Intelligent Reflecting Surface-Assisted Multiple Access with User Pairing: NOMA or OMA?

Intelligent reflecting surface (IRS) has recently attracted growing attention and is envisioned as an innovative technology for the beyond fifth-generation (B5G) communication system, due to its potential of achieving significant improvement in communication coverage, throughput, and energy efficiency [1, 2, 3]. Specifically, IRS is a planar meta-surface composed of a large number of reconfigurable passive elements, which are attached with a smart controller to enable dynamic adjustment on the signal reflections for different purposes, such as signal power enhancement and interference suppression. In particular, compared to conventional techniques such as active relaying/beamforming, IRS not only reflects signals in a full-duplex and noise-free manner without incurring self-interference, but also greatly saves energy consumption and hardware/deployment cost by using lightweight passive components only [1, 3].

On the other hand, non-orthogonal multiple access (NOMA) has also received significant attention and shown superiority over orthogonal multiple access (OMA) in conventional wireless systems without IRS, for improving the spectral efficiency, balancing user fairness, and enlarging network connections. In the downlink NOMA, the user of stronger channel with the base station (BS) or access point (AP) employs the successive interference cancellation (SIC) technique to cancel the co-channel interference from the users of weaker channels, prior to decoding its own message. As a result, the decoding order depends on user channel power gains, which are determined by the propagation environments and user locations. In contrast, since IRS is capable of reconfiguring user channels by controlling the reflected signal amplitudes and/or phase shifts, the user decoding order of NOMA can be permuted by adjusting the IRS reflection to achieve more flexible performance trade-offs among the users. Nevertheless, for IRS to be integrated into the future wireless network, it still remains unknown whether NOMA is always superior to OMA as in conventional systems without IRS. Although some relevant works on the application of IRS to NOMA have recently appeared [4, 5, 6, 7], the theoretical performance comparison between NOMA and OMA for IRS-assisted wireless communications is not well understood yet, to the best of our knowledge.

To address the above issue, in this letter we investigate the theoretical performance comparison between NOMA and OMA in an IRS-assisted downlink communication system, where two types of OMA schemes, i.e., frequency division multiple access (FDMA) and time division multiple access (TDMA), are considered, as shown in Fig. 1. The problems for minimizing the transmit power at the AP are formulated for both OMA and NOMA, subject to the discrete unit-modulus reflection constraint at the IRS and the users’ target rates. By analyzing the relationship of minimum transmit powers required by different multiple access schemes, we unveil that the minimum transmit power of FDMA is always no lower than that of the other two counterparts (TDMA and NOMA), while the minimum power comparison between NOMA and TDMA depends on the target rates and locations of the users. Specifically, TDMA requires lower transmit power than NOMA when two near-IRS users are paired and have symmetric rates, whereas the relationship is reversed otherwise. Moreover, to avoid the exponentially high complexity of the brute-force search for the optimal discrete IRS phase shifts, we propose an efficient low-complexity algorithm based on the linear approximation initialization to effectively balance the user channel power gains for minimizing the transmit power, followed by the alternating optimization to achieve near-optimal performance.

As depicted in Fig. 1, we consider an IRS-assisted downlink communication system, where an IRS is deployed to assist in the transmission from a single-antenna AP to multiple single-antenna users. Similar to [8, 9], an IRS composed of $N$ reflecting elements is divided into $M$ sub-surfaces, each of which consists of ${\bar{N}}=N/M$ adjacent elements to share a common reflection coefficient for reducing the implementation complexity. Moreover, the passive IRS is connected to a smart controller that enables dynamic adjustment on the reflections of IRS elements and also plays the role of exchanging information between the IRS and AP via a separate wireless link [1, 3]. For ease of exposition, we focus on the case with any two users sharing two given adjacent time-frequency resource blocks (RBs) in practice, where the channels are assumed to be frequency-flat fading and constant over the two adjacent time-frequency RBs (see Fig. 1). It is worth pointing out that by adopting the concept of user pairing, the two-user case can be extended to the general multi-user case. Without loss of generality, it is assumed that user 1 is located in the vicinity of the IRS while user 2 can be arbitrarily located within the coverage of the AP (i.e., in or out of the IRS’s coverage). As shown in Fig. 1, we consider two types of OMA schemes, i.e., FDMA and TDMA, which serve two users over two adjacent RBs separated in the frequency and time domains, respectively; while the NOMA scheme serves two users simultaneously over the two adjacent RBs either in the frequency- or time-domain, for fair comparison with OMA.

