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Is NOMA Efficient in Multi-Antenna Networks? A Critical Look at Next Generation Multiple Access Techniques

Bruno Clerckx, Yijie Mao, Robert Schober, Eduard Jorswieck, David J. Love, Jinhong Yuan, Lajos Hanzo, Geoffrey Ye Li, Erik G. Larsson, Giuseppe Caire

arXiv:2101.04802v1cs.ITeess.SP

TL;DR

The paper addresses the limited emphasis on comparing multi-antenna NOMA with MU-LP and rate-splitting, analyzing multiplexing gains and comparing these schemes in MISO broadcast channels. It concludes that NOMA loses multiplexing gain and high-SNR rate versus conventional multiuser precoding while increasing receiver complexity, whereas 1-layer RS improves sum-rate and MMF-rate over NOMA at reduced complexity.

  • Problem

    The literature emphasizes comparing multi-antenna NOMA with OMA, with less emphasis on comparisons against MU-LP and other multi-antenna baselines, including 1-layer RS.

    Source: §I · p. 2, E. Shortcomings of Multi-Antenna NOMA · p. 16

  • Method

    The paper analyzes multiplexing gains and compares multi-antenna NOMA with conventional multiuser precoding and multi-antenna rate-splitting in MISO broadcast channels.

    Source: §IX · p. 22

  • Results

    Multi-antenna NOMA loses multiplexing gain and high-SNR rate versus conventional multiuser precoding while increasing receiver complexity; 1-layer RS gains sum-rate and MMF rate over NOMA at reduced complexity.

    Source: §IX · p. 22, C. Discussions · p. 22

  • Takeaways & Limitations

    In multi-antenna networks, 1-layer RS offers a better trade-off between rate performance gains and SIC layers than MISO NOMA.

    Source: C. Discussions · p. 22

    The multiplexing-gain analysis and numerical evaluations are limited to sum-rate and MMF-rate metrics and the MISO broadcast channel.

    Source: §IX · p. 23

Abstract

from arXiv · show

In this paper, we take a critical and fresh look at the downlink multi-antenna NOMA literature. Instead of contrasting NOMA with OMA, we contrast NOMA with two other baselines. The first is conventional Multi-User Linear Precoding (MULP). The second is Rate-Splitting Multiple Access (RSMA) based on multi-antenna Rate-Splitting (RS) and SIC. We show that there is some confusion about the benefits of NOMA, and we dispel the associated misconceptions. First, we highlight why NOMA is inefficient in multi-antenna settings based on basic multiplexing gain analysis. We stress that the issue lies in how the NOMA literature has been hastily applied to multi-antenna setups, resulting in a misuse of spatial dimensions and therefore loss in multiplexing gains and rate. Second, we show that NOMA incurs a severe multiplexing gain loss despite an increased receiver complexity due to an inefficient use of SIC receivers. Third, we emphasize that much of the merits of NOMA are due to the constant comparison to OMA instead of comparing it to MULP and RS baselines. We then expose the pivotal design constraint that multi-antenna NOMA requires one user to fully decode the messages of the other users. This design constraint is responsible for the multiplexing gain erosion, rate loss, and inefficient use of SIC receivers in multi-antenna settings. Our results confirm that NOMA should not be applied blindly to multi-antenna settings, highlight the scenarios where MULP outperforms NOMA and vice versa, and demonstrate the inefficiency, performance loss and complexity disadvantages of NOMA compared to RS. The first takeaway message is that, while NOMA is not beneficial in most multi-antenna deployments. The second takeaway message is that other non-orthogonal transmission frameworks, such as RS, exist which fully exploit the multiplexing gain and the benefits of SIC to boost the rate in multi-antenna settings.

I. INTRODUCTION · II. TWO-USER MISO NOMA WITH PERFECT CSIT: THE BASIC BUILDING BLOCK · A. System Model

The paper reassesses downlink multi-antenna NOMA against MU-LP and RS rather than OMA, arguing that NOMA’s design can waste spatial multiplexing gain and use SIC inefficiently. It introduces a two-user MISO NOMA model as a basic building block for the analysis.

