Performance of the lattice sequence estimator

In many practical communication systems such as digital microwave radio, the main cause of transmission errors is usually due to the presence of intersymbol interference, rather than the noise. For such systems the sequence estimator significantly outperforms the symbol-by-symbol detector, even when a certain form of equalization techniques is used. The key obstacle to the applicability of sequence estimator is its large complexity. Denote the channel memory length by ν and alphabet size by m. Using a Viterbi-like implementation, the estimator with truncation depth δ requires O(m^ν+1) arithmetic operations per symbol, and O(δm^ν) storage elements. In most practical situations, δ is chosen such that δ=O(ν). We propose the lattice sequence estimator (LSE), which only requires O(δ)² arithmetic operations per symbol, and O(δ) storage elements. For simplicity, the multilevel PAM system is considered