To characterize the optimal performance of different multiple access schemes in the IRS-assisted system, we assume perfect channel state information (CSI) available at the AP. Note that the channel estimation methods proposed in [1, 8] can be applied to acquire the CSI of the two users independently. The baseband equivalent channels from the AP to IRS, from the IRS to user $k$, and from the AP to user $k$ are denoted by ${\bm{h}}_{r}\in{\mathbb{C}^{M\times 1}}$, ${\bm{g}}^{H}_{k}\in{\mathbb{C}^{1\times M}}$, and $h_{d,k}\in{\mathbb{C}}$, respectively, with $k\in\{1,2\}$. Let ${\bm{\theta}}\triangleq[{\theta_{1}},{\theta_{2}},\ldots,{\theta_{M}}]^{T}=[\beta_{1}e^{j\phi_{1}},\beta_{2}e^{j\phi_{2}},\ldots,\beta_{M}e^{j\phi_{M}}]^{T}$ denote the equivalent reflection coefficients of the IRS, where $\phi_{m}\in[0,2\pi)$ and $\beta_{m}\in[0,1]$ are the phase shift and reflection amplitude of the $m$-th sub-surface, respectively. To maximize the signal power reflected by the IRS and reduce the hardware cost, we set $\beta_{m}=1,\forall m=1,\ldots,M$ and consider the practical discrete unit-modulus constraint ${\cal F}=\left\{e^{j\phi}\big{|}\phi\in\{0,\Delta\phi,\ldots,(L-1)\Delta\phi\}\right\}$ for each phase shift coefficient $\theta_{m}$, where $\Delta\phi=2\pi/L$ with $L$ denoting the number of discrete phase-shift levels [10].

In this section, we present simulation results to numerically validate our analytical results (Propositions 1 and 2) and compare the performance of OMA (TDMA and FDMA) with NOMA in an IRS-assisted two-user system. The total number of reflecting elements of the IRS is set to $N=100$, which is divided into $M=5$ sub-surfaces.¹¹1The number of sub-surfaces is kept to be small for implementing the brute-force search to obtain the optimal solution and provide the performance upper bound for the proposed algorithm. The path loss exponents of the AP$\rightarrow$users, IRS$\rightarrow$users, and AP$\rightarrow$IRS links are set as $3.2$, $2.6$, and $2.5$, respectively, and the path loss at the reference distance of 1 meter (m) is set as $30$ dB for each individual link [3, 8, 10]. Moreover, the small-scale fading is characterized by Rayleigh fading for each individual link. We consider two deployment cases shown in Fig. 2, where $d_{I}=4$ m and $d_{A}=50$ m. The results are averaged over $100$ independent fading channel realizations, with $L=8$ and ${\sigma^{2}}=-80$ dBm.