I. INTRODUCTION

  • Multi-antenna NOMA always wastes multiplexing gain relative to RS, while it can gain or lose relative to MU-LP depending on the scenario.The analysis spans single-antenna receivers, perfect and imperfect CSIT, and underloaded and overloaded regimes.Source: §I · p. 2
  • More SIC operations in multi-antenna NOMA can mean higher receiver complexity but lower sum multiplexing gain and high-SNR sum-rate.The paper says MU-LP and RS can achieve higher multiplexing gains with fewer SIC operations and lower receiver complexity.Source: §I · p. 2
  • The paper attributes NOMA’s multiplexing loss and inefficient SIC to forcing one user to fully decode other users’ messages, a constraint suited to the degraded single-antenna BC but not necessarily multi-antenna networks.The authors argue that prevalent comparisons with OMA, rather than MU-LP and RS, contribute to misconceptions about NOMA’s merits.Source: §I · p. 2

II-C. Discussions

  • A supplied section marker identifies a discussion titled “III-A. MISO NOMA System Model.”This marker is listed under the subsection label II-C. Discussions.Source: §II-C · p. 3

V-C. Multiplexing Gains with Imperfect CSIT

  • The supplied section markers identify RS system modeling, imperfect-CSIT multiplexing gains, and NOMA comparisons with MU-LP and misconceptions.They list “VI-A. Rate-Splitting System Model,” “VII-A. NOMA vs. Baseline I (MU–LP),” and “VII-C. Misconceptions of Multi-Antenna NOMA.”Source: §V-C · p. 3, §VI-C · p. 3

VIII-C. Discussions

  • RS can use one SIC layer to partially decode other users’ messages and outperform both MU-LP and NOMA in some settings.The paper presents RS as exploiting multi-antenna multiplexing and SIC in both underloaded and overloaded regimes with perfect and imperfect CSIT.Source: §VIII-C · p. 3

II. TWO-USER MISO NOMA WITH PERFECT CSIT: THE BASIC BUILDING BLOCK

  • The paper uses the two-user, single-antenna-receiver MISO BC with perfect CSIT as a basic building block for studying NOMA against MU-LP.In this limited setting, the authors say NOMA’s potential merits are less obvious when compared with MU-LP rather than OMA.Source: §II · p. 3

A. System Model

  • In the model, both users decode stream s2, while user 1 uses SIC to cancel it before decoding s1; the rate for s2 is limited by the less capable of the two decoding channels.The setup has two single-antenna users, a transmitter with M ≥2 antennas, perfect CSIT and CSIR, and perfect SIC.Source: A. System Model · p. 4

B. Definition of Multiplexing Gain

The section defines multiplexing gain (DoF) as a high-SNR measure of how effectively a strategy uses spatial dimensions, with user, sum, and max-min-fairness versions. It is asymptotic rather than an exact finite-SNR rate measure, but provides theoretical grounds for comparisons and design.

B. Definition of Multiplexing Gain

  • A user’s multiplexing gain is the high-SNR pre-log of its rate, interpretable as the number or fraction of interference-free streams delivered to that user.A larger user multiplexing gain means its rate grows faster with SNR.Source: B. Definition of Multiplexing Gain · p. 5
  • Sum multiplexing gain is the high-SNR pre-log of sum-rate and represents the total number of interference-free streams simultaneously communicated to all users.A larger sum multiplexing gain means sum-rate grows faster with SNR.Source: B. Definition of Multiplexing Gain · p. 5
  • The MMF multiplexing gain, or symmetric multiplexing gain, is the maximum gain simultaneously achievable by all users and the high-SNR pre-log of the MMF rate.A larger MMF multiplexing gain means the MMF rate grows faster with SNR.Source: B. Definition of Multiplexing Gain · p. 5
  • Multiplexing gain is asymptotic and does not precisely describe finite-SNR rates, but it provides theoretical grounds for comparisons and guides efficient strategy design.It also impacts finite-SNR performance, as shown in prior work and the paper’s simulations.Source: B. Definition of Multiplexing Gain · p. 5

C. Discussions

For the two-user MISO broadcast channel, NOMA’s sum multiplexing gain is at most one, while MU–LP can use two interference-free streams. The discussion attributes NOMA’s loss to its decoding constraints and shows that adaptive decoding order does not remove the multiplexing-gain limit.

