International Telemetering Conference Proceedings / October 25-28, 1999 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Three different demodulators applicable to the coherent demodulation of binary Gaussian Minimum Shift Keying (GMSK) signal are described and their performance compared. These include a near-optimal trellis demodulator, which utilizes two matched filters and Viterbi algorithm to carry out maximum likelihood sequence estimation, and a singlefilter threshold demodulator with and without pulse equalization. The performance of these demodulators in noise and adjacent channel interference (ACI) are compared for several signal BT products. The equalized threshold demodulator is shown to perform nearly as well as the near-optimal trellis demodulator in additive white Gaussian noise (AWGN), and substantially outperform the trellis demodulator under severe ACI condition.

Adaptive LMS equalizers are widely used in digital communication systems for their simplicity in implementation. Conventional adaptive filtering theory suggests the upper bound of the performance of such equalizer is determined by the performance of a Wiener filter of the same structure. However, in the presence of a narrowband interferer the performance of the LMS equalizer is better than that of its Wiener counterpart. This phenomenon, termed a non-Wiener effect, has been observed before and substantial work has been done in explaining the underlying reasons. In this work, we focus on the Bit Error Rate (BER) performance of LMS equalizers. At first a model “the Gaussian Mixture (GM) model“ is presented to estimate the BER performance of a Wiener filter operating in an environment dominated by a narrowband interferer. Simulation results show that the model predicts BER accurately for a wide range of SNR, ISR, and equalizer length. Next, a model similar to GM termed the Gaussian Mixture using Steady State Weights (GMSSW) model is proposed to model the BER behavior of the adaptive NLMS equalizer. Simulation results show unsatisfactory performance of the model. A detailed discussion is presented that points out the limitations of the GMSSW model, thereby providing some insight into the non-Wiener behavior of (N)LMS equalizers. An improved model, the Gaussian with Mean Square Error (GMSE), is then proposed. Simulation results show that the GMSE model is able to model the non-Wiener characteristics of the NLMS equalizer when the normalized step size is between 0 and 0.4. A brief discussion is provided on why the model is inaccurate for larger step sizes. / Master of Science

Adaptive Least Mean Square (LMS) equalizers are widely used in digital communication systems primarily for their ease of implementation and lack of dependence on a priori knowledge of input signal statistics. LMS equalizers exhibit non-Wiener characteristics in the presence of a strong narrowband interference and can outperform the optimal Wiener equalizer in terms of both mean square error (MSE) and bit error rate (BER). There has been significant work in the past related to the analysis of the non-Wiener characteristics of the LMS equalizer, which includes the discovery of the shift in the mean of the LMS weights from the corresponding Wiener weights and the modeling of steady state MSE performance. BER performance is ultimately a more practically relevant metric than MSE for characterizing system performance. The present work focuses on modeling the steady state BER performance of the normalized LMS (NLMS) equalizer operating in the presence of a strong narrowband interference. Initial observations showed that a 2 dB improvement in MSE may result in two orders of magnitude improvement in BER. However, some differences in the MSE and BER behavior of the NLMS equalizer were also seen, most notably the significant dependence (one order of magnitude variation) of the BER behavior on the interference frequency, a dependence not seen in MSE. Thus, MSE cannot be used as a predictor for the BER performance; the latter further motivates the pursuit of a separate BER model. The primary contribution of this work is the derivation of the probability density of the output of the NLMS equalizer conditioned on a particular symbol having been transmitted, which can then be leveraged to predict its BER performance. The analysis of the NLMS equalizer, operating in a strong narrowband interference environment, resulted in a conditional probability density function in the form of a Gaussian Sum Mixture (GSM). Simulation results verify the efficacy of the GSM expression for a wide range of system parameters, such as signal-to-noise ratio (SNR), interference-to-signal (ISR) ratio, interference frequency, and step-sizes over the range of mean-square stable operation of NLMS. Additionally, a low complexity approximate version of the GSM model is also derived and can be used to give a conservative lower bound on BER performance. A thorough analysis of the MSE and BER behavior of the Bi-scale NLMS equalizer (BNLMS), a variant of the NLMS equalizer, constitutes another important contribution of this work. Prior results indicated a 2 dB MSE improvement of BNLMS over NLMS in the presence of a strong narrowband interference. A closed form MSE model is derived for the BLMS algorithm. Additionally, BNLMS BER behavior was studied and showed the potential of two orders of magnitude improvement over NLMS. Analysis led to a BER model in the form of a GSM similar to the NLMS case but with different parameters. Simulation results verified that both models for MSE and BER provided accurate prediction of system performance for different combinations of SNR, ISR, interference frequency, and step-size. An enhanced GSM (EGSM) model to predict the BER performance for the NLMS equalizer is also introduced, specifically to address certain cases (low ISR cases) where the original GSM expression (derived for high ISR) was less accurate. Simulation results show that the EGSM model is more accurate in the low ISR region than the GSM expression. For the situations where the derived GSM expression was accurate, the BER estimates provided by the heuristic EGSM model coincided with those computed from the GSM expression. Finally, the two-interferer problem is introduced, where NLMS equalizer performance is studied in the presence of two narrowband interferers. Initial results show the presence of non-Wiener characteristics for the two-interferer case. Additionally, experimental results indicate that the BER performance of the NLMS equalizer operating in the presence of a single narrowband interferer may be improved by purposeful injection of a second narrowband interferer. / PHD / Every practical communication system requires effective interference mitigation schemes that are able to nullify unwanted signals without distorting the desired signal. Adaptive equalizers are among the prevalent systems used to cancel interfering signals. In particular, for narrowband interference (a particular class of interference) mitigation with (normalized) least mean square type (NLMS) equalizers has been found to be extremely effective. In fact, in the narrowband interference-dominated environment, NLMS equalizers have been found to work better than the solution with the same structure that is optimal according to linear filtering theory. This departure from the linear filtering theory is a result of the non-Wiener characteristics of NLMS type equalizers. This work investigates the bit error rate (BER) behavior, a common metric used to characterize the performance of wireless communication systems, of the NLMS equalizer in the presence of a strong narrowband interference. The major contribution of this dissertation is the derivation of an accurate expression that links the BER performance of the NLMS equalizer with the system parameters and signal statistics. Another variant of the NLMS equalizer known as the Bi-scale LMS (BLMS) equalizer was also studied. Similar to the NLMS case, an accurate BER expression for the BLMS equalizer was also derived. Additionally, situations were investigated where the non-Wiener characteristics of the NLMS equalizers can be leveraged. Overall, this dissertation hopes to add to the existing body of work that pertains to the analysis of non-Wiener effects of NLMS equalizers and thus, in general, to the work related to analysis of adaptive equalizers.