[Paper Review] Coding for Two-User SISO and MIMO Multiple Access Channels

J. Harshan, B. Sundar Rajan|ArXiv.org|Jan 1, 2009

Advanced Wireless Communication Techniques22 references10 citations

TL;DR

This paper proposes rotation-based signaling and trellis-coded modulation (TCM) schemes for two-user SISO and MIMO multiple access channels (MAC) with finite constellations, achieving near-capacity sum rates and significantly reduced ML decoding complexity. For SISO MAC, it introduces a rotation metric to maximize constellation-constrained (CC) capacity region and proves that Ungerboeck labeling on rotated M-PAM pairs maximizes sum-trellis distance. For MIMO MAC, it designs space-time block code (STBC) pairs from real orthogonal designs (RODs) that enable single-symbol decoding with perfect interference cancellation and low complexity, validated via BER simulations showing superior performance over alternative designs.

ABSTRACT

Constellation Constrained (CC) capacity regions of a two-user SISO Gaussian Multiple Access Channel (GMAC) with finite complex input alphabets and continuous output are computed in this paper. When both the users employ the same code alphabet, it is well known that an appropriate rotation between the alphabets provides unique decodability to the receiver. For such a set-up, a metric is proposed to compute the angle(s) of rotation between the alphabets such that the CC capacity region is maximally enlarged. Subsequently, code pairs based on Trellis Coded Modulation (TCM) are designed for the two-user GMAC with $M$-PSK and $M$-PAM alphabet pairs for arbitrary values of $M$ and it is proved that, for certain angles of rotation, Ungerboeck labelling on the trellis of each user maximizes the guaranteed squared Euclidean distance of the extit{sum trellis}. Hence, such a labelling scheme can be used systematically to construct trellis code pairs for a two-user GMAC to achieve sum rates close to the sum capacity of the channel. More importantly, it is shown for the first time that ML decoding complexity at the destination is significantly reduced when $M$-PAM alphabet pairs are employed with extit{almost} no loss in the sum capacity. \indent A two-user Multiple Input Multiple Output (MIMO) fading MAC with $N_{t}$ antennas at both the users and a single antenna at the destination has also been considered with the assumption that the destination has the perfect knowledge of channel state information and the two users have the perfect knowledge of only the phase components of their channels. For such a set-up, two distinct classes of Space Time Block Code (STBC) pairs derived from the well known class of real orthogonal designs are proposed such that the STBC pairs are information lossless and have low ML decoding complexity.

Motivation & Objective

• To compute the Constellation-Constrained (CC) capacity region of a two-user SISO Gaussian MAC with finite complex input alphabets and continuous output.
• To design TCM-based code pairs for M-PSK and M-PAM input alphabets that achieve sum rates close to the CC sum capacity.
• To reduce the maximum-likelihood (ML) decoding complexity at the receiver in two-user SISO and MIMO MAC by exploiting alphabet rotation and signal set design.
• To propose STBC pairs for a two-user MIMO fading MAC with single-antenna destination and perfect phase-CSIT, enabling low-complexity single-symbol decoding.
• To establish theoretical and simulation-based performance gains in terms of CC capacity, coding gain, and BER for the proposed schemes.

Proposed method

• Proposes a metric to compute the optimal rotation angle between identical signal sets (e.g., M-PSK or M-PAM) at two users to maximize the CC capacity region of a SISO MAC.
• Designs TCM-based code pairs using Ungerboeck partitioning on trellises, proving that for specific rotation angles, the sum-trellis minimum squared Euclidean distance is maximized.
• Employs M-PAM signal sets with rotated constellations to achieve near-CC capacity with significantly reduced ML decoding complexity compared to complex constellations.
• Proposes two classes of STBC pairs derived from real orthogonal designs (RODs) for a two-user MIMO MAC with Nt antennas per user and single-antenna destination.
• Designs STBC pairs such that each real symbol is decodable independently in R, enabling single-symbol ML decoding and eliminating inter-user interference.
• Validates the performance of the proposed STBC pairs via BER simulations over Rayleigh fading channels with Nt = 2 and Nt = 4, comparing ROD-based and SOD-based designs.

Experimental results

Research questions

• RQ1 What is the optimal rotation angle between identical signal constellations at two users in a SISO MAC that maximizes the Constellation-Constrained (CC) capacity region?
• RQ2 Can Ungerboeck labeling on trellises of users with rotated M-PAM constellations maximize the minimum squared Euclidean distance of the sum trellis, thereby improving coding gain?
• RQ3 To what extent does using M-PAM instead of complex constellations reduce ML decoding complexity in a two-user SISO MAC with no loss in sum capacity?
• RQ4 Can STBC pairs derived from real orthogonal designs (RODs) be constructed for a two-user MIMO MAC with phase-CSI at users and perfect phase-CSIT to enable single-symbol decoding?
• RQ5 How does the BER performance of ROD-based STBC pairs compare to SOD-based STBC pairs in terms of coding gain and decoding complexity?

Key findings

• The proposed rotation metric successfully identifies angles that maximize the CC capacity region for two-user SISO MAC with identical M-PSK and M-PAM constellations.
• For M-PAM alphabet pairs with optimal rotation, Ungerboeck labeling on individual trellises maximizes the guaranteed minimum squared Euclidean distance of the sum trellis, ensuring robust error performance.
• Using M-PAM signal sets with appropriate rotation reduces ML decoding complexity at the destination by up to a factor of 4 compared to complex constellations, with negligible loss in sum capacity.
• STBC pairs derived from real orthogonal designs (RODs) enable single-symbol maximum-likelihood decoding for both users in a two-user MIMO MAC, achieving full diversity and zero inter-user interference.
• BER simulations show that ROD-based STBC pairs outperform SOD-based STBC pairs for both Nt=2 and Nt=4, with gains attributed to independent real-symbol decoding and absence of interference.
• The proposed schemes achieve sum rates close to the theoretical CC sum capacity of the channel, particularly when using M-PAM with optimal rotation and Ungerboeck labeling.