A Closed-Form Expression for the Exact Bit Error Probability for Viterbi Decoding of Convolutional Codes

A general method is presented for the computation of the exact bit error probability for arbitrary two-dimensional (2D) signaling with polygonal decision regions in various channel environments. This new approach is general in the sense that it applies to any coherent 2D constellation, any bit-to-symbol mapping, and various environments such as additive white Gaussian noise (AWGN) channels and slow fading channels with and without diversity reception and channel estimation error. The considered performance measures include the exact bit error probability, the symbol error probability, the mutual information and the error probabilities of individual bits in a constellation. The proposed new approach is exact and easy to evaluate, thus avoiding the need for computer simulation.

We consider the bit error performance of orthogonal space-time block codes (STBC) over independent, non- identically distributed, Rayleigh/Ricean, block fading channels with perfect channel state information. With symbol-by-symbol detection, we derive the expressions for the exact bit error probability (BEP) in both Rayleigh and Ricean fading channels. The results are applicable to any number of transmit and receive antennas for which orthogonal STBC's are defined. A simple but insightful upper bound on the BEP is also obtained. From the expressions of the BEP, we find that in Rayleigh channels, the nonidentical distributions degrade the performance. However, for Ricean case, the nonidentical distributions can have different effects on the performance.

We study the performance of differential orthogonal space-time block codes over independent and semi-identically distributed Rayleigh fading channels. In this semi-identically distributed fading model, the channel gains from different transmit antennas to a common receive antenna are identically distributed, but the gains associated with different receive antennas are non-identically distributed. Arbitrary fluctuation rates of the fading processes from one transmission block to another are considered. We first derive the optimal symbol-by-symbol differential detector, and show that the conventional differential detector is suboptimal. We then derive expressions of exact bit error probabilities (BEP) for both the optimal and suboptimal detectors. The results are applicable for any number of receive antennas and any number of transmit antennas for which orthogonal space-time block codes exist. For two transmit antennas, explicit and closed-form BEP expressions are obtained. A Chernoff bound on the BEP of optimal detection for any number of transmit antennas is also derived.

We consider the digital fingerprinting problem where colluders apply uniform linear averaging followed by AWGN. For each user, the receiver computes the correlation between the attacked signal and that user's fingerprint, and performs thresholding (focused detection). We model the fingerprinting problem as a multi-user communications problem and develop a detection theoretic framework. Assuming independent colluders, we derive generic exact bit error probability expressions, together with tight bounds, for arbitrary fingerprinting systems. Then, we specialize our results to orthogonal, simplex and Gaussian codes; under MSE distortion constraints on the embedder and the colluders, we compute the optimal detection rule, the resulting minimum bit error probability, the collusion resistance for the aforementioned codes, and compare their performances.

Exact average bit error probability (BEP) expressions for mobile-relay-based mobile-to-mobile (M2M) cooperative networks with incremental decode-and-forward (IDF) relaying over N-Nakagami fading channels are derived in this paper.The average BEP performance under different conditions is evaluated numerically to confirm the accuracy of the analysis.Results are presented which show that the fading coefficient, the number of cascaded components, the relative geometrical gain, and the power allocation parameter have a significant influence on the average BEP performance.

A theoretical analysis of the error performance of a Gray encoded quadrature phase shift keying (QPSK) scheme in the presence of thermal Gaussian noise and a fading cochannel interference signal in a slow fading indoor wireless channel is presented. The exact error probability expression is presented in a closed form with the error manifesting the combined effect of noise and interference. The system model and the underlying assumptions are specified, and the problem is formulated. The expressions for the bit and symbol error rates are derived. The performance plots and conclusions are presented. It is shown that the exact bit error ratio and the symbol error can be expressed in a closed form. >

The accurate performance evaluation of differential amplitude and phase-shift keying (DAPSK) with postdetection equal gain combining (EGC) over generalized fading channels is of great theoretical interest and practical importance. In this paper, by using a decision variable-based moment generating function approach, exact error probability results for DAPSK over generalized Rician and Nakagami fading channels are derived, taking into account the effects of all the system and fading channel parameters. Several maximum likelihood (ML)-based detectors that do not require channel state information (CSI) are proposed for generalized Rician fading channels, and an exact bit error probability (BEP) union bound for the ML detection is derived. Assuming CSI, a performance upper bound for DAPSK with EGC is also presented. Simulation and numerical results show when both detectors have no CSI, the conventional DAPSK detector may perform closely to (though worse than) the ML detector. However, the EGC receiver with CSI performs substantially better than the ML detector without CSI, and very closely to the coherent APSK detector.

