Compared to full feedback of the CSI in the SVD design in , the partial information, which between the RS and the MSs and is fed back to the BS, is a Gaussian integer matrix bounded by a modulo operation. Besides, this LR-aided precoder significantly improves the bit error rate (BER) performance of multiuser MIMO relay networks with only a small increase in complexity.
To achieve the performance better than that of ZF criterion, THP is implemented with aid of LR at the BS, while the RS just needs a simple modulo operation. By applying QR decomposition to W, a lower triangular matrix B with unit diagonal is obtained as:
To reduce the amplitude of the channel symbol x, to the boundary of the modulation alphabet, a modulo operation
M(.) should be employed which is defined element-wise as
The permutation of a set can be obtained by integer addition modulo operation which is a mathematical tool that helps in getting numbers which are less than the pivoting number (the divisor).
where Z(N) denotes modulo operation with a positive integer N.
Contract awarded for Modulo operation
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In the past, a number of generators were implemented with the modulo operation based on 2"' where m is the number of register bits available for the magnitude of an integer.
Though algorithmically different, the procedure just derived is mathematically equivalent to a previous scheme  to avoid the division implicit in the modulo operation.
In accordance with structure of polynomial p(x) are performed (on corresponding cells) the read and modulo operations
. Continue this operations until the final state will
This is unfortunate because now we need three modulo operations
in total, and these are slow in comparison to the other machine operations.