Closed-form Expressions For Bit Error Probability Research Articles

A New Approach to Deriving Closed-Form Bit Error Probability Expressions of MPSK Signals

In conventional approach, the bit error probability (BEP) expressions of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary phase-shift keying (MPSK) signals over additive white Gaussian noise (AWGN) channel are derived by averaging error probabilities for all bits of MPSK symbol. The closed-form BEP expressions of MPSK signals over AWGN channel can also be derived by using the weighted conditional symbol error probability (SEP) expressions, which has not been reported. In this paper, we derive the conditional SEP expressions of MPSK signals in terms of Gaussian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and Owen’s <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> functions by changing the domain of integration from a plane bounded by two rays into a quadrant. By weighting the conditional SEP expressions according to average distance spectrum, the closed-form BEP expressions of MPSK signals over AWGN channel are obtained. Only two summations involving two parameters are required. The closed-form BEP expressions of MPSK signals over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channel are derived by using the BEP expressions over AWGN channel and the moment generating function-based approach. The approximate BEP expressions of MPSK signals over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channel are obtained by using elementary functions-based approximations of Gaussian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and Owen’s <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> functions. The conciseness and computational complexity of our BEP expressions are verified by the comparison with existing results.

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.

Narrowband Interference Suppression in Time-Hopping Impulse Radio Ultra-Wideband Communications

Ultra-wideband (UWB) technology has been considered an innovative solution for future short-range high-speed wireless communications. Interference suppression is important for the UWB devices to operate over spectrum occupied by narrowband systems. In this paper, the use of a notch filter in time-hopping impulse radio (TH-IR) for UWB communication is considered, where a Gaussian monopulse is employed with pulse position modulation. Lognormal channel fading is assumed, and a complete analytical framework is provided for the performance evaluation of using a transversal-type notch filter to reject narrowband interference (NBI). A closed-form expression of bit-error probability is derived, and the numerical results show that the use of a notch filter can improve the system performance significantly. Furthermore, a performance comparison between TH-IR and multicarrier code-division multiple-access (MC-CDMA) UWB systems is made under the conditions of the same transmit power, the same data rate, and the same bandwidth. It is shown that in the presence of NBI, the TH-IR system and MC-CDMA system achieve similar performance when both use a notch filter

The Effect of Narrowband Interference on Wideband Wireless Communication Systems

This paper evaluates the performance of wideband communication systems in the presence of narrowband interference (NBI). In particular, we derive closed-form bit-error probability expressions for spread-spectrum systems by approximating narrowband interferers as independent asynchronous tone interferers. The scenarios considered include additive white Gaussian noise channels, flat-fading channels, and frequency-selective multipath fading channels. For multipath fading channels, we develop a new analytical framework based on perturbation theory to analyze the performance of a Rake receiver in Nakagami-m channels. Simulation results for NBI such as GSM and Bluetooth are in good agreement with our analytical results, showing the approach developed is useful for investigating the coexistence of ultrawide bandwidth systems with existing wireless systems.

Bit-Error Probability for Optimum Combining of Binary Signals in the Presence of Interference and Noise

We derive an exact bit-error probability (BEP) expression for coherent detection of binary signals with optimum combining in wireless systems in the presence of multiple cochannel interferers and thermal noise. A flat Rayleigh fading environment with space diversity, uncorrelated equal-power interferers, and additive white Gaussian noise is considered. The approach is to use the chain rule of conditional expectation together with the joint probability density function (pdf) of the eigenvalues of the interference correlation matrix. This joint pdf is related to the Vandermonde determinant. Let N/sub A/ denote the number of antennas and N/sub I/ the number of interferers. We consider both the cases of an overloaded system, in which N/sub I//spl ges/N/sub A/, and an underloaded system, in which N/sub I/<N/sub A/. Using averaging techniques that make use of the properties of the Vandermonde determinant, we obtain in each of the two cases a closed-form BEP expression as a finite sum, and the only special function that this expression contains is the Gaussian Q-function. This makes it a powerful tool for analysis and computation.

Bit error probability for MDPSK and NCFSK over arbitrary Rician fading channels

In this paper, we analyze the bit error probability (BEP) of binary and quaternary differential phase shift keying (2/4 DPSK) and noncoherent frequency shift keying (NCFSK) with postdetection diversity combining in arbitrary Rician fading channels. The model is quite general in that it accommodates fading correlation and noise correlation between different diversity branches as well as between adjacent symbol intervals. We show that the relevant decision statistic can be expressed in a noncentral Gaussian quadratic form, and its moment generating function (MGF) is derived. Using the MGF and the saddle point technique, we give an efficient numerical quadrature scheme to compute the BEP. The most significant contribution of the paper, however, lies in the derivation of a closed-form cumulative distribution function (cdf) for the decision statistic. As a result, a closed-form BEP expression in the form of an infinite series of elementary functions is developed, which is general and unifies previous published BEP results for 2/4 DPSK and NCFSK for multichannel reception in Rician fading. Specialization to some important cases are discussed and, as a byproduct, a new and general finite-series expression for the BEP in arbitrarily correlated Rayleigh fading is obtained. The theory is applied to study 2/4 DPSK and NCFSK performance for independent and correlated Rician fading channels; and some interesting findings are presented.

Bit-error probabilities for 2- and 4-DPSK in general Nakagami fading channels with correlated Gaussian noise

Exact bit-error probability (BEP) expressions are derived for 2- and 4-ary differential phase shift keying (2- and 4-DPSK) with post-detection equal gain combining (EGC) in arbitrarily correlated slow Nakagami fading channels. Unlike previous work, the effect of noise correlation between adjacent symbol intervals is considered and shown explicitly in the BEP expressions. The characteristic function method is used to give a BEP expression in a general form for 2- and 4-DPSK. Furthermore, closed-form BEP expressions are derived for 2-DPSK with coloured noise, and for 4-DPSK with white noise and integer fading parameter m. The theoretical result is demonstrated by analysing two antenna configurations, giving some interesting findings.