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

## 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

10,366 citations

### "A* Algorithm Inspired Memory-Effici..." refers methods in this paper

...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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### "A* Algorithm Inspired Memory-Effici..." refers methods in this paper

...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....

[...]

334 citations

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