis of OFDM Systems with Frequency Offset

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for orthogonal frequency division multiplexing (OFDM) systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in additive white Gaussian noise (AWGN), frequency flat and frequency selective Rayleigh fading channels. The BER/ SER performances of BPSK and QPSK modulation schemes are analyzed for AWGN and frequency-flat Rayleigh fading channels while BPSK is considered for frequency-selective Rayleigh fading channels. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions.     

Coded Error Probability for DS Spread-Spectrum Systems with Periodic Pulsed Multiple-Tone Interference

The coded error probability for direct sequence (DS) BPSK or QPSK spread-spectrum systems, used with or without interleaving, and operating in the presence of pulsed multiple-tone interference, is investigated. We consider the worst-case channel error probability under conditions of pulsed multiple-tone jamming for the various systems, and present coded error probability as a function of interleaving delay for(n, k)block codes with hard-decision decoding. It is shown that when the maximum level of continuous multiple-tone interference does not exceed the level of the desired signal, the duty cycle of the corresponding pulsed interference which yields the worst-case error probability is usually small, and that the smaller the duty factor of the jamming, the more considerable is the performance improvement due to the use of interleaving in conjunction with the coding.     

A New Upper Bound on the Block Error Probability After Decoding Over the Erasure Channel

Motivated by cryptographic applications, we derive a new upper bound on the block error probability after decoding over the erasure channel. The bound works for all linear codes and is in terms of the generalized Hamming weights. It turns out to be quite useful for Reed-Muller codes for which all the generalized Hamming weights are known whereas the full weight distribution is only partially known. For these codes, the error probability is related to the cryptographic notion of algebraic immunity. We use our bound to show that the algebraic immunity of a random balanced m-variable Boolean function is of order ^m/₂(1-o(1)) with probability tending to 1 as m goes to infinity     

A Tighter Bhattacharyya Bound for Decoding Error Probability

The Bhattacharyya bound has been widely used to upper bound the pair-wise probability of error when transmitting over a noisy channel. However, the bound as it appears in most textbooks on channel coding can be improved by a factor of 1/2 when applied to the frame error probability. For the particular case of symmetric channels, the pairwise error probability can also be improved by a factor of 1/2. This letter provides a simple proof of these tighter bounds that has the same simplicity as the proof of the standard Bhattacharyya bound currently found in textbooks     

Effect of Channel Estimation Error on Bit Error Probability in OFDM Systems over Rayleigh and Ricean Fading Channels

A characteristic function-based method is used to derive closed-form bit error probability (BEP) expressions for orthogonal frequency-division multiplexing (OFDM) systems in the presence of channel estimation error over frequency-selective Rayleigh fading channels and frequency-selective Ricean fading channels. Both single channel reception and diversity reception with maximal ratio combining (MRC) are examined. The BEP expressions are shown to be sums of several conditional probability functions which can be calculated by using proper complex Gaussian random variable theory and a characteristic function method. The closed-form BEP expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models. The performances of two interpolation methods, a sine interpolator with Hamming windowing and a Wiener interpolator, are compared.     

Probability of Error Analysis of BPSK OFDM Systems with Random Residual Frequency Offset

In this paper, we derive closed form bit error rate (BER) expressions for orthogonal frequency division multiplexing (OFDM) systems with residual carrier frequency offset (CFO). Most of the published work treats CFO as a nonrandom parameter. But in our study we consider it as a random parameter. The BER performance of binary phase shift keying (BPSK) OFDM system is analyzed in the cases of additive white Gaussian noise (AWGN), frequency-flat and frequency-selective Rayleigh fading channels.We further discuss how these expressions can be related to systems with practical estimators. The simulation results are provided to verify the accuracy of these error rate expressions.     

