**6.2. Numerical results**

In this subsection, we present simulation results with the MIMO channels of *σ*<sup>2</sup> *<sup>h</sup>* = 1. The SNR is defined by the energy per bit to the noise power spectral density ratio *Eb*/*N*0. We used 16 quadrature amplitude modulation (16-QAM) for signaling with Gray mapping. CLLL is carried out for the lattice basis reduction.

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Lattice Reduction-Based User Selection in Multiuser MIMO Systems

Alternatively, the LR-based SIC detector with the MD criterion can exploit a full diversity as the ML detector with the MDist criterion. It it noteworthy that a full diversity gain cannot be achieved by the LR-based MMSE-SIC detection with the MMI criterion, although the performance can be improved by using the ODR criterion, there is still a BER gap compared to the one with the MD criterion. Overall, it is shown that the best user selection criterion for

M = P = 2, K = 5, N = 4, 16−QAM

<sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>12</sup> <sup>14</sup> <sup>10</sup>−6

Eb /N0 (dB)

To see the performance of different multiple users selection criteria, the BER results are shown in Fig. 2 for the case of *M* = *P* = 2. We assume that *K* = 5 and *N* = 4. It is shown that, when BER drops from 10−<sup>5</sup> to 10<sup>−</sup>6, SNR increases by approximately 1.2 dB. Thus, an estimate of the diversity gain from the simulation becoms *G* ≃ 8.3, which is greater than the lower bound, *Glow* = *<sup>N</sup>*⌊*K*/*M*⌋ = 8, derived from the theoretical analysis in Section 6.1. Moreover, it is shown that the user selection approach with the LR-based detectors has the same diversity gain as in the ML detector, whereas the approach with the MMSE detector has a lower diversity gain. In general, we can show that system of LR-based MMSE-SIC detector with UBLRG can provide a reasonably good performance. Note that, compared with the LR-based MMSE-SIC detector with MD criterion and combinatorial selection, the proposed UBLRG system provides a similar performnace; however, as shown in Table 2, by decreasing the number of column swapping, complexity can also be reduced remarkably with more

the LR-based MMSE-SIC detection is the MD criterion.

*6.2.2. Multiple users selection*

10−5

MMSE (ME Criterion) ML (MDist Criterion)

efficient implementations for the proposed UBLRG approach.

LR−based MMSE−SIC (MD Criterion) LR−based MMSE−SIC (UBLRG)

**Figure 2.** BER performance of various multiuser MIMO systems with 16-QAM, *M* = *P* = 2, *N* = 4, and *K* = 5.

10−4

10−3

BER

10−2

10−1
