Ising Machines' Dynamics and Regularization for Near-Optimal Large and Massive MIMO Detection

TL;DR

This work tackles the challenge of near-optimal MIMO detection with computationally tractable methods by mapping ML-MIMO into an Ising problem and deploying Coherent Ising Machines (CIMs). The authors introduce Regularized Ising MIMO (RI-MIMO) to suppress an error floor inherent in prior Ising-based detectors and extend it with a tree-search extension (TRIM) for higher-order modulations. Through CIM simulations and extensive evaluation, RI-MIMO and TRIM demonstrate substantial BER improvements and significant throughput gains over MMSE, especially in large and massive MIMO settings, while highlighting hardware-throughput considerations for practical CIM implementations. The results indicate that a CIM-based detector, with appropriate regularization and hierarchical search, can approach near-optimal detection in realistic wireless scenarios, potentially enabling higher user densities and modulation schemes before quantum hardware maturity. Practical deployment will require parallel CIM resources and careful precision management, but the framework presents a promising path toward scalable, high-performance MIMO detection beyond traditional linear receivers.

Abstract

Optimal MIMO detection has been one of the most challenging and computationally inefficient tasks in wireless systems. We show that the new analog computing techniques like Coherent Ising Machines (CIM) are promising candidates for performing near-optimal MIMO detection. We propose a novel regularized Ising formulation for MIMO detection that mitigates a common error floor problem and further evolves it into an algorithm that achieves near-optimal MIMO detection. Massive MIMO systems, that have a large number of antennas at the Access point (AP), allow linear detectors to be near-optimal. However, the simplified detection in these systems comes at the cost of overall throughput, which could be improved by supporting more users. By means of numerical simulations, we show that in principle a MIMO detector based on a hybrid use of a CIM would allow us to add more transmitter antennas/users and increase the overall throughput of the cell by a significant factor. This would open up the opportunity to operate using more aggressive modulation and coding schemes and hence achieve high throughput: for a $16\times16$ large MIMO system, we estimate around 2.5$\times$ more throughput in mid-SNR regime ($\approx 12 dB$) and 2$\times$ more throughput in high-SNR regime( $>$ 20dB) than the industry standard, Minimum-Mean Square Error decoding (MMSE).

Figures (14)

• Figure 1: Uplink Maximum Likelihood MIMO detection (ML-MIMO) using Ising Machines, illustrating the differences between the proposed regularised Ising approach and the direct application of the Ising formulation.
• Figure 2: Bit Error Rate (BER) Curves for (Left) 16$\times$16, (Center) 20$\times$20, (Right) 24$\times$24 MIMO and BPSK modulation, illustrating the error floor problem and performance of various solvers.
• Figure 3: BER vs. $N_a$ for (A) $16\times16$, (B) $20\times20$ MIMO and BPSK modulation at 5, 7.5 and 10 dB SNR: Illustrating that the BER of RI-MIMO reduces rapidly with increase in number of anneals per instance and asymptotically approaches the optimal BER. (C) N$_a$TB vs. MIMO Size ($N$) for $N\times N$ large MIMO systems: Illustrating the exponential growth in the number of anneals required to achieve a BER which is $1.1\times$, $1.2\times$ and $1.5\times$ the optimal BER.
• Figure 4: Bit Error Rate at 10 dB and 15 dB SNR , illustrating the performance of RI-MIMO on Coherent based Ising Machines (CIM) for various value of regularisation factor with different MIMO sizes and modulation (using 64 anneals per instance).
• Figure 5: Bit Error Rate Curves higher order modulation schemes, illustrating the performance of RI-MIMO and TRIM on Coherent based Ising Machines (CIM). TRIM executes total 64 anneals for each instance (same as RI-MIMO-64).