C. Discussions

  • Adaptive decoding order increases NOMA’s sum rate when the stronger-channel user decodes the weaker-channel user’s message.The sum-rate bound is considered across decoding orders, but the sum multiplexing gain remains at most one.Source: C. Discussions · p. 5
  • Two-user MISO NOMA has sum multiplexing gain at most 1 regardless of decoding order, the same as OMA.At high SNR, its sum rate scales at most as log2(P).Source: C. Discussions · p. 5
  • For any SNR, the two-user MISO NOMA sum rate is no higher than OMA’s.This holds for the basic two-user MISO NOMA building block, not only in the SISO case.Source: C. Discussions · p. 5
  • NOMA’s sum multiplexing gain of 1 can be split equally, yielding an MMF multiplexing gain of 1/2.At high SNR, its MMF rate scales at most as 1/2 log2(P).Source: C. Discussions · p. 5
  • With non-aligned channel directions, MU–LP achieves sum multiplexing gain 2 and MMF multiplexing gain 1, strictly outperforming NOMA and OMA at high SNR.Two streams with uniform power allocation and zero-forcing beamforming suffice to achieve these gains.Source: C. Discussions · p. 6
  • NOMA requires the shared s2 message to be decodable by both users, unlike MU–LP’s independent encoding and separate interference-as-noise decoding.The multiplexing-gain loss persists even with NOMA’s best precoders because the analysis uses an upper bound.Source: C. Discussions · p. 6

III. K-USER MISO NOMA WITH PERFECT CSIT · A. MISO NOMA System Model

The section defines a perfect-CSIT K-user MISO NOMA model with grouped users, shared-codebook message decoding, and SIC. It sets up the analysis of sum and MMF multiplexing gains.

III. K-USER MISO NOMA WITH PERFECT CSIT

  • The analysis derives sum and MMF multiplexing gains for K-user MISO NOMA with perfect CSIT.This is the stated focus of the section.Source: §III · p. 6

A. MISO NOMA System Model

  • A transmitter with M antennas serves K single-antenna users in G groups of g users, with K = gG and 1 ≤ G < K.The architecture is illustrated in Fig. 3.Source: A. MISO NOMA System Model · p. 6, Figure 3 · p. 7
  • Within each group, the designated strong user decodes the other g − 1 users’ messages, while subsequent users perform progressively fewer SIC layers.The multiplexing-gain analysis allows any ordering; simulations order users by ascending channel strength, so strong users have the largest channel norms.Source: A. MISO NOMA System Model · p. 6
  • The case G = K is MU–LP, not MISO NOMA, because users independently encode messages into separate streams and treat residual interference as noise.There is no shared codebook or decoding of other users’ messages in that case.Source: A. MISO NOMA System Model · p. 6
  • Although common choices are G = 1 – and G = K/2 –, the model covers any 1 ≤ G < K.The two-user building block is the special case K = 2 and G = 1.Source: A. MISO NOMA System Model · p. 7
  • Messages requiring within-group cancellation use codebooks shared with decoding users, and the K streams are linearly precoded and superposed under a total power constraint.The constraint is ∑ Pk ≤ P, where Pk = ∥pk∥²; forcing one precoder for all users in a group further reduces optimization space and rate performance.Source: A. MISO NOMA System Model · p. 7
  • Each user uses SIC to decode messages in its group in descending user-index order, treating interference from other groups as noise.A message’s rate must permit decoding by every user in its group that is required to decode it.Source: A. MISO NOMA System Model · p. 7

B. Multiplexing Gains · IV. K-USER MISO NOMA WITH IMPERFECT CSIT · A. CSIT Error Model

The section characterizes MISO NOMA’s multiplexing gains under perfect CSIT and extends the analysis to imperfect CSIT using ergodic rates. Its CSIT model makes estimation quality scale with SNR, from fixed-quality feedback to perfect CSIT in the multiplexing-gain sense.

B. Multiplexing Gains

  • With perfect CSIT, the sum multiplexing gain of K-user MISO NOMA is min(M, G), achievable with ZFBF streams to min(M, G) groups.Here M is the number of transmit antennas and G the number of groups.Source: B. Multiplexing Gains · pp. 7–9
  • Each group achieves at most one sum multiplexing gain because its strong user decodes all messages in that group.The group-rate upper bounds scale as log2(P)+δ at large P.Source: B. Multiplexing Gains · p. 7
  • With perfect CSIT and one-shot transmission, the MMF multiplexing gain is 1/g when M ≥ K−g+1, but collapses to 0 when M < K−g+1.The analysis excludes time-sharing between strategies, an assumption suited to rigid scheduling or tight latency constraints.Source: B. Multiplexing Gains · p. 8

