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Rate-Splitting Unifying SDMA, OMA, NOMA, and Multicasting in MISO Broadcast Channel: A Simple Two-User Rate Analysis
Bruno Clerckx, Yijie Mao, Robert Schober, H. Vincent Poor
TL;DR
The paper asks how one non-orthogonal transmission framework can relate SDMA, OMA, NOMA, and multicasting in a two-user MISO broadcast channel. It analyzes linearly precoded RS with SIC under perfect CSIT, showing that RS unifies, outperforms, and specializes to these strategies as channel geometry and strength disparity vary. In evaluations, RS is preferred for about 75% of high-SNR channel realizations in the reported two-antenna setting.
Problem
The paper examines how SDMA, OMA, NOMA, and physical-layer multicasting can be understood within a common framework for two-user MISO broadcast channels.
Method
It analyzes linearly precoded Rate-Splitting with SIC receivers, splitting messages into common and private parts and adjusting power allocation with fixed zero-forcing private precoders.
Results
RS unifies, outperforms, and specializes to SDMA, OMA, NOMA, and multicasting as channel-strength disparity and channel-direction angle vary.
Takeaways & Limitations
RS bridges the NOMA regime of closely aligned, similarly strong users and the SDMA regime of sufficiently separated channel directions, while covering OMA and multicasting cases.
Abstract
from arXiv · showhide
Considering a two-user multi-antenna Broadcast Channel, this paper shows that linearly precoded Rate-Splitting (RS) with Successive Interference Cancellation (SIC) receivers is a flexible framework for non-orthogonal transmission that generalizes, and subsumes as special cases, four seemingly different strategies, namely Space Division Multiple Access (SDMA) based on linear precoding, Orthogonal Multiple Access (OMA), Non- Orthogonal Multiple Access (NOMA) based on linearly precoded superposition coding with SIC, and physical-layer multicasting. The paper studies the sum-rate and shows analytically how RS unifies, outperforms, and specializes to SDMA, OMA, NOMA, and multicasting as a function of the disparity of the channel strengths and the angle between the user channel directions.
I. INTRODUCTION
The paper positions linearly precoded Rate-Splitting (RS) with SIC receivers as a robust non-orthogonal transmission strategy for multi-antenna wireless networks. It studies RS in a two-user MISO BC to unify four transmission strategies according to channel-strength disparity and channel-direction angle.
- RS with SIC receivers is presented as a powerful non-orthogonal transmission and interference-management strategy for multi-antenna wireless networks.
- The paper considers perfect-CSIT two-user MISO BCs and relates RS to SDMA, OMA, NOMA, and physical-layer multicasting.
- RS is analytically shown to unify, outperform, and specialize to the four strategies as channel-strength disparity and channel-direction angle vary.
II. SYSTEM MODEL: RATE-SPLITTING ARCHITECTURE
The system splits each user message into common and private parts, creating one common stream and two private streams. SIC users decode the common stream first, then their private streams, while power allocation recovers SDMA, NOMA, OMA, and multicasting as special cases.
- Each message is split into common and private parts, producing one common stream and two independently encoded private streams.The common stream contains parts of both users’ messages, while each private stream carries the remaining part for one user.
- Each user decodes the common stream first, subtracts it using SIC, and then decodes its private stream while treating the other private stream as noise.
- RS sum-rate equals the common-stream rate plus the two private-stream rates, with common-rate portions assigned across the users.
- SDMA uses no common-stream power, while NOMA, OMA, and multicasting arise through progressively disabling private streams or allocating power to the common stream.
- SDMA and RS can achieve DoF 2 with zero-forcing private precoding, whereas OMA, NOMA, and multicasting achieve at most DoF 1.The paper associates the lower DoF of OMA, NOMA, and multicasting with high-SNR rate loss in general multi-antenna settings.
III. SUM-RATE ANALYSIS
The analysis fixes zero-forcing private precoding and adjusts stream powers to obtain tractable sum-rate expressions. It parameterizes channel geometry and strength disparity while noting that simulations support the conclusions for optimized precoders.
- The paper fixes zero-forcing directions for private streams and varies power allocation instead of jointly optimizing precoding directions and powers.
- The channel-direction parameter ρ is defined so that ρ = 0 corresponds to aligned channels and ρ = 1 to orthogonal channels.
- Simulations in Section IV report that the conclusions from the simple precoders also hold with numerically optimized precoders.
A. Sum-Rate at Finite SNR
At finite SNR, the private-stream power split is obtained by water-filling for a chosen private-power fraction, while the optimal regime depends on channel geometry and strength disparity. When the private-power threshold is not exceeded, only the stronger user’s private stream is active, yielding multicasting, NOMA, or OMA as endpoints.
- A fraction t of total power is assigned to private streams, with the remaining power allocated to the common stream.For fixed t, private-stream powers are selected using the water-filling solution.
- The threshold regime is governed by the channel-direction parameter ρ and the disparity between channel strengths.
- For tP ≤ Γ, water-filling sets P2 = 0 and P1 = tP, so only the stronger user’s private stream is active.
