*6.2.1. Single user selection*

In order to illustrate the impact of the diversity gain to multiuser MIMO systems, we first present the bit error rate (BER) performance of various multiuser MIMO systems in Fig. 1, where only a single user is selected at one time (i.e., *M* = 1). Five multiuser MIMO systems are considered with *P* = *N* = 4 and *K* = 10, namely:


**Figure 1.** BER performance of various multiuser MIMO systems with 16-QAM, *P* = *N* = 4, *M* = 1, and *K* = 10.

From Fig. 1, we can observe that the optimal performance is guaranteed by the ML detection under MDist criterion. On the other hand, the conventional MMSE detector with the ME criterion provides poor performance as they cannot fully exploit spatial diversity. 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 the LR-based MMSE-SIC detection is the MD criterion.

#### *6.2.2. Multiple users selection*

16 Recent Trends in Multiuser MIMO Communications

carried out for the lattice basis reduction.

LR-based MMSE-SIC (MMI).

10−5

10−4

10−3

BER

10−2

10−1

MMSE-SIC (ODR)

are considered with *P* = *N* = 4 and *K* = 10, namely:

1. MMSE detection under ME criterion: MMSE (ME). 2. ML detection under MDist criterion: ML (MDist).

In this subsection, we present simulation results with the MIMO channels of *σ*<sup>2</sup>

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

In order to illustrate the impact of the diversity gain to multiuser MIMO systems, we first present the bit error rate (BER) performance of various multiuser MIMO systems in Fig. 1, where only a single user is selected at one time (i.e., *M* = 1). Five multiuser MIMO systems

3. LR-based MMSE-SIC detection under maximize mutual information (MMI) criterion:

4. LR-based MMSE-SIC detecton under optimal decision region (ODR) criterion: LR-based

MMSE (ME Criterion)

ML (MDist Criterion)

LR−based MMSE−SIC (MMI Criterion) LR−based MMSE−SIC (ODR Criterion) LR−based MMSE−SIC (MD Criterion)

<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>12</sup> <sup>10</sup>−6

Eb /N0 (dB)

From Fig. 1, we can observe that the optimal performance is guaranteed by the ML detection under MDist criterion. On the other hand, the conventional MMSE detector with the ME criterion provides poor performance as they cannot fully exploit spatial diversity.

**Figure 1.** BER performance of various multiuser MIMO systems with 16-QAM, *P* = *N* = 4, *M* = 1, and *K* = 10.

5. LR-based MMSE-SIC detection under MD criterion: LR-based MMSE-SIC (MD)

<sup>100</sup> P = N = 4, K = 10, M=1, 16−QAM.

*<sup>h</sup>* = 1. The

**6.2. Numerical results**

*6.2.1. Single user selection*

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

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 efficient implementations for the proposed UBLRG approach.
