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Bit interleaved coded modulation (BICM) because of its improved diversity over fast fading channels is an attractive transmission scheme for future wireless systems. For coded BICM systems, receivers need to employ max log MAP demodulators (demappers) that calculate soft-decision metrics i.e. log-likelihood ratios (LLRs) for the decoder. The complexity of the calculation of these LLRs is exponential in the number of bits per symbol and moreover for systems exploiting spatial dimension (MIMO), the complexity further increases exponentially in the number of transmit antennas. In this paper we propose matched filter (MF) based low complexity max log MAP bit metrics for BICM single input single output (SISO) and low dimensional BICM MIMO systems using Gray encoded M-ary quadrature amplitude modulation (QAM) alphabets. For SISO systems, the maximum likelihood (ML) detector needs computation and comparison of minimum distances between the received symbol and M constellation points on the complex plane for the calculation of each LLR. In this paper we show that these LLRs can be computed precisely from the MF output and therefore do not necessitate any minimum distance calculations. For low dimensional BICM MIMO systems, we further propose a MF based bit metric which successfully trims down one complex dimension of the system thereby reducing complexity. Both these metrics substantially reduce the number of calculations needed for each LLR without compromising the performance and MF being an integral part of all receiver structures facilitates their hardware implementation. Simulation results over Rayleigh fading channels verify similar performance of the simplified metrics as those of the original metrics but with a significant reduction in the complexity.