- For tP ≤ Γ, RS specializes to multicasting at t = 0, NOMA for 0 < t < 1, and OMA at t = 1.
2) RS/SDMA Regime:
In the RS/SDMA regime, both private streams receive positive power, and the sum-rate is optimized by adjusting the common/private allocation parameter t. When t⋆<1, RS provides a non-zero sum-rate enhancement over SDMA.
- RS/SDMA Regime:: The value of t maximizing Rs is obtained by solving the stationarity condition ∂Rs/∂t = 0, with the optimum constrained by t ≤ 1.The resulting optimizer is given in closed form in equation (14).
- RS/SDMA Regime:: For t⋆<1, RS yields a non-zero sum-rate enhancement over SDMA, whose operating point corresponds to t = 1.
- RS/SDMA Regime:: When P1>0 and P2>0, the coefficients a, b, c, and d are independent of t, even though c and d depend on fc.The paper explains that fc is not a function of t in this regime.
- RS/SDMA Regime:: The channel-dependent quantity fc depends on the channel directions, not on t or the disparity in channel strengths.
B. Sum-Rate at High SNR
At high SNR, the power allocation gives both private streams positive power, leaving RS and SDMA as the suitable strategies. RS achieves a constant sum-rate advantage over SDMA, while its advantage over lower-DoF strategies grows without bound.
- B. Sum-Rate at High SNR: At high SNR, the solution allocates power uniformly across the two private streams as P1 = P2 = tP/2.
- B. Sum-Rate at High SNR: Only RS and SDMA are suitable strategies at high SNR, and both achieve a DoF of 2.
- B. Sum-Rate at High SNR: RS brings a constant sum-rate enhancement over SDMA at high SNR.
- B. Sum-Rate at High SNR: The high-SNR sum-rate gap between RS and NOMA, OMA, or multicasting grows unbounded as P → ∞ because their degrees of freedom differ.
C. Discussions
The analysis links preferred transmission strategies to channel geometry and strength disparity. Lower alignment favors single-private-stream regimes, while stronger separation supports two private streams; RS bridges these conditions.
- Lower ρ favors allocating power to one private stream, widening the NOMA, OMA, or multicasting operating range.The common stream also experiences less interference in this regime.
- Higher ρ improves the effective SNRs of both private streams and supports the RS/SDMA regime.
- At increasing transmit power, private-stream SNRs grow while common-stream SINR saturates, so the common stream provides constant high-SNR improvement while private streams provide DoF 2.
- Figures 3 and 4 map optimum private-stream power fraction t and preferred operating regions across channel conditions and transmit powers.Figure 3 uses P = 100W, while Figure 4 compares P = 10W and 1000W.
- Greater channel-strength disparity shifts water-filling power toward the stronger user and can turn off the weaker user's private stream.Beyond a certain disparity, RS specializes to NOMA/OMA.
IV. EVALUATIONS
The evaluations identify which strategy is preferred across channel geometry, strength disparity, transmit power, and weighting. RS consistently matches or exceeds SDMA and NOMA, and becomes increasingly dominant as power rises.
- NOMA is preferred for closely aligned users with small channel-strength ratio, SDMA for sufficiently separated directions, and RS between these extremes.OMA is preferred when the channel-strength ratio is very small.
- As transmit power increases from 10W to 1000W, RS becomes the dominant strategy for most deployment conditions.
- RS provides explicit sum-rate gains over dynamic SDMA/NOMA switching, with gains over SDMA at low-to-medium ρ and over NOMA at medium-to-large ρ at low SNR.At higher SNR, RS gains over NOMA occur across all ρ and γdB values.
- With WMMSE precoding and arbitrary user weights, RS always provides the same or better performance than SDMA and NOMA.When the weaker user receives higher weight, NOMA can outperform SDMA; equal or stronger-user weights provide NOMA no benefit over SDMA.
- Under i.i.d. Rayleigh fading with nt = 2, OMA is preferred at low power and disparity, while RS is preferred for about 75% of high-SNR realizations and SDMA for the remaining 25%.For nt = 4, NOMA nearly disappears; SDMA is preferred for about 60% and RS for the remaining 40%.
V. CONCLUSIONS
The paper concludes that RS provides a unified framework encompassing several transmission strategies and improving over dynamic alternatives across evaluated settings. Its reported gains include both unweighted and weighted sum-rate comparisons.
- RS unifies SDMA, OMA, NOMA, and physical-layer multicasting under a single non-orthogonal transmission framework.
- The framework is presented as relevant to non-orthogonal transmission, multiple access, and interference management design and optimization.
- Figure 5 measures RS relative sum-rate gain over dynamic switching between SDMA and NOMA for nt = 2.
- Figure 6 measures RS relative weighted sum-rate gain over dynamic SDMA/NOMA switching across user weights using WMMSE-optimized precoders.
- Figure 7 reports the percentage of operation for RS, SDMA, NOMA, OMA, and multicasting across transmit powers with nt = 2.