We first consider Case 1 in Fig. 2, where the two users are both located in the vicinity of the IRS with equal distances from the IRS as well as the AP. In Fig. 3(a), we compare the AP transmit powers required by different multiple access schemes versus the common target rate $\gamma_{1}=\gamma_{2}=\gamma_{0}$ for the two users. Apparently, compared to the schemes without IRS, the required transmit power at the AP is significantly reduced with the aid of IRS. Moreover, one can observe that without IRS, the required transmit power by NOMA is always lower than that of OMA (same for TDMA and FDMA). In contrast, when the IRS is deployed to assist two users in its vicinity, the above conclusion is not valid in general. For example, we observe that the required transmit power by TDMA is lower than that of NOMA for the common target rate $\gamma_{0}$ less than 3 bps/Hz. This is due to the use of different IRS phase-shift designs for the two users by exploiting the IRS’s time selectivity via TDMA. Moreover, FDMA always requires higher transmit power than the other two counterparts, which is in accordance with Propositions 1 and 2. On the other hand, by increasing the common target rate $\gamma_{0}$, the power growth rate with TDMA is slightly higher than that with NOMA, which can be well understood since the required power by TDMA in (30) is the sum of two exponential functions with a higher exponent of $2\gamma_{0}$, as compared to that in (12) or (14) with NOMA.

To draw more insight for Case 1, we depict the AP transmit powers required by different transmission schemes versus user 1’s target rate $\gamma_{1}$ in Fig. 3(b), with the two users’ sum rate fixed as $\gamma_{1}+\gamma_{2}=4$ bps/Hz. First, we can observe that TDMA requires lower transmit power than NOMA when the target rates of the two users are close (i.e., symmetric). Second, the transmit powers of both TDMA and FDMA are observed to dramatically increase when the two users’ rates become more asymmetric, which is attributed to the exponentially increasing of the dominant user target rate, i.e., $\text{max}\{\gamma_{1},\gamma_{2}\}$ in (24) and (30). In contrast, it is observed that the required transmit power by NOMA is almost insensitive to the disparity of user target rates, thus providing a more robust performance. Third, to show the performance of the proposed suboptimal solution in Section III-C (i.e., the LA method with $B=8$ followed by the AO method with $I=2$), we consider two benchmark schemes: 1) the optimal solution by the brute-force search and 2) the random phase shift (RPS) initialization followed by the AO method with $10$ iterations (which has the same complexity as the proposed one for fair comparison). One can observe that our proposed solution achieves near-optimal performance, whereas a non-negligible performance loss is observed for the RPS-based initialization as compared to the optimal solution. The above result shows the effectiveness of the low-complexity LA method.

Next, unlike Case 1 with two near-IRS users (namely, symmetric user deployment), we consider another setup of Case 2 with one near-IRS user and one far-IRS user (namely, asymmetric user deployment). As one user moves far away from the IRS and thus needs more power directly from the AP, it is observed in Figs. 4(a) and 4(b) that the transmit power required at the AP increases drastically compared to Figs. 3(a) and 3(b). This is expected since it is more energy efficient when both users are located in the vicinity of the IRS to reap its passive beamforming gain for saving the AP transmit power. Moreover, one can observe from Figs. 4(a) and 4(b) that the required transmit power by NOMA is always lower than that by OMA, regardless of whether TDMA or FDMA is used. This can be explained by the fact that NOMA has higher spectrum efficiency than OMA under asymmetric user channels, even with IRS deployed to assist one of the two users. Furthermore, since the IRS reflection has negligible effect on the far-IRS user, TDMA and FDMA show nearly the same performance in the IRS-assisted system.

In this letter, we have optimized the IRS reflection with discrete phase shifts for the IRS-assisted NOMA and OMA systems to minimize the AP transmit power with given user rates. The minimum transmit powers required by different multiple access schemes have been compared analytically and a low-complexity algorithm has been proposed to achieve near-optimal performance. In particular, our work has revealed that NOMA may perform worse than TDMA for near-IRS users with symmetric rates. This thus provides an important guideline for user paring in IRS-aided systems with a large number of users and RBs (e.g., IRS-assisted orthogonal FDMA (OFDMA)): it is preferable to pair users with asymmetric rates and/or asymmetric deployment (i.e., with distinct distances from the IRS, regardless of the distances from the AP) to exploit the NOMA gain over OMA.