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SCMA Codebook Design
Mahmoud Taherzadeh, Hosein Nikopour, Alireza Bayesteh, Hadi Baligh
TL;DR
SCMA addresses multidimensional non-orthogonal multiple access by combining bit mapping and sparse spreading in layer-specific codebooks. The paper proposes a multi-stage lattice-based design using rotated multidimensional constellations and layer-specific operators, and simulations report gains over LDS and OFDMA in AWGN and fading channels.
Problem
SCMA codebook design is complicated because multiple layers are multiplexed using different codebooks, motivating a systematic design approach.
Method
The paper uses a multi-stage design that creates a multidimensional mother constellation, applies lattice rotation, and then applies layer-specific operators to build sparse codebooks.
Results
SCMA outperforms LDS, OFDMA, and SC-FDMA, with a gain over 2 dB compared to OFDMA and SC-FDMA in uplink fading channels.
Takeaways & Limitations
SCMA retains LDS benefits such as overloading and moderate-complexity detection while avoiding LDS's poor link performance, according to the paper's conclusion.
Abstract
from arXiv · showhide
Multicarrier CDMA is a multiple access scheme in which modulated QAM symbols are spread over OFDMA tones by using a generally complex spreading sequence. Effectively, a QAM symbol is repeated over multiple tones. Low density signature (LDS) is a version of CDMA with low density spreading sequences allowing us to take advantage of a near optimal message passing algorithm (MPA) receiver with practically feasible complexity. Sparse code multiple access (SCMA) is a multi-dimensional codebook-based non-orthogonal spreading technique. In SCMA, the procedure of bit to QAM symbol mapping and spreading are combined together and incoming bits are directly mapped to multi-dimensional codewords of SCMA codebook sets. Each layer has its dedicated codebook. Shaping gain of a multi-dimensional constellation is one of the main sources of the performance improvement in comparison to the simple repetition of QAM symbols in LDS. Meanwhile, like LDS, SCMA enjoys the low complexity reception techniques due to the sparsity of SCMA codewords. In this paper a systematic approach is proposed to design SCMA codebooks mainly based on the design principles of lattice constellations. Simulation results are presented to show the performance gain of SCMA compared to LDS and OFDMA.
I. INTRODUCTION
SCMA combines bit mapping and sparse spreading into layer-specific multidimensional codebooks, retaining LDS-compatible detection benefits while adding shaping gain. The paper proposes a systematic lattice-based design procedure for these codebooks.
- SCMA structure: SCMA directly maps incoming bits to sparse multidimensional complex codewords, with a dedicated codebook for each layer.This merges QAM mapping and CDMA/LDS spreading into one operation.
- SCMA structure: Sparse SCMA codewords enable iterative MPA detection with moderate complexity, including overloaded systems where layers exceed spreading resources.The factor graph limits the number of colliding layers at each resource node.
- Motivation: SCMA uses multidimensional codebooks instead of QAM modulation followed by LDS repetition, providing shaping or coding gain while retaining LDS overloading benefits.The paper identifies multidimensional shaping as a source of improved spectral efficiency relative to LDS.
- Proposed direction: The proposed procedure designs a multidimensional constellation with a good Euclidean distance profile, rotates it for product distance, and applies layer-specific operators to form sparse codebooks.The procedure is motivated by lattice code design for fast-fading point-to-point communication.
- SCMA structure: An SCMA encoder maps log_2(M) bits to a K-dimensional complex codebook of size M, with codewords sharing K−N zero dimensions.A mapping matrix places the nonzero constellation dimensions into the K-dimensional codeword.
III. SCMA CODEBOOK DESIGN
SCMA codebook design is formulated as a multidimensional optimization over constellation and mapping structure. Because the full criterion and solution are unknown, the paper uses a multi-stage approach to obtain a sub-optimal design.
- Optimization formulation: The SCMA code design problem jointly optimizes the mapping structure and codebook-related variables under a specified design criterion.The formulation is expressed for an SCMA code with parameters (J, M, N, K).
- Optimization formulation: A multi-stage optimization approach is proposed because the appropriate multidimensional design criterion and its solution are unknown.The resulting design is explicitly characterized as sub-optimal.
A. Mapping Matrix
The mapping matrix determines which resources each sparse layer occupies and therefore how many layers interfere at each resource. A maximum-overloading construction inserts zero rows into the nonzero mapping structure.
- Mapping matrix: Mapping matrices determine the number of layers interfering at each resource node, which in turn determines MPA detection complexity.Sparser codewords reduce the number of interfering branches and lower detection complexity.
- Mapping matrix: For maximum overloading, the construction inserts K−N all-zero row vectors among the rows of the mapping matrix.The resulting structure constrains the overlap between distinct resource-occupancy vectors.
B. Constellation Points and Multi-dimensional Mother
The paper designs SCMA mother constellations by combining Euclidean-distance, product-distance, and complexity considerations. It uses lattice-based constructions, real–imaginary shuffling, and rotation to balance performance with detection complexity.
