On the impact of Phase shifting IRS NOMA

Address
Author Zhiguo Ding, Hi H. Vincent Poor,
Princeton

Phrases

Abstract

This letter aims to study the impact of two phase shifting designs on the IRS assisted NOMA.

1. co-phasing
2. random -phasing
   By using the CLT (central limit theorem), the author derived a closed form outage probability.

Introduction

Despite its superior performance, coherent phase shifting might not be applicable in practice because of the finite resolution of practical IRS phase shifters and the excessive system overhead caused by acquiring channel state information (CSI) at the source.
There have been some works justifing the trival performanace loss of phase shifting design even when low-bit phase shifters adopted.

The author just mentioned a few works about IRS, and nearly no related works about NOMA.

System model

The author considered a scenario where
s and Ui are both equapped with single antenna
IRS-- UPA array
s—> IRS —> U1
s—> IRS ----> U2 s-----> U2

and 3 different systems:

1. IRS-NOMA
   s–> U1
   –>U2 simultaneously
   
   It should be noticed that the author pre-supposed the distance of reflected path and point out that the path loss of reflected link is much higher than the direct link for U2. ( This assumption is appropriate in most cases except for the `hot-spot’ area. )

2. conventional relaying

   The author explained the convetional relay scheme as OMA without IRS, thus two phases are needed.
   <1>. first phase: two time slot: $\mathrm{I}$, s—>U2 (with messege s1), $\mathrm{I}\mathrm{I}$ if U2 can decode it, U2—> U1 (with messege s1); if not, U2 silent.
   <2> second phase: s—> U2 (with messege s2)

3. IRS-OMA
   Two phases:
   <1> s —>IRS—> U1 with s1
   <2> s—>IRS—> U2 with s2

Analysis

1. co-phasing scheme:
   the first part is easy to understand since there hase been a simple version in QingQing Wu’s paper
   Another upperbound is a little hard because I’m not familiar with Laplace transform, the math tricks is to be seen in another blog.

   The main contirubution here is obtain two upperbounds of outage probability of IRS-NOMA, and explained the diversity $N$ can be achieved.

2. randome phasing scheme
   The author adopt an idea that, they sperate the Real part the Imag part and prove that they can be approximated by Gaussian random variable with CLT.

A better trade off is realized by using $Q$ random phase shifts, and U1 just pick the best one.

Simulation results

The basis results are

1. Conventional relaying can outperforms the IRS-NOMA
2. IRS-NOMA > IRS OMA
3. $N$ increasing, the performance loss gap can be reduced

Question

1. The comparison seems to be unfair as the total transmit power is not equal for different scheme, the conventional relay still needs a relay transmit power $P_r$
   

2. The reason why the upper bound obtained by CLT is unaccurte when low SNR case? One may be the $N$ is not large enough.

By the way, the math is accurate and magic.