IV. K-USER MISO NOMA WITH IMPERFECT CSIT

  • The imperfect-CSIT analysis generalizes the perfect-CSIT results and defines achievable rates, sum multiplexing gain, and MMF multiplexing gain using ergodic rates.The rates are evaluated over long sequences spanning almost all possible joint channel states.Source: §IV · p. 8, A. CSIT Error Model · p. 8

A. CSIT Error Model

  • The transmitter models each user’s channel as an estimate plus an estimation error, with the joint fading process assumed stationary and ergodic and its distribution known.The long-term ergodic rates average performance over joint channel states.Source: A. CSIT Error Model · p. 8
  • Assuming identical error variances across users, the model sets normalized CSIT error variance to P^-α, with α truncated to [0, 1] for multiplexing-gain analysis.α=0 represents CSIT that does not improve with SNR, 0<α<1 partial CSIT, and α=1 perfect CSIT in the multiplexing-gain sense.Source: A. CSIT Error Model · p. 8

B. Multiplexing Gains … B. Multiplexing Gains with Perfect CSIT

This section quantifies how imperfect CSIT affects MISO NOMA multiplexing gains and establishes MU–LP’s perfect-CSIT multiplexing gains and receiver model as a baseline.

B. Multiplexing Gains

  • With imperfect CSIT, K-user MISO NOMA has sum multiplexing gain max(1, min(M, G) α).The stated result applies to G groups of g = K/G users. Achievability uses ZFBF streams to strong users, or one stream when min(M, G) α < 1.Source: B. Multiplexing Gains · p. 9
  • For NOMA, sum and MMF multiplexing gains with G > 1 decay as CSIT quality α decreases, while with G = 1 they are unaffected by α.The G = 1 gains are robust to imperfect CSIT but cannot exploit CSIT, remaining the same as with α = 0.Source: B. Multiplexing Gains · p. 9

V. BASELINE SCHEME I:

A. MU–LP System Model

  • In the MU–LP system model, users independently encode messages and decode their intended messages while treating other users’ interference as noise.Each user has a single antenna, and the transmitter has M antennas.Source: A. MU–LP System Model · p. 9

B. Multiplexing Gains with Perfect CSIT

  • With perfect CSIT, K-user MU–LP achieves sum multiplexing gain min(M, K), using ZFBF to transmit min(M, K) interference-free streams.The result is also identified as the optimal sum multiplexing gain of the K-user MISO broadcast channel.Source: B. Multiplexing Gains with Perfect CSIT · pp. 9–10
  • For perfect-CSIT MU–LP, when M < K the MMF multiplexing gain collapses, leading to high-SNR rate saturation.When M ≥ K, ZFBF can fully eliminate interference.Source: B. Multiplexing Gains with Perfect CSIT · p. 10

C. Multiplexing Gains with Imperfect CSIT … B. Multiplexing Gains with Perfect CSIT

With imperfect CSIT, MU–LP’s sum multiplexing gain depends on CSIT quality and can fall below the information-theoretic optimum. Under perfect CSIT, 1-layer RS achieves sum multiplexing gain min(M, K) by splitting messages into common and private parts decoded with one SIC layer.

C. Multiplexing Gains with Imperfect CSIT

VI. BASELINE SCHEME II: RATE-SPLITTING

  • The paper identifies multi-antenna RS and RSMA for the broadcast channel as its second baseline, extending rate-splitting to multi-antenna non-orthogonal transmission –,.Source: §VI · p. 10

A. Rate-Splitting System Model

  • In 1-layer RS, each user’s message is split into common and private parts, creating one common stream and K private streams.The common parts are combined into a stream decoded by all users; each private stream carries the remainder intended for one user.Source: A. Rate-Splitting System Model · p. 10
  • Each user decodes the common stream while treating private streams as noise, then uses SIC to decode its own private stream and reconstruct its message.The architecture uses a single common stream and one SIC layer per user.Source: A. Rate-Splitting System Model · pp. 10–11

B. Multiplexing Gains with Perfect CSIT

C. Multiplexing Gains with Imperfect CSIT · VII. SHORTCOMINGS AND MISCONCEPTIONS OF MULTI-ANTENNA NOMA · A. NOMA vs. Baseline I (MU–LP)

The section compares RS, multi-antenna NOMA, and MU–LP through sum and max-min-fairness (MMF) multiplexing gains under perfect and imperfect CSIT. It finds that NOMA’s relative performance depends on the antenna, user, group, and CSIT regimes, while 1-layer RS is sum-multiplexing-optimal when M ≥ K.

