Symbol-by-symbol adaptive null-space exploiting (SANE) channel truncation for fading OFDM channels

In multicarrier systems, cyclic prefix (CP) is introduced between two symbols to mitigate inter block interference (IBI). The CP length should be equal or more than channel impulse response (CIR) to ensure IBI free system. However, in the interest of spectral efficiency, if the CP is chosen to be less than the (worst case) CIR length, then a time domain channel shortening prefilter (CSP) can be used to truncate or shape the CIR. In [1], we proposed a null-space exploiting CSP (NE-CSP) which is has a lower complexity when compared to the linear minimum mean square error (LMMSE) [2]. In this paper, we propose a symbol-by-symbol adaptive null-space exploiting CSP (SANE-CSP) scheme based on the NE-CSP structure, which is computationally inexpensive. The order of complexity of SANE-CSP is O(n_c²), whereas the computational complexity order for NE-CSP [1] is O(n_c³) and that of the decoding-delay optimised LMMSE [2] is close to for O(n_c⁴). The SANE-CSP for n_c = 100, has a block error rate performance 3 dB poorer than the decoding-delay optimised LMMSE, but with only 0.01% computational complexity.