# A* Algorithm Inspired Memory-Efficient Detection for MIMO Systems

TL;DR: Modified best-first detection algorithms in which the order of nodes is determined by both the original cost and the estimated future cost associated with each node are proposed, as inspired by an improved shortest path algorithm (A* algorithm).

Abstract: Implementation of a best-first detection algorithm for multiple-input multiple-output (MIMO) systems requires large amounts of memory especially in large systems with high-order modulation. In this letter, we propose modified best-first detection algorithms in which the order of nodes is determined by both the original cost and the estimated future cost associated with each node, as inspired by an improved shortest path algorithm (A* algorithm). The modified algorithms maintain the detection optimality, reduce the memory requirement and sorting complexity, and achieve improved detection performance in memory-constrained scenarios.

## Summary (1 min read)

### Introduction

- Best-first search (BFS) detection schemes [2]–[6] based on the Dijkstra’s (or ) algorithm maintains a list of nodes sorted in some defined cost and explores the nodes in such order.
- Imposing a memory constraint [6] facilitates hardware implementation and reduces the search complexity at the cost of some performance degradation.
- The proposed methods are described Manuscript received June 18, 2012.

### II. TRANSMISSION SYSTEM AND BEST-FIRST DETECTION

- Transmitted symbol vector x̃c contains uncorrelated entries selected equiprobably from the squared quadrature amplitude modulation (QAM) alphabet S = {a + ib | a, b ∈ Q} and has zero mean and covariance matrix σ2xINT , where Q is the pulse amplitude modulation (PAM) alphabet and INT is the NT ×NT identity matrix.
- Hc has independent and identically distributed (i.i.d.).
- Gaussian entries with zero mean and covariance matrix σ2HINR , where σ2H = 1.
- The channel information is assumed perfectly known to the receiver.
- The authors reach (9) by rewriting the objective function, where the second and third terms do not depend on xk−11 .

### A. Complexity Evaluation

- Here, the authors evaluate the overall computational complexity of the proposed algorithms in comparison with conventional methods.
- Since all processing is conducted on real values based on (2), all the calculations below refer to real operations.
- The complexity of a tree-search detection scheme is evaluated in terms of the number of nodes visited and expanded (defined respectively by nodes that ever occupy a position and become the best node in the node list).
- Similar calculations can be carried out for the BFS-LA2 algorithm.

### B. Simulation Results

- Here, the authors present the simulation results: symbol error rate (SER) performance in Fig. 1, memory usage in Fig. 2, and complexity in terms of floating-point operations in Table I (one real multiplication/addition each counts a flop).
- Similar observations can be made in Fig. 1(b).
- Fig. 2 illustrates the memory-reduction capability of the proposed schemes.

### V. CONCLUSION

- Modified BFS-based MIMO detection algorithms incorporating an efficient look-ahead mechanism have been presented.
- Simulation results demonstrated that the proposed algorithms maintain exact ML detection capability while achieving memory savings and enhanced performance in memory-constrained scenarios.
- Complexity analysis was conducted to confirm the computational feasibility of the proposed algorithms.

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##### References

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...THE PROPOSED BEST-FIRST DETECTION ALGORITHMS The A∗ algorithm [8] speeds up the search of the shortest path in a graph by considering both the travelled distance thus far and the estimated distance ahead (the heuristic)....

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...In this letter, we propose an optimal BFS detection scheme inspired by the A∗ algorithm [8] which speeds up the original Dijkstra’s algorithm without losing algorithm optimality (shortest path is guaranteed)....

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...The more accurate is the estimate, the better performance of the algorithm can be achieved [9]....

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...Best-first search (BFS) detection schemes [2]–[6] based on the Dijkstra’s (or stack) algorithm maintains a list (stack) of nodes sorted in some defined cost and explores the nodes in such order....

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