C. Multiplexing Gains with Imperfect CSIT

  • With imperfect CSIT, 1-layer RS achieves sum multiplexing gain 1 + (min(M, K) − 1)α and is optimal when M ≥ K.Its optimality means MU–LP and multi-antenna NOMA cannot exceed RS’s multiplexing-gain region; they may at best match it.Source: C. Multiplexing Gains with Imperfect… · p. 11
  • For M < K, the CSIT quality α can be reduced without affecting 1-layer RS’s MMF multiplexing gain.When M ≥ K, RS’s MMF gain combines an evenly shared common-stream contribution with one private-stream contribution per user.Source: C. Multiplexing Gains with Imperfect… · p. 11

VII. SHORTCOMINGS AND MISCONCEPTIONS OF MULTI-ANTENNA NOMA

  • The section compares NOMA’s sum and MMF multiplexing gains with MU–LP and 1-layer RS under perfect and imperfect CSIT to identify regimes of gain or loss.These comparisons are used to examine misconceptions and shortcomings of multi-antenna NOMA.Source: §VII · p. 12

A. NOMA vs. Baseline I (MU–LP)

  • MISO NOMA never achieves a higher sum multiplexing gain than MU–LP, and can either match or fall below it depending on M, K, G, and α.With perfect CSIT, NOMA has a strictly lower sum multiplexing gain when M > G; for G = 1 it loses in every multi-antenna configuration, while for G = K/2 it loses when M > K/2.Source: A. NOMA vs. Baseline I (MU–LP) · p. 12
  • Under imperfect CSIT, NOMA’s sum-gain loss versus MU–LP occurs in medium-CSIT regimes or with M > G and sufficiently high CSIT quality; with poor CSIT and M ≤ G, their gains match.The cited comparison describes these regimes in terms of α and min(M,G), without requiring a single condition across all configurations.Source: A. NOMA vs. Baseline I (MU–LP) · p. 12
  • For MMF multiplexing gain, NOMA may outperform or underperform MU–LP depending on M, G, K, and α.For G > 1, imperfect-CSIT α does not change the regimes of gain or loss; for G = 1, NOMA incurs a loss when M ≥ K and α is sufficiently large.Source: A. NOMA vs. Baseline I (MU–LP) · pp. 12–13
  • With perfect CSIT, NOMA with G = 1 loses MMF multiplexing gain when M ≥ K, while G = 1 and G = K/2 can match or outperform MU–LP when M < K.The G = K/2 case allows this outcome when M < K − 1.Source: A. NOMA vs. Baseline I (MU–LP) · p. 13

B. NOMA vs. Baseline II (RS)

Across antenna/user counts and CSIT conditions, 1-layer RS matches or exceeds MISO NOMA’s sum and MMF multiplexing gains while requiring only one SIC; using MISO NOMA can therefore mean a gain loss and/or greater receiver complexity.

B. NOMA vs. Baseline II (RS)

  • For all M, K, and α, 1-layer RS achieves the same or higher sum and MMF multiplexing gains than the best MISO NOMA scheme, with only one SIC.MISO NOMA may require more SICs, so using it over 1-layer RS can incur multiplexing-gain loss and/or increased receiver complexity.Source: B. NOMA vs. Baseline II (RS) · p. 13
  • MISO NOMA never achieves a higher sum multiplexing gain than 1-layer RS.This holds across the compared MISO NOMA schemes, including different values of G and numbers of SICs.Source: B. NOMA vs. Baseline II (RS) · p. 13
  • Neither MISO NOMA with G = 1 nor with G > 1 achieves a higher MMF multiplexing gain than 1-layer RS.The comparison covers both NOMA group-size cases discussed in the corollaries.Source: B. NOMA vs. Baseline II (RS) · p. 13
  • For multi-antenna broadcast channels with imperfect CSIT, RS achieves the optimal multiplexing-gain region, while NOMA, MU–LP, and MU-MIMO incur a loss –.Source: B. NOMA vs. Baseline II (RS) · p. 13

C. Misconceptions of Multi-Antenna NOMA

This section argues that multi-antenna NOMA often sacrifices multiplexing gain and uses SIC inefficiently, despite added receiver complexity. It identifies misleading comparisons with OMA and shows that 1-layer RS can exploit spatial dimensions and SIC more effectively.

