SCMA (Sparse Code Multiple Access) maps each user's data bits directly to a multi-dimensional codeword selected from a user-specific codebook, rather than using conventional modulation followed by spreading. Each codebook has K codewords (one per constellation point) of length N (the spreading factor), where each codeword has only d_v non-zero elements (d_v less than N, typically d_v = 2 out of N = 4). The sparsity means each user occupies only d_v of the N resource elements, and each resource element is shared by only d_f users (d_f typically 3 to 4). With J users sharing N resources, the overloading factor is J/N, typically 150 to 300% (6 to 12 users on 4 resource elements). The receiver uses a message passing algorithm (MPA) on the factor graph defined by the sparse indicator matrix. Each resource node sends messages to the d_f users sharing it, and each user node combines messages from its d_v resource nodes. After 5 to 10 iterations, the algorithm converges to near-optimal multi-user detection. The computational complexity is O(J * M^d_f) per iteration where M is the codebook size, manageable because d_f is small (3 to 4).

How does code-domain NOMA differ from power-domain NOMA?

Power-domain NOMA superimposes users on the same time-frequency resources using different power levels, relying on successive interference cancellation (SIC) at the receiver to separate users by decoding the strongest first and subtracting it. It works best when users have significantly different channel conditions (near vs far). Code-domain NOMA separates users through their unique spreading codes or codebooks, which provides separation even when users have similar channel conditions and power levels. This makes code-domain NOMA better suited for scenarios like massive IoT where many devices with similar path loss transmit simultaneously. Code-domain NOMA also supports grant-free access more naturally: each device is pre-assigned a codebook or spreading sequence and can transmit without scheduling, with the base station performing blind detection to identify active devices and decode their data. Power-domain NOMA requires the base station to control power allocation, which needs scheduling. In practice, hybrid approaches combining both power and code domain are being studied for 6G.

What are the practical challenges of code-domain NOMA?

Three main challenges limit practical deployment. Receiver complexity is the primary concern: MPA decoding for SCMA scales exponentially with d_f and the codebook size M, requiring O(J * M^d_f) operations per iteration. At 300% overloading with M=4 and d_f=4, this is manageable, but higher overloading or larger codebooks become impractical for real-time processing. Simplified algorithms (partial marginalization, list detection) reduce complexity by 5 to 10x with 0.5 to 1 dB performance loss. Channel estimation for overloaded systems is harder than for orthogonal systems because pilot sequences must also be non-orthogonal when users exceed the coherence dimension, causing pilot contamination. Compressed sensing and activity detection algorithms address this but add processing delay. Finally, the performance advantage over orthogonal access (OFDMA) diminishes as individual user data rates increase. Code-domain NOMA is most beneficial for massive connectivity with small packets (100 to 1,000 bits), which is exactly the mMTC scenario, but provides limited gains for high-rate eMBB traffic.

Wireless Protocols

Code Domain Noma

/kohd doh-mayn noh-muh/

Code-domain NOMA uses sparse or non-orthogonal spreading codes to serve more users than available time-frequency resources (overloading). SCMA (Huawei): sparse multi-dimensional codebooks, 150 to 300% overloading, MPA decoding. MUSA (ZTE): short complex spreading sequences. NOCA (Nokia): low cross-correlation codes. Targets grant-free massive IoT (mMTC) in 5G-Advanced and 6G, enabling millions of devices without scheduling overhead.

Category: Wireless Protocols

Overloading: 150 to 300%

Target: mMTC / 6G

Understanding Code-Domain NOMA

Conventional orthogonal multiple access (OFDMA in LTE/5G) assigns each user exclusive time-frequency resources, ensuring no mutual interference but limiting the number of simultaneously served users to the number of available resource elements. Code-domain NOMA breaks this constraint: by assigning each user a unique spreading code or codebook and allowing multiple users to share the same resources, the system can serve more users than available resource slots. The price is inter-user interference, which must be resolved by sophisticated multi-user detection at the receiver.

The key insight enabling code-domain NOMA is sparsity. In SCMA, each user's codeword has only 2 non-zero elements out of 4 resource elements, meaning each user interferes with only a subset of other users on each resource. This sparse structure creates a factor graph (bipartite graph connecting users to resources) where message passing algorithms can iteratively resolve the multi-user interference with near-optimal performance. The sparsity keeps the factor graph tree-like locally, ensuring that the message passing algorithm converges rapidly (5 to 10 iterations). With proper codebook design (maximizing minimum distance between codewords), SCMA can achieve 300% overloading (12 users on 4 resources) with only 1 to 2 dB loss compared to orthogonal access at the same total throughput.

Code-Domain NOMA Parameters

Overloading Factor:
λ = J/N × 100% (J users, N resource elements)

SCMA Factor Graph:
d_v = non-zero elements per codeword ; d_f = users per resource

MPA Complexity:
O(J × M^d_f × I) per code block

Where M = codebook size (e.g., 4-point), I = iterations (5 to 10). SCMA example: N=4, J=6, d_v=2, d_f=3. λ=150%. Complexity: O(6 × 4³ × 10) = 3,840 operations per code block. At J=12, d_f=4: 30,720 operations.

Code-Domain NOMA Schemes

Scheme	Proponent	Spreading	Overloading	Detection
SCMA	Huawei	Sparse codebooks	150 to 300%	MPA (iterative)
MUSA	ZTE	Complex sequences	150 to 300%	SIC
NOCA	Nokia	Low cross-corr codes	100 to 200%	MMSE-SIC
IDMA	Academic	User-specific interleavers	200 to 400%	Turbo MUD
PDMA	CATT/Datang	Pattern diversity	150 to 300%	SIC / MPA

Common Questions

Frequently Asked Questions

How does SCMA work?

Maps data bits directly to sparse multi-dimensional codewords (d_v=2 non-zero of N=4). Each resource shared by d_f=3 to 4 users. 6 to 12 users on 4 resources (150 to 300%). MPA on factor graph: resource nodes ↔ user nodes, 5 to 10 iterations. Complexity O(J×M^d_f) per iteration, manageable for small d_f.

How does it differ from power-domain NOMA?

Power-domain: separates by power level (SIC), needs dissimilar channel conditions. Code-domain: separates by spreading codes, works with similar power levels. Code-domain better for mMTC (many similar devices). Supports grant-free access (pre-assigned codebooks, no scheduling). Power-domain needs scheduling for power allocation. Hybrid approaches studied for 6G.

What are the practical challenges?

MPA complexity scales exponentially with d_f (mitigated by partial marginalization, 5 to 10x reduction, 0.5 to 1 dB loss). Channel estimation harder with non-orthogonal pilots (compressed sensing helps). Performance advantage over OFDMA limited for high-rate traffic; best for small packets (100 to 1,000 bits) in mMTC scenario.

Related Terms

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