**2. System model**

2 Recent Trends in Multiuser MIMO Communications

single-user detection.

on opportunistic communication.

goes to infinity for any given user's SNR.

frequency reuse.

transmit message sharing across all the BSs, a virtual MIMO-BC channel is equivalently formed. Therefore, existing single-cell downlink precoding techniques can be applied (see, e.g., [10] [11] [12] and references therein) with a non-trivial modification to deal with the per-BS power constraints as compared to the conventional sum-power constraint for the single-cell MIMO-BC case. In contrast, if transmit messages are only locally known at each BS, coordinated precoding/beamforming can be implemented among BSs to control the inter-cell interference (ICI) to their best effort [13] [14]. In [15] [16] [17], various parametrical characterizations of the Pareto boundary of the achievable rate region have been obtained for the multiple-input single-output (MISO) IC with coordinated transmit beamforming and

More important, most of the proposed precoding schemes, in single- or multi-cell case, rely on the assumption of perfect channel state information (CSI) for all the intra- and inter-cell links at the transmitter, which may not be realistic in practical cellular systems with a large number of users. Consequently, the study of quantized channel feedback for the MIMO BC has been recently a very active area of research (see, e.g., [18] and references therein).

The single-beam "opportunistic beamforming (OBF)" and multi-beam "random beamforming (RBF)" schemes for the single-cell MISO-BC, introduced in [19] and [20], respectively, therefore attract a lot of attention since they require only *partial* CSI feedback to the BS. The fundamental idea is to exploit the multi-user diversity gain, by employing *opportunistic user scheduling*, to combat the inter-beam interferences. The achievable sum-rate with RBF in a single-cell system has been shown to scale identically to that with the optimal DPC scheme assuming perfect CSI as the number of users goes to infinity, for any given user's signal-to-noise ratio (SNR) [20] [21]. Essentially, the result implies that the intra-cell interference in a single-cell RBF system can be completely eliminated when the number of users are sufficiently large, and an "interference-free" MU broadcast system is attainable. This thus shows the optimality of the single-cell RBF and motives other studies

Although substantial subsequent investigations and/or extensions of the single-cell RBF have been pursued, there are very few works on the performance of the RBF scheme in a more realistic multi-cell setup, where the ICI becomes a dominant factor. It is worth noting that as the universal frequency reuse becomes more favourable in future generation cellular systems, ICI becomes a more serious issue as compared to the traditional case with only a fractional

One objective of this chapter is to present a literature survey on the vast body of works studying the single-cell OBF/RBF. The main purpose, however, is to introduce the recent investigations on multi-cell RBF systems. In this chapter, we first review the achievable rates of multi-cell RBF in finite-SNR regime. Such results, albeit important, do not provide any insight to the impact of the interferences on the system throughput. This motivates us to introduce the high-SNR/DoF analysis proposed in [22] and [23], which is useful in characterizing the performance of RBF under multi-user diversity and interference effects. Furthermore, it provides new insights on the role of *spatial receive diversity* in RBF, which is not well understood so far. It is revealed that receive diversity is significantly beneficial to the rate performance of multi-cell RBF systems [24]. This conclusion, interestingly, sharply contrasts with one based on the traditional asymptotic analysis, i.e., assuming that the number of users This section introduces the multi-cell system model and RBF schemes used throughout this chapter. Particularly, we consider a *C*-cell MIMO-BC system with *Kc* mobile stations (MSs) in the *c*-th cell, *c* = 1, ··· , *C*. For the ease of analysis, we assume that all BSs/MSs have the same number of transmit/receive antennas, denoted as *NT* and *NR*, respectively. We also assume a "homogeneous" channel setup, in which the signal and ICI powers between users of one cell are identical. At each communication time, the *<sup>c</sup>*-th BS transmits *Mc* ≤ *NT* orthonormal beams with *Mc* antennas and selects *Mc* from *Kc* users for transmission. Suppose that the channels are flat-fading and constant over each transmission period of interest. The received signal of user *k* in the *c*-th cell is

$$\boldsymbol{y}\_{k}^{(c)} = \mathbf{H}\_{k}^{(c,c)} \sum\_{m=1}^{M\_{\mathcal{L}}} \boldsymbol{\Phi}\_{m}^{(c)} \boldsymbol{s}\_{m}^{(c)} + \sum\_{\substack{l=1,\ l \neq c}}^{\mathcal{C}} \sqrt{\gamma\_{l,c}} \mathbf{H}\_{k}^{(l,c)} \sum\_{m=1}^{M\_{l}} \boldsymbol{\Phi}\_{m}^{(l)} \boldsymbol{s}\_{m}^{(l)} + \mathbf{z}\_{k}^{(c)},\tag{1}$$

where *<sup>H</sup>*(*l*,*c*) *<sup>k</sup>* <sup>∈</sup> **<sup>C</sup>***NR*×*Ml* denotes the channel matrix between the *<sup>l</sup>*-th BS and the *<sup>k</sup>*-th user of the *c*-th cell, which consists of independent and identically distributed (i.i.d.) ∼ CN (0, 1) elements; *<sup>φ</sup>*(*c*) *<sup>m</sup>* <sup>∈</sup> **<sup>C</sup>***Mc*×<sup>1</sup> and *<sup>s</sup>* (*c*) *<sup>m</sup>* are the *m*-th randomly generated beamforming vector of unit norm and transmitted data symbol from the *c*-th BS, respectively; it is assumed that each BS has the total sum power, *PT*, i.e., **Tr E**[*s***c***s***<sup>H</sup> c** ] ≤ *PT*, where *<sup>s</sup><sup>c</sup>* = [*<sup>s</sup>* (*c*) *<sup>1</sup>* , ··· ,*<sup>s</sup>* (*c*) *Mc* ] *T*; *<sup>γ</sup>l*,*<sup>c</sup>* < 1 stands for the signal attenuation from the *<sup>l</sup>*-th BS to any user of the *<sup>c</sup>*-th cell, *<sup>l</sup>* �= *c*; and *z* (*c*) *<sup>k</sup>* <sup>∈</sup> **<sup>C</sup>***NR*×<sup>1</sup> is the additive white Gaussian noise (AWGN) vector, of which each element is ∼ CN (0, *σ*2), ∀*k*, *c*. In the *c*-th cell, the total SNR, the SNR per beam, and the interference-to-noise ratio (INR) per beam from the *<sup>l</sup>*-th cell, *<sup>l</sup>* �= *<sup>c</sup>*, are denoted as *<sup>ρ</sup>* = *PT*/*σ*2, *η<sup>c</sup>* = *PT*/(*Mcσ*2), and *µl*,*<sup>c</sup>* = *γl*,*cPT*/(*Mlσ*2), respectively.
