Bit error rate estimation using probability density function estimators

The concept of real-time bit error rate (BER) estimation based on probability density function (PDF) estimators of the decision statistic is discussed. Communications systems need techniques to approximate real-time BER estimation without resorting to brute-force error counting methods. Due to the dynamic nature of the wireless channel, a priori (deductive) estimation techniques (e.g., where knowledge of signal impairments is assumed before demodulation) are often unreliable. A posteriori (inductive) estimation techniques (e.g., where knowledge of signal impairments is acquired after the signal is demodulated) are preferable because they assume no prior knowledge of the channel. Two a posteriori techniques are described that yield reliable BER estimates over small observation intervals: (1) the Gram-Charlier series approximation for PDFs and (2) Parzenʹs PDF estimator. Robust estimators of location and scale are also employed to improve the performance of Gram-Charlier estimation. The performance of BER estimation based on the PDF estimators is validated by simulations. A 1-bit differential demodulator (DD1) is used to demodulate a Gaussian minimum shift keying signal, and Gram-Charlier-based and Parzen (1962) based BER estimations are compared to measured DD1 results. Comparisons are made for BER estimation versus measured BER in additive white Gaussian noise (AWGN) and cochannel interference (CCI) channels and in urban multipath with AWGN and CCI.