An efficient optimal algorithm for integer-forcing linear MIMO receivers design

The integer-forcing (IF) linear multiple-input and multiple-output (MIMO) receiver is a recently proposed suboptimal receiver which nearly reaches the performance of the optimal maximum likelihood receiver for the entire signal-to-noise ratio (SNR) range and achieves the optimal diversity multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas in the high SNR regime. The optimal integer coefficient matrix A* ϵ Z
^Nt×N
_t
for IF maximizes the total achievable rate, where Nt is the column dimension of the channel matrix. To obtain A
^*
, a successive minima problem (SMP) on an N
_t
-dimensional lattice that is suspected to be NP-hard needs to be solved. In this paper, an efficient exact algorithm for the SMP is proposed. For efficiency, our algorithm first uses the LLL reduction to reduce the SMP. Then, different from existing SMP algorithms which form the transformed A
^*
column by column in N
_t
iterations, it first initializes with a suboptimal matrix which is the N
_t
× N
_t
identity matrix with certain column permutations that guarantee this suboptimal matrix is a good initial solution of the reduced SMP. The suboptimal matrix is then updated, by utilizing the integer vectors obtained by employing an improved Schnorr-Euchner search algorithm to search the candidate integer vectors within a certain hyper-ellipsoid, via a novel and efficient algorithm until the transformed A
^*
is obtained in only one iteration. Finally, the algorithm returns the matrix obtained by left multiplying the solution of the reduced SMP with the unimodular matrix that is generated by the LLL reduction. Simulation results show the optimality of our novel algorithm and indicates that the new one is much more efficient than existing optimal algorithms.