This paper presents space division multiplexing (SDM) as a technology to satisfy the user demand for ever higher bit rates in wireless local area network technology. SDM uses multiple transmit and receive antennas to increase the bit rate proportionally, without reducing the range, delay spread tolerance and spectrum occupancy. The optimal SDM receiver is the maximum likelihood decoder, which has the problem that its computational complexity is exponential in the number of antennas. This paper discusses complexity reduction, looks at existing, approximate algorithms and proposes new, exact algorithms. The symbol error rate performance and the computational complexity are compared and discussed.