Nonlinear Predictor and Interpolator

Nonlinear Predictor and Interpolator

For narrowband interference added to a spread-spectrum signal in an AWGN environment, the prediction of the interferer takes place in the presence of both Gaussian and non-Gaussian noise. The non-Gaussian noise is the spread-spectrum signal itself. In such a non-Gaussian environment, linear methods are no longer optimal, and nonlinear techniques offer improved suppression capability over linear methods, as demonstrated in Section 7.3. Essentially, the nonlinear filters provide decision feedback that suppresses the spread-spectrum signal from the observations. When the decision feedback is accurate, the filter adaptation is done in essentially Gaussian noise (i.e., observations from which the spread-spectrum signal has been removed).

Based on the discussion above, we can obtain similar SINR upper bounds for the nonlinear predictive/interpolative methods. The idea is that we assume that the decision feedback part of the nonlinear filter accurately estimates the SS signal, and the SS signal is always subtracted from the observations, so that the NBI signal is estimated only in the presence of Gaussian noise. More specifically, consider the signal model (7.5). Assume that for the purpose of estimating the NBI signal, a genie provides an SS-signal-free observation

A linear predictor or interpolator is then employed to obtain and estimate î_n of the NBI signal, which is then subtracted from the received signal to form the decision statistic for the SS data bit b,

Equation 7.124

where _n is the prediction error of the linear predictor (interpolator) (i.e., _n = i_n - î_n + u_n). Modeling {c_n,1} as a sequence of i.i.d. random variables such that with probability ½, the output SINR of this ideal system is then

Equation 7.125

Substituting the lower bounds for the mean-square prediction errors given by the linear predictor and linear interpolator [310, 311], we obtain the following very optimistic SINR upper bounds for the nonlinear estimator-subtracter methods:

Equation 7.126

Equation 7.127

Now assume that the NBI is a pth-order AR signal, given by (7.94). Its power spectral density function is given by

Equation 7.128

Substituting (7.128) into (7.127) and letting s 0, we get the SINR upper bound for the nonlinear interpolator when the NBI is an AR signal in the absence of background noise:

Equation 7.129

Notice that this is the same output SINR value for the linear MMSE detector when the NBI is an AR signal in the absence of noise, given by (7.106).