Misconception 1: NOMA exploits spatial dimensions efficiently

  • For K users, NOMA generally loses sum multiplexing gain: G=1 yields 1 regardless of M, while G=K/2 reaches min(M, K/2), versus min(M, K) for MU–LP and 1-layer RS.1-layer RS achieves the information-theoretic optimal sum multiplexing gain with perfect or imperfect CSIT.Source: C. Misconceptions of Multi-Antenna NOMA · p. 14

Misconception 2: SIC complexity brings a performance gain

  • In the two-user MISO BC with perfect CSIT, NOMA achieves only half MU–LP’s sum and MMF multiplexing gains while requiring one SIC receiver; MU–LP needs none.For M>1, MU–LP achieves sum multiplexing gain 2 and MMF multiplexing gain 1.Source: C. Misconceptions of Multi-Antenna NOMA · p. 14

Misconception 1: NOMA exploits spatial dimensions efficiently

  • For MMF with α=1, NOMA loses to MU–LP when M≥K, but G=1 exceeds both G=K/2 and MU–LP when M<K−1; 1-layer RS outperforms NOMA.Even where NOMA gains over MU–LP in overloaded settings, its MMF multiplexing gain with G=1 is independent of M.Source: C. Misconceptions of Multi-Antenna NOMA · p. 14
  • As CSIT quality α decreases, NOMA with G=1 retains its multiplexing gains but cannot exploit available CSIT; 1-layer RS has larger sum and MMF gains than NOMA and MU–LP.MU–LP, NOMA with G>1, and 1-layer RS gains decay as α decreases.Source: C. Misconceptions of Multi-Antenna NOMA · p. 14

Misconception 2: SIC complexity brings a performance gain

  • NOMA’s sum multiplexing gain can decrease as its SIC count rises, while 1-layer RS achieves optimal sum multiplexing gain with a single SIC per user.For MMF, one SIC in 1-layer RS achieves a larger gain than the K−1 SIC layers required by NOMA with G=1.Source: C. Misconceptions of Multi-Antenna NOMA · p. 15
  • In the two-user example, SIC raises or maintains user 1’s rate but can lower user 2’s rate because NOMA limits it to min(log2(1 + A), RM,2).For fixed precoders, NOMA’s user-1 rate is at least MU–LP’s, while its user-2 rate is at most MU–LP’s.Source: C. Misconceptions of Multi-Antenna NOMA · p. 15

Misconception 3: OMA is a sufficient baseline for NOMA

  • Comparing multi-antenna NOMA only with OMA can mislead; MU–LP and RS, not simply OMA, should be baselines for NOMA design and evaluation.1-layer RS guarantees a rate equal to or higher than MU–LP because MU–LP is an RS instance with no common-stream power.Source: C. Misconceptions of Multi-Antenna NOMA · p. 15

Misconception 4: NOMA is efficient in overloaded regimes

  • NOMA can lose sum multiplexing gain when M>G, including overloaded cases K>M>G, and loses MMF gain to 1-layer RS when M≠K−g+1.NOMA with G=1 has an MMF multiplexing gain of 1/K in the overloaded regime, constant with M and below 1-layer RS’s gain, which increases with M.Source: C. Misconceptions of Multi-Antenna NOMA · p. 15

D. Illustration of the Misconceptions with an Example · E. Shortcomings of Multi-Antenna NOMA · VIII. NUMERICAL RESULTS

The example and numerical results show the multiplexing-gain cost of multi-antenna NOMA, while the shortcomings analysis traces it to forced full decoding and contrasts it with RS’s flexible partial decoding.

D. Illustration of the Misconceptions with an Example

E. Shortcomings of Multi-Antenna NOMA

  • NOMA loses multiplexing gain because it forces one user to fully decode every stream in its group, making that user a single-antenna MAC receiver with sum multiplexing gain one.Unlike MU–LP and 1-layer RS, which let each receiver decode its intended private stream while treating residual interference as noise, NOMA also requires decoding co-scheduled streams.Source: E. Shortcomings of Multi-Antenna NOMA · p. 17
  • Adding SIC layers does not necessarily restore sum multiplexing gain: forcing a user to decode the other g − 1 users’ messages reduces gain in each NOMA group.The authors attribute this anomaly to applying the single-antenna NOMA principle directly to multi-antenna settings.Source: E. Shortcomings of Multi-Antenna NOMA · p. 17
  • In the two-user case, 1-layer RS includes MU–LP, NOMA, and multicasting as special cases, but in the general K-user case it is not a superset of NOMA.K-user 1-layer RS is a subscheme of the broader RSMA framework, which also embraces multi-layer schemes such as 2-layer HRS.Source: E. Shortcomings of Multi-Antenna NOMA · p. 17
  • RS flexibly splits messages between common and private streams, allowing receivers to partially decode interference and treat the remainder as noise.By building on MU–LP, 1-layer RS retains its rate and multiplexing gains or improves on them; NOMA cannot reduce to K-user MU–LP.Source: E. Shortcomings of Multi-Antenna NOMA · p. 18