Iterative MAP Equalization and Decoding in Wireless Mobile Coded OFDM

Orthogonal frequency division multiplexing (OFDM) system suffers extra performance degradation in fast fading channels due to intercarrier interference (ICI). Combining frequency domain equalization and bit-interleaved coded modulation (BICM), the iterative receiver is able to harvest both temporal and frequency diversity. Realizing that ICI channels are intrinsically ISI channels, this paper proposes a soft-in soft-out (SISO) maximum a posteriori (MAP) equalizer by extending Ungerboeck's maximum likelihood sequence estimator (MLSE) formulation to ICI channels. The SISO MAP equalizer employs BCJR algorithm and computes the bit log-likelihood ratios (LLR) for the entire received sequence by efficiently constructing a trellis that takes into account of the ICI channel structure. A reduced state (RS) formulation of the SISO MAP equalizer which provides good performance/complexity tradeoff is also described. Utilizing the fact that ICI energy is clustered in adjacent subcarriers, frequency domain equalization is made localized. This paper further proposes two computational efficient linear minimum mean square error (LMMSE) based equalization methods: recursive q-tap SIC-LMMSE equalizer and recursive Sliding-Window (SW) SIC-LMMSE equalizer respectively. Simulations results demonstrate that the iterative SISO RS-MAP equalizer achieves the performance of no ICI with normalized Doppler frequency f_dT_s up to 20.46% in realistic mobile WiMAX environment.     

Probability of Error in Pseudonoise (PN)-Modulated Spread Spectrum Binary Communication Systems

The probability of error in a binary communication system using pseudonoise (PN) modulation to spread the transmitted spectrum is influenced by noise, bandlimiting, and synchronization errors. In this paper the average probability of error is determined, using a series expansion of the characteristic function of the intersymbol interference. It is shown that the effects of intersymbol interference are reduced by spreading and that local code synchronization errors become the dominant factor in the probability of error when the system bandwidth is large.     

Considerations on Error Probability in Correlated-Symbol Systems

An approach to evaluate the error probability in conventional PAM digital data transmission systems with correlated symbols in the presence of intersymbol interference and additive noise is formulated in general and it is applied to the Gram-Charlier series expansion method. It is shown that the technique of conditioning few symbols before and/or after the symbol to be detected increases substantially the range of signal-to-noise ratios with an acceptable increase of numerical work. This technique also improves existing bounds on error probability, as, e.g, Glave's bound.     

A Quadrature Coded OFDM for Reducing Effects of Frequency Offset in Wireless Transmission System

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Probability of Error in Binary Communication Systems with Causal Band-Limiting Filters--Part I: Nonreturn-to-Zero Signal

Upper and lower bounds to probability of error in binary communication systems with intersymbol interference are presented. Closed-form formulas are given for systems with filters having a finite number of lumped elements. Explicit results are given when the filters are Butterworth filters of orderN = 1, 2,..., 10. Four systems are considered: with a sample detector (SD), with an integrate-integrated-and-dump detector (IDD), with a filter in receiver only, and with filters in receiver and transmitter. The transmitted signal is assumed to be of the nonreturn-nonreturn-to-zero (NRZ) form.     

Probability of Error in Binary Communication Systems with Causal Band-Limiting Filters--Part II: Split-Phase Signal

The probability of error is computed in four binary communication systems withNth order (N = 1, 2,...,10) Butterworth filters and split-phase signals. The systems have either a sampling detector or an integrating-and-dumping detector; the filter is either in the receiver only or both in the receiver and transmitter. A lower bound to the probability of error is also computed for modified binary communication systems in which prior to the decision the contribution of the past transmitted symbols is eliminated. In all systems the sampling time is optimized and the effect of nonoptimal sampling time on probability of error is demonstrated.     

A Simplified Expression for the Probability of Error for Binary Multichannel Communications

We present a simplified expression for the probability of error, P_e, for binary multichannel communications. The original expression was derived by Proakis in 1968. More recently, Simon and Alouini presented an expression involving the generalised Marcum Q-function. In this letter we present a simplified form of Simon and Alouini's expression. The application of this result to the calculation of performance metrics for communications over fading channels is also discussed.     

Threshold Effect on Error Probability in QAM Systems

This paper considers the effect of the carrier phase error on the probability of error in a binary quadrature amplitude modulation (QAM) data transmission system in the presence of intersymbol interference and additive Gaussian noise. The analysis shows that there exists a threshold value of the carrier phase error such that the error probability remains almost unchanged as long as the carrier phase error is less than that threshold value, but increases rapidly once the threshold is exceeded. Good agreement between theory and computer simulations is obtained. Some practical implications of this threshold effect are discussed.