**3.5. Other studies**

10 Recent Trends in Multiuser MIMO Communications

i.e., *RRBF*

*<sup>M</sup>*

large-number-of-users analysis.

them [41]

*3.2.2. Large system*

user's SNR. Essentially, the result implies that the intra-cell interference in a single-cell RBF system can be completely eliminated when the number of users is sufficiently large, and an "interference-free" MU broadcast system is attainable. This important result therefore establishes the optimality of single-cell RBF and motivates further studies on opportunistic communication. Various MIMO-BC transmission schemes with different assumptions on the fading model, feedback scheme, user scheduling, etc., can be shown achieving *NT* log2 log *K* as *K* → ∞, suggesting that it is a very universal rate scaling law (see, e.g., [30] [31] [28] [32] [33] [34]). Finally, it is worth noting that the RBF sum rate grows only *logarithmically* with *K*,

discussions on the large-number-of-users analysis will be given in Section 4.1.2 and 4.2.

consider opportunistic scheduling, which is one of the main features of RBF.

**3.4. Non-orthogonal RBF and Grassmanian line packing problem**

**3.3. Reduced and quantized feedback in OBF/RBF**

The large-system analysis is a well-known and widely-accepted method to investigate the performance of communication systems. A recent application to single-cell RBF is introduced in [35], in which a general MIMO-BC setup with MMSE receiver and different fading models is considered. Assuming the numbers of transmit/receive antennas and data beams to approach infinity at the same time with fixed ratios for any given finite SNR, Couillet *et. al.* obtain "almost closed-form" numerical solutions which provide deterministic approximations for various performance criteria. Note that although these results are derived under the large-system assumption, Monte-Carlo simulations demonstrate that they can be applied to study small-dimensional systems with modest errors. However, [35] does not

In practical systems, only a limited number of bits representing the quantized channel gain/SINR can be sent from each user to the corresponding BS. Note that the feedback schemes in Section 2.1 and [20] require the transmission of 2*MK* and 2*K* scalar values from *K* users, respectively, i.e., a linear increase with respect to the number of users. It is thus of great interest to develop schemes which can reduce the numbers of users and/or bits to be fed back. The idea of using only one-bit feedback is introduced in several works, e.g., [36] [37] [38]. In this scheme, the user sends "1" when the SINR value is above a pre-determined threshold, and "0" vice-versa. Since the performance of OBF/RBF only depends on the favourable channels, one bit of feedback per user can capture almost all gain available due to the multi-user diversity. Optimal quantization strategy for OBF systems with more than one bit feedback is proposed in [36]. It is also worth noting the group random access-based feedback scheme in [39] and the multi-user diversity/throughput tradeoff analysis in [40]. The main tool to study the performance of OBF/RBF under reduced feedback schemes is the

Denote the space of unit-norm transmit beamforming vectors in **<sup>C</sup>***NT*×<sup>1</sup> as **<sup>O</sup>**(*NT*, 1). A distance function of *<sup>v</sup>*1, *<sup>v</sup>*<sup>2</sup> ∈ **<sup>O</sup>**(*NT*, 1) can be defined to be the sine of the angle between

*<sup>M</sup>*−<sup>1</sup> log2 *<sup>K</sup>* <sup>→</sup> <sup>1</sup> as *<sup>K</sup>* <sup>→</sup> <sup>∞</sup>, when the background noise is ignored [30] [33]. More

Beam selection and beam power control algorithms for single-cell RBF are proposed in [46] [47] [33] [48]. The objective is to improve the rate performance especially when the number of users is not so large. The idea of employing a codebook of predetermined orthonormal beamforming matrices is introduced in [30] [31] [27]. While [30] [31] investigate RBF when quantized, normalized channel vectors are fed back to the BS, [49] studies the codebook design problem and the rate performance assuming that opportunistic selection is also performed on the codebook. These problems are related to Section 3.3 and the GLPP in Section 3.4. Fairness scheduling problem is studied in [19], in which the "*proportional fair scheduling* (PFS)" scheme is proposed. It is not surprising that most of the later developments approach PFS from a network layer's perspective. Notably, the convergence of PFS algorithm for many-user cases under general network conditions is proved in [50], and a global PFS for multi-cell systems is introduced in [51].
