Improving Log-Likelihood Ratio Estimation with Bi-Gaussian Approximation under Multiuser Interference Scenarios

Accurate estimation of channel log-likelihood ratio (LLR) is crucial to the decoding of modern channel codes like turbo, low-density parity-check (LDPC), and polar codes. Under an additive white Gaussian noise (AWGN) channel, the calculation of LLR is relatively straightforward since the closed-form expression for the channel likelihood function can be perfectly known to the receiver. However, it would be much more complicated for heterogeneous networks where the global noise (i.e., noise plus interference) may be dominated by non-Gaussian interference with an unknown distribution. Although the LLR can still be calculated by approximating the distribution of global noise as Gaussian, it will cause performance loss due to the non-Gaussian nature of global noise. To address this problem, we propose to use bi-Gaussian (BG) distribution to approximate the unknown distribution of global noise, for which the two parameters of BG distribution can easily be estimated from the second and fourth moments of the overall received signals without any knowledge of interfering channel state information (CSI) or signaling format information. Simulation results indicate that the proposed BG approximation can effectively improve the word error rate (WER) performance. The gain of BG approximation over Gaussian approximation depends heavily on the interference structure. For the scenario of a single BSPK interferer with a 5 dB interference-to-noise ratio (INR), we observed a gain of about 0.6 dB. The improved LLR estimation can also accelerate the convergence of iterative decoding, thus involving a lower overall decoding complexity. In general, the overall decoding complexity can be reduced by 25 to 50%.