Cobro del Canon en el Perú

where m = 2π/λ, with λ being the wavelength of the carrier signal. The inter-element spacing d in the ULA is set to half-wavelength λ/2.

3.3

Problem Statement

Each user in the network is assumed to require a minimum guaranteed QoS. In Chapter 4, the QoS requirement is specified in terms of SINR, with the k-th user demanding a minimum SINR of ωk. An SINR ωk offers, as dictated by the Shannon channel capacity

formula, a data rate of Rk= log2(1 + ωk) bps/Hz with an arbitrarily small error rate.

Alternatively, for a fixed data rate (when the modulation scheme is fixed), the SINR determines the average SER achieved at the user.

In Chapter 5, Chapter 6, and Chapter 7, the CI-based hybrid precoding approach is considered. In such systems, the interference plays a constructive role, and it does not necessarily cause symbol errors; therefore, the SINR is not an appropriate metric to measure the quality of received signals in this system. In order to quantify the QoS in a noisy environment, in this thesis we introduce a new metric threshold-margin-to-noise

power ratio (TNR), which is defined as TNRk , Γ_σk2

k. It is the ratio of the threshold-

margin between the CI-region and the corresponding decision boundaries to the noise power, and it directly controls the achieved SER.

Our goal is to obtain the power-efficient hybrid precoders, i.e., analog precoders ar, ∀r ∈ R, and digital precoders dk, ∀k ∈ K. The average transmit power at the BS

is given by Pavrg = PK_k=1||Adk||2 and the instantaneous transmit power in a given

symbol-interval can be expressed as Pinst=

     A PK k=1dksk       2

3.3 Problem Statement 33

efficient hybrid precoding techniques that minimize Pavrg(Chapter 4) or Pinst (Chapter

5, Chapter 6, and Chapter 7), while fulfilling the QoS requirement (SINR or TNR) at each user.

In Chapter 4 and Chapter 5, we design precoding schemes to compute the power- efficient hybrid precoders based on interference suppression and interference exploita- tion techniques, respectively. In Chapter 6, we assume that the PSs used for the realization of analog precoding are imperfect due to phase and/or magnitude errors, and develop algorithms to compute power-efficient and robust hybrid precoders. Fur- thermore, Chapter 7 aims to minimize the transmit power while fulfilling the QoS constraints in a heterogeneous network with a distributed hybrid precoding technique.

35

Chapter 4

Interference Suppression-Based Hybrid

Precoding

4.1

Introduction

To enhance spectral efficiency in a cellular network, the BSs are generally required to communicate with multiple users over the same time-frequency resource block. As a consequence, along with the useful information-bearing signals the users also receive the signals intended for the other users, which is referred to as multiuser interference, resulting in reduced SINRs at the users. One approach to lower the multiuser interfer- ence in a MIMO system is to employ the precoding before transmission of signals. There are numerous precoding schemes, having different objectives, developed for the con- ventional MIMO systems in the literature, as discussed in Chapter 2. Due to inherent differences in the fully-digital precoding architecture and hybrid precoding architec- ture, these schemes are not readily extendable to the hybrid precoding. Accordingly, there is an imminent need for novel precoding schemes that are specifically designed for the hybrid precoding architecture in massive MIMO systems, which exploit special structures and also incorporate limitations present in this low-cost architecture.

In [SB04], the authors consider the problem of designing precoders that fulfill SINR requirements of users with a minimum total transmit power in a multiuser MIMO down- link system with the fully-digital precoding architecture. A nonconvex optimization program is formulated for this downlink precoding problem. To solve this program, firstly, the authors construct a dual virtual uplink problem. Moreover, they demon- strate that the global optimum of the downlink precoding problem can be equivalently obtained from solving the simpler dual uplink problem—which is popularly known as uplink-downlink duality. Making use of special structures in the uplink problem a rapidly converging iterative method is proposed. We extend, in this chapter, the uplink-downlink duality framework to a codebook-based hybrid precoding problem. In

36 Chapter 4: Interference Suppression-Based Hybrid Precoding

particular, we devise power-efficient low-complexity hybrid precoding schemes using the uplink-downlink duality theory.

In a network with a large number of users, serving all the users over the same time-frequency resource block may drastically reduce the network throughput due to severe multiuser interference. One way to overcome this challenge is to employ time and frequency multiplexing, where users are appropriately grouped, and only one group of users is served in a given resource block. This approach also helps in further en- hancing the network capacity by exploiting the multiuser diversity, where for each time-frequency resource block users are meticulously selected considering their channel conditions. In the hybrid precoding, the analog precoders are shared by all the users served in a given resource block. Accordingly, it is judicious to perform the hybrid precoding jointly with the user selection. Motivated by this, in the second part of this chapter, we propose a joint user selection and hybrid precoding scheme.

For clarity, we summarize the contribution of this chapter below:

• The hybrid precoding problem in a multiuser downlink MIMO system is for- mulated as an optimization problem. Solving this original downlink problem is computationally prohibitive. To address this challenge, the uplink-downlink duality framework has been extended to the hybrid precoding system; the prop- erties of and the relationship between the solutions of the uplink problem and that of the downlink problem are established.

• An optimal algorithm and a low-complexity suboptimal algorithm are proposed for solving the newly formulated virtual uplink-based hybrid precoding problem. The computational complexities of the proposed methods are assessed analyti- cally.

• We design a joint hybrid precoding and user selection algorithm to enhance the network energy efficiency by exploiting the multiuser diversity. A novel technique is proposed in the algorithm to select users and analog precoders judiciously, which yields a superior performance when compared to state-of-the-art methods.