VIII. NUMERICAL RESULTS

  • 1-layer RS guarantees the optimal sum multiplexing gain across underloaded and overloaded settings with perfect or imperfect CSIT, while improving MMF performance and reducing receiver complexity versus NOMA.The numerical evaluation also finds 1-layer RS more robust to CSIT inaccuracy.Source: §VIII · p. 18
  • The numerical evaluations compare five strategies under perfect and imperfect CSIT, using K = 6 and results averaged over 100 channel realizations.For NOMA with G = 3, optimizing group selection would require 15 times as many optimization runs as MU–LP, 1-layer RS, or OMA, so the simulations fix the grouping.Source: §VIII · p. 19

A. Perfect CSIT

Under perfect CSIT, multi-antenna MISO NOMA can lose multiplexing gain and rate relative to MU–LP and RS while imposing greater complexity; OMA alone is an inadequate baseline.

A. Perfect CSIT

  • 3 is the MISO NOMA (G=3) sum multiplexing gain at M=6, versus 6 for 1-layer RS and MU–LP; MISO NOMA (G=1) and OMA are limited to 1.At M=3, the sum multiplexing gains of 1-layer RS, MU–LP, and MISO NOMA (G=3) approach 3. The comparisons use K=6 users, with equal channel variances in some cases and variances randomly generated from [0.1, 1] in others.Source: A. Perfect CSIT · pp. 19–20, Figure 10 · p. 20
  • MISO NOMA combines the highest transmitter and receiver complexity with worse sum-rate performance than MU–LP, despite its use of SIC.Its transmitter scheduling jointly optimizes user grouping, decoding order, and precoders; each receiver uses multiple SIC layers, with the layer count increasing with K.Source: A. Perfect CSIT · p. 20
  • In overloaded M=3/4/5 systems, MISO NOMA’s low MMF multiplexing gains yield poor max-min rates, and its overloaded-regime rate is worse than 1-layer RS.The reported MMF multiplexing gain of 1-layer RS is 2 for M=3/4/5.Source: Figure 11 · p. 20, A. Perfect CSIT · pp. 20–21
  • Because OMA and MISO NOMA (G=1) have the worst sum-rate performance, comparing NOMA with OMA alone is insufficient; MU–LP and 1-layer RS are necessary baselines.Source: A. Perfect CSIT · p. 20

B. Imperfect CSIT · C. Discussions · IX. CONCLUSIONS AND FUTURE RESEARCH

Across imperfect-CSIT results and the paper’s discussion and conclusions, the authors argue that multi-antenna NOMA’s full-decoding constraint wastes spatial multiplexing, while partial-decoding RS delivers stronger rates with less SIC complexity.

B. Imperfect CSIT

  • Under imperfect CSIT, MISO NOMA (G = 1) has the worst ergodic sum-rate, always trails MU–LP, while 1-layer RS improves over all strategies.The paper reports that NOMA’s poor sum-rate persists in the overloaded setting with channel-strength disparities.Source: Figure 13 · p. 21, B. Imperfect CSIT · p. 21
  • Under perfect and imperfect CSIT, MISO NOMA cannot improve user fairness and has much worse MMF ergodic rate than 1-layer RS, whose MMF multiplexing gains are significantly higher.These MMF results hold across the paper’s perfect- and imperfect-CSIT settings.Source: Figure 14 · p. 21, Figure 15 · p. 22, B. Imperfect CSIT · p. 22
  • With imperfect CSIT, 1-layer RS is more robust to estimation errors because it partially decodes interference and treats the remainder as noise.The authors report generally larger rate gaps between RS and MU–LP or multi-antenna NOMA under imperfect than perfect CSIT.Source: B. Imperfect CSIT · p. 22