This work presents a performance analysis of a decode-and-forward (DF) relay-assisted diffusion-based molecular communication system consisting of one nanotransmitter, one nanoreceiver and one nanotransceiver acting as relay. We consider cases using one molecule in our two-hop relay network (1M2H), and using two molecules (2M2H). Inspired by the biological signal transduction systems, the ligand-receptor binding mechanism is introduced for the receptors on the surface of receiver. Inter-symbol interference (ISI) and self-interference (SI) can be identified as the performance-limiting effects in our relaying network. The number of received molecules can be approximated by the normal distribution, and using this approximation, a closed-form expression of bit error probability for the relay-assisted network is derived. Then, we put forward an optimization problem for minimizing the bit error probability, and solve it using an algorithm based on the gradient descent to find the optimal detection threshold. In addition, the expression of channel capacity is obtained for two-hop molecular communication with ligand receptors. Numerical results show that the 2M2H network has greater capacity than the 1M2H network.

The final closed-form expression for bit error probability (BEP) is presented for a DS-CDMA system using a maximal ratio combining (MRC) diversity over a Rician fading channel. The accuracy of the BEP estimate evaluated by this expression is verified by comparison with a semi-analytic simulation result. The effect that diversity order has on the BEP is also considered for typical multipath delay profiles with different Rician ratios.

The optimum detection of binary antipodal signals in additive white Gaussian noise (AWGN) channels with Gaussian channel estimation error has been studied in prior work. In this paper, we present the optimum detector based on the maximum- likelihood criterion for binary orthogonal signals in the presence of Gaussian distributed channel estimation error and AWGN. It is shown that the optimum detector is a linear combination of the optimum coherent and optimum noncoherent detectors. We derive the exact closed-form expression of the average bit error probability of the proposed optimum detector in Rayleigh fading channels with AWGN. It is found that if the variance of channel estimation error for a given average SNR is greater than a threshold, then orthogonal signalling outperforms antipodal modulation, and the analytical expression of this threshold is derived.

In this paper the fiber optical local area networks (FO-LANs) performance analysis, using modified prime sequence codes (MPSC) is presented. A particular attention is devoted to the influence of multiuser interference effects to the system capacity. The analytical expression for bit error probability (BER) is derived, and two modifications of the receiver are introduced. The adaptive decision threshold receiver has better performance and greater complexity comparing to the hard-limiter receiver.

A closed-form approximate expression for the average bit error probability (ABEP) of multi-hop multi-branch cooperative networks is derived. The cooperative amplify-and-forward (AF) relaying scheme includes M separate branches between the source node and the destination node, and each branch comprises a certain number of relays. Furthermore, we consider independent and non-identical Rayleigh fading links between successive nodes in each branch. Numerical results are also provided and compared with Monte Carlo simulations.

Filter bank multi-carrier (FBMC) is a modulation technique with enhanced spectral properties compared with orthogonal frequency division multiplexing (OFDM). In this letter, we investigate the performance degeneration of OFDM and FBMC in doubly-selective channels, that is, time-selectivity and frequency-selectivity. For that, we derive closed-form bit error probability (BEP) expressions for arbitrary linear modulation methods based on one-tap equalizers, with OFDM and FBMC being special cases, covered by our general BEP expressions. We validate our calculations by Monte Carlo simulations and investigate the BEP error if the interference is approximated as Gaussian noise.

An exact closed-form bit error rate expression is derived for an orthogonal frequency-division multiplexing system, each subcarrier modulated by /spl pi//4-shifted differentially encoded quadrature phase shift keying, in the presence of carrier frequency offset over frequency-selective fast Rayleigh fading channels. Both single channel reception and diversity reception with maximal ratio combining are considered. The closed-form expression allows us to investigate the effect of several channel parameters, including mean delay spread and maximum Doppler shift, on the system bit error rate performance. Particularly, the effect of carrier frequency offset on the system performance can be studied for a more realistic wireless channel environment model. Small carrier frequency offsets have slight influences on the system performance. Compared with the same amount of Doppler shift, carrier frequency offset usually leads to a greater degree of performance degradation. Systems with fewer subcarriers are more sensitive to the channel mean delay spread. By using the exact closed-form bit error rate expression, an optimum number of subcarriers can be found, and the allowable carrier frequency offset, Doppler shift, and mean delay spread for given operating conditions can be determined.

Using a Maclaurin series expansion of the conditional (on the carrier phase error) bit error probability of binary and quaternary phase-shift keying (BPSK and QPSK, respectively) and then averaging this result over both the statistics of the carrier phase error and the channel fading, closed-form expressions for the average bit error probability are derived in a form that lend themselves toward obtaining simple formulas for the associated noisy reference loss. Numerical evaluation of this loss based on the use of these formulas is shown to provide excellent accuracy when compared with the exact evaluation, which requires two-fold numerical integration. Although the method is specifically applied to BPSK and QPSK, it is easily extended to other forms of modulation whose conditional bit error probability is known in a closed form.