  In this paper, we propose a MIMO receiver algorithm that exploits {\em
channel hardening} that occurs in large MIMO channels. Channel hardening refers
to the phenomenon where the off-diagonal terms of the ${\bf H}^H{\bf H}$ matrix
become increasingly weaker compared to the diagonal terms as the size of the
channel gain matrix ${\bf H}$ increases. Specifically, we propose a message
passing detection (MPD) algorithm which works with the real-valued matched
filtered received vector (whose signal term becomes ${\bf H}^T{\bf H}{\bf x}$,
where ${\bf x}$ is the transmitted vector), and uses a Gaussian approximation
on the off-diagonal terms of the ${\bf H}^T{\bf H}$ matrix. We also propose a
simple estimation scheme which directly obtains an estimate of ${\bf H}^T{\bf
H}$ (instead of an estimate of ${\bf H}$), which is used as an effective
channel estimate in the MPD algorithm. We refer to this receiver as the {\em
channel hardening-exploiting message passing (CHEMP)} receiver. The proposed
CHEMP receiver achieves very good performance in large-scale MIMO systems
(e.g., in systems with 16 to 128 uplink users and 128 base station antennas).
For the considered large MIMO settings, the complexity of the proposed MPD
algorithm is almost the same as or less than that of the minimum mean square
error (MMSE) detection. This is because the MPD algorithm does not need a
matrix inversion. It also achieves a significantly better performance compared
to MMSE and other message passing detection algorithms using MMSE estimate of
${\bf H}$. We also present a convergence analysis of the proposed MPD
algorithm. Further, we design optimized irregular low density parity check
(LDPC) codes specific to the considered large MIMO channel and the CHEMP
receiver through EXIT chart matching. The LDPC codes thus obtained achieve
improved coded bit error rate performance compared to off-the-shelf irregular
LDPC codes.