C. Discussions

  • Across underloaded and overloaded regimes, 1-layer RS matches or exceeds other strategies’ sum-rate and MMF performance, especially on fairness-focused metrics under overload.Its advantage in managing multi-user interference grows when all users are active, antennas are limited, and interference is stronger; it needs no user grouping or decoding-order optimization and only one SIC layer per user, reducing complexity relative to MISO NOMA.Source: C. Discussions · p. 22
  • Multi-layer RS can further improve rates over 1-layer RS by splitting user messages multiple times and implementing multiple SIC layers at receivers.The paper points to prior demonstrations of this approach,,,,.Source: C. Discussions · p. 22

IX. CONCLUSIONS AND FUTURE RESEARCH

  • The paper’s multiplexing-gain analysis identifies scenarios where NOMA gains or loses against conventional multiuser precoding, but finds NOMA always below rate-splitting despite using more SIC layers.Simulations in the paper confirm the theoretical analysis.Source: §IX · p. 22
  • The authors conclude that forcing one user to fully decode co-scheduled users’ messages is inefficient for multi-antenna NOMA, and recommend partial decoding with remaining interference treated as noise.They caution that multi-antenna NOMA’s benefits for future downlink networks should be considered carefully.Source: §IX · p. 23
  • The evaluation covers sum-rate and MMF metrics in the MISO broadcast channel; the authors identify weighted sum-rate, other scenarios, and uplink multi-antenna RSMA as further research directions.They also outline a broad RSMA agenda spanning multi-user and multi-cell networks, interference management, implementation, and standardization.Source: §IX · p. 23

APPENDIX A PROOF OF PROPOSITION 4

For multiple groups, the proof bounds and achieves an MMF multiplexing gain of α/g when M ≥ K − g + 1, while the gain collapses to zero below that antenna threshold. For a single group, the gain is 1/K.

APPENDIX A PROOF OF PROPOSITION 4

  • When G > 1 and M ≥ K − g + 1, the MMF multiplexing gain is α/g, achieved by splitting each group’s multiplexing gain equally among its g users.The proof uses ZFBF precoders and power allocation that makes each user’s SINR scale as P^(α/g).Source: Appendix A · p. 23
  • For K = 4, G = 2, g = 2, and M ≥ 3, the construction makes all four streams’ SINRs scale as P^(α/2), achieving an MMF multiplexing gain of α/2.Precoding nulls each group’s signals toward the other group’s channel estimates, and SIC decodes and cancels the higher-power stream.Source: Appendix A · p. 23
  • When G > 1 and M < K − g + 1, the MMF multiplexing gain is zero, as in the perfect-CSIT setting.Source: Appendix A · p. 23
  • When G = 1, the single group’s sum multiplexing gain of one is split equally among K users, yielding an MMF multiplexing gain of 1/K.The proof establishes achievability using power allocation that makes each user’s SINR scale as P^(1/K).Source: Appendix A · pp. 23–24

APPENDIX B WMMSE OPTIMIZATION FRAMWORK

The appendix formulates rate and max-min optimization as WMMSE problems, then uses alternating optimization to obtain KKT solutions. It connects each stream’s rate to its minimum weighted MSE and specifies the equalizer and weight updates underlying the method.

APPENDIX B WMMSE OPTIMIZATION FRAMWORK

  • At user j, equalizer g_j,k estimates stream s_k after previously decoded streams are removed, and the corresponding MSE supports its rate calculation.The equalizer is used for streams indexed k ≥ j within group K_i.Source: Appendix B · p. 24
  • The rate-WMMSE relation gives min_{u_j,k,g_j,k} ξ_j,k = 1 − R_j,k, linking a stream’s rate to its minimum weighted MSE.The MMSE equalizer and weight are obtained by optimizing the weighted MSE.Source: Appendix B · p. 24
  • WMMSE problem (53) yields a solution to rate problem (41): its KKT points satisfy the KKT conditions of (41).The appendix states that substituting the MMSE equalizers and weights into (53) reduces it to (41).Source: Appendix B · p. 24
  • Alternating optimization updates MMSE equalizers and weights for fixed precoders, then optimizes the precoders; it converges to a KKT solution of (41).The transformed problem is block-wise convex in the precoders and in the equalizer-weight variables, although it remains non-convex overall.Source: Appendix B · p. 24
  • Replacing problem (53) with the max-min WMMSE problem (54) in the alternating-optimization algorithm yields a KKT solution to max-min problem (42).The appendix obtains the max-min transformation by following the same procedure as for the sum-rate formulation.Source: Appendix B · p. 24

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