Full Diversity Unitary Precoded Integer-Forcing

We consider a point-to-point flat-fading MIMO channel with channel state information known both at transmitter and receiver. At the transmitter side, a lattice coding scheme is employed at each antenna to map information symbols to independent lattice codewords drawn from the same codebook. Each lattice codeword is then multiplied by a unitary precoding matrix ${\bf P}$ and sent through the channel. At the receiver side, an integer-forcing (IF) linear receiver is employed. We denote this scheme as unitary precoded integer-forcing (UPIF). We show that UPIF can achieve full-diversity under a constraint based on the shortest vector of a lattice generated by the precoding matrix ${\bf P}$. This constraint and a simpler version of that provide design criteria for two types of full-diversity UPIF. Type I uses a unitary precoder that adapts at each channel realization. Type II uses a unitary precoder, which remains fixed for all channel realizations. We then verify our results by computer simulations in $2\times2$, and $4\times 4$ MIMO using different QAM constellations. We finally show that the proposed Type II UPIF outperform the MIMO precoding X-codes at high data rates.Comment: 12 pages, 8 figures, to appear in IEEE-TW

Unitary precoding for integer-forcing MIMO linear receivers

Abstract—A flat fading point-to-point multiple-antenna chan-nel is considered where the channel state information is known at both transmitter and receiver. At the transmitter side, we use a lattice encoder to map information symbols to lattice codewords. The lattice coded layers are then precoded using unitary matrices satisfying non-vanishing minimum product distance. At the receiver side, an integer-forcing linear receiver is employed. This scheme is called ‘unitary precoded integer-forcing’. We show that by applying the proposed precoding technique full-diversity can be achieved. We then verify this result by conducting computer simulations in a 2 × 2 and 4 × 4 multiple-input multiple-output (MIMO) channel using full-diversity algebraic rotation precoder matrices. Index Terms—Integer-Forcing, unitary precoding, lattice codes, full-diversity. I