Weighted Sum-Rate Maximization for Intelligent Reflecting Surface Enhanced Wireless Networks

Abstract

Intelligent reflecting surface (IRS) is a promising solution to build a programmable wireless environment for future communication systems. In practice, an IRS consists of massive low-cost elements, which can steer the incident signal in fully customizable ways by passive beamforming. In this paper, we consider an IRS-aided multiuser multiple-input single-output (MISO) downlink communication system. In particular, the weighted sum-rate of all users is maximized by joint optimizing the active beamforming at the base-station (BS) and the passive beamforming at the IRS. In addition, we consider a practical IRS assumption, in which the passive elements can only shift the incident signal to discrete phase levels. This non-convex problem is firstly decoupled via Lagrangian dual transform, and then the active and passive beamforming can be optimized alternatingly. The active beamforming at BS is optimized based on the fractional programming method. Then, three efficient algorithms with closed-form expressions are proposed for the passive beamforming at IRS. Simulation results have verified the effectiveness of the proposed algorithms as compared to different benchmark schemes.Index Terms-Intelligent reflecting surface (IRS), large intelligent surface (LIS), passive radio, beamforming, multiple-inputmultiple-output (MIMO), fractional programming.

Sum Rate Optimization for Two Way Communications With Intelligent Reflecting Surface

“…For the other two cases F 2 and F 3 , the constraints on θ m , m = 1, ..., M , become non-convex and the sub-problem (17) is not convex too. Here we adopt the idea in [4]. We still apply the proposed iterative algorithm, except for the sub-problem (17).…”

“…where s i is the data symbol vector with unit covariance matrix I N and F i is the N -by-N source precoder subject to the power constraint tr F i F H i ≤ P . The IRS re-scatters the superposition of all incident signals [4], [5]. Assuming only first-order reflection from IRS [5], the reflected signal is:…”

“…where H i , i = 1, 2, denotes the M -by-N channel matrix from the source S i to the IRS, and Θ = √ ηdiag (θ 1 , θ 2 , ..., θ M ) is the phase shift matrix of IRS, where η ≤ 1 is the reflection efficiency, θ m , m = 1, ..., M , is the reflection coefficient of the mth IRS element. Considering the practical implementation of IRS, three cases for the feasibility set of θ m are assumed [4]: 1) Each IRS element can continuously control both the amplitude and phase of the reflected signal, i.e., θ m ∈ F 1 θ m |θ m | 2 ≤ 1 .…”

“…Note that the achievable rate (5) of the source S i is derived from I (s i ; yī) where the input probability distribution p (s i ) is CN (0, I N ) and the channel transition probability p(yī|s i ) is from (4). Then according to Lemma 1,(5) can also be reexpressed as:…”

“…Thus far, IRS has been considered to be incorporated into various wireless communications and technologies, such as the MIMO system, e.g., [4]- [7], simultaneous wireless information and power transfer (SWIPT) [8], index modulation [9], and non-orthogonal multiple access (NOMA) [10], etc. Multi-IRS scenario has been investigated in [11].…”