- Design Metrics: SCMA constellation design must induce dependency among codeword dimensions so colliding layers can be recovered from other tones.Power imbalance across dimensions also creates near-far effects among colliding layers.
- Constellation Design: The design starts from a multidimensional constellation with a good Euclidean distance profile, then rotates it to obtain reasonable product distance.The rotation follows fast-fading code-design principles while preserving the Euclidean distance profile.
- Rotated Lattice Constellations: Lattice constellations provide a structured base construction, including Cartesian products of orthogonal QAM planes and Gray labeling.Unitary rotations of QAM lattices are used to optimize minimum product distance in dimensions 2 to 4.
- Shuffling Multi-dimensional Constellations: Separating real and imaginary components can reduce MPA complexity from M_d_f to M_d_f/2 while maintaining the multidimensional constellation's dependency structure.The shuffling constructs a complex mother constellation from Cartesian products of two N-dimensional real constellations.
- Rotation to Minimize Projection Points: Rotation to reduce projected points requires a trade-off because minimizing projections can make minimum product distance zero and degrade high-SNR performance.The method therefore balances high-SNR performance against MPA complexity.
C. Constellation Function Operato
SCMA codebooks are built from a shared mother constellation and layer-specific operators. These operators can adjust phase rotation and layer power, with phase design especially relevant for downlink collision avoidance.
- SCMA layer codebooks are constructed from a mother constellation and a layer-specific operator.
- Layer-specific operators may include phase rotation and layer power offset.
- In downlink layers sharing the same channel, carefully designed phase rotations and power levels can avoid destructive codeword collisions.
IV. NUMERICAL RESULTS
The numerical-results section studies SCMA at link level and establishes its performance gain over LDS and OFDMA.
- The study evaluates SCMA link-level performance.
- SCMA is evaluated against LDS.
- SCMA is evaluated against OFDMA, with the comparison establishing performance gain over both baselines.
A. Dimensional Power Variation of SCMA Codewords
SCMA codewords use dimensional power variation, unlike LDS. The rotated-lattice-derived variation helps the MPA receiver cancel inter-layer interference more efficiently.
- Unlike LDS, SCMA codewords transmit signals with different powers across their non-zero tones.
- This power variation is identified as a benefit of the rotated lattice constellation.
- Power variation helps MPA operate more efficiently when cancelling inter-layer interference.
B. Constellation Shaping Gain
SCMA’s multi-dimensional codebooks provide shaping gain over LDS repetition coding, particularly for larger constellations such as 16QAM. This advantage is evaluated alongside SCMA’s dimensional power variation for interference cancellation.
- Shaping gain: SCMA’s 16-point multi-dimensional codebooks provide shaping gain compared with the repetitive 16QAM constellation used by LDS.The comparison uses two layers, turbo code rate 0.5, and an overall rate of 1 bit/tone.
C. Performance in Uplink Fading Channels
Uplink simulations in a SIMO pedestrian-B fading channel compare SCMA with LDS, OFDMA, and SC-FDMA under matched spectral-efficiency and transmit-power conditions. SCMA achieves the strongest reported performance, including a gain above 2 dB over OFDMA and SC-FDMA, with goodput gains increasing at higher SNR.
- Simulation setup: The evaluation uses uplink transmission over a pedestrian B fading channel with one transmit and two uncorrelated receive antennas.The carrier frequency is 2.6 GHz, tone spacing is 15 kHz, and the payload occupies 24 LTE resource blocks.
- BLER comparison: SCMA outperforms LDS, OFDMA, and SC-FDMA in uplink BLER performance, with a gain over 2 dB versus OFDMA and SC-FDMA.The comparison fixes spectral efficiency at 1.5 bits/tone, selects the best MCS and layer count for each waveform, and uses equal total transmit power.
- Goodput comparison: SCMA goodput exceeds LDS and OFDM across a wide SNR range, and its gain grows as SNR increases.For each SNR, the appropriate MCS and number of layers are selected for each waveform.
V. CONCLUSION
The paper concludes with a systematic multi-stage SCMA codebook design based on lattice rotation and layer-specific operators. Simulations show gains over LDS and OFDMA while retaining key LDS multi-access and detection benefits.
- Codebook design: The proposed design begins with a lattice-based mother constellation and applies rotation to induce dimensional dependency and power variation.The rotation maintains the Euclidean distance profile while shaping the constellation for SCMA.
- Codebook design: Layer-specific operators are then applied to the mother constellation to construct a codebook for every SCMA layer.The conclusion describes this as part of the proposed systematic multi-stage procedure.
- Performance: Simulations show SCMA gains over LDS and OFDMA in both AWGN and fading channels.The reported conclusion covers both channel conditions rather than a single evaluation setting.
- Performance: SCMA retains LDS benefits including overloading, moderate detection complexity, and interference whitening while avoiding LDS’s poor link performance.The conclusion frames these as combined multi-access benefits of the proposed approach.