# Early Neighbor Rejection-Aided Tabu Search Detection for Large MIMO Systems
## 4 Simulation Results  
In our experiments, the BER performance and computational complexity of the proposed ENR-TS with a layer ordering scheme were evaluated for various MIMO configurations. Although Section 3.1 describes the proposed ENR-QR-TS scheme, it can also be applied to the original TS without QR decomposition. In the simulation results, ENR-QR-TS represents the former and ENR-TS the latter. The ENR-QR-TS scheme can be incorporated with a layer ordering scheme, as explained in Section 3.2. The complexities of the proposed ENR-TS algorithms are compared with that of the conventional TS algorithm. The total computational complexity was measured by summing the average number of real multiplications, additions, comparisons, and sorting operations. In the simulations, we used two MIMO configurations: \((N_{r},N_{t},\Omega)=(16,16,4)\) and \((32,32,4)\), where the number of iterations \(M\) are 400 and 800, respectively. The number of excluded neighbors in each layer is \(k=1\) and 2.  
Figure 2 shows the BER comparison results for a MIMO system with \(N_{r}=16\), \(N_{t}=16\) and 4-QAM. We can observe that the performance of the proposed ENR-TS algorithms is almost the same as that of the conventional TS. Figure 3 compares the BER performance for \(N_{r}=32\), \(N_{t}=32\), and 4-QAM. Similarly to Figure 2, this figure demonstrates that the ENR-TS and ENR-QR-TS schemes achieve a BER performance nearly identical to that of conventional TS scheme. It is worth noting that the ENR-QR-TS algorithm with the layer ordering scheme also performs nearly as well as the conventional QR-TS. Moreover, the ENR-QR-TS scheme with \(k=2\) achieves comparable BER performance with respect to the conventional TS.  
Figure 2: Comparison of the BER performance of TS algorithms for a \(16\times 16\) MIMO system with 4-QAM.  
Figure 4 shows the complexity comparison for a MIMO system with \(N_{r}=16\), \(N_{t}=16\), and 4-QAM. Figure 4 shows that the ENR-QR-TS with layer ordering requires the lowest complexity of the compared schemes. Specifically, compared with the conventional TS, the ENR-QR-TS with layer ordering at \(\text{SNR}=12\) dB reduces complexity by approximately 73%, while achieving almost the same BER performance. The QR-ENR-TS scheme provides a 33% reduction in complexity compared with the conventional QR-TS.  
Figure 5 illustrates the comparison of the complexity of a MIMO system with \(N_{r}=32\), \(N_{t}=32\), and 4-QAM. Similarly to Figure 4, this figure shows that the proposed ENR-QR-TS scheme reduces complexity significantly compared to the conventional TS and QR-TS algorithms. With layer ordering at \(\text{SNR}=12\) dB, the ENR-QR-TS with \(k=2\) reduces the complexity of the conventional TS by about 82%. At \(\text{SNR}=12\) dB, the ENR-QR-TS scheme with \(k=2\) achieves a complexity reduction of approximately 70% compared to the QR-TS.  
Figure 4: Comparison of the computational complexity of TS algorithms for a 16 \(\times\) 16 MIMO system with 4-QAM.  
Figure 3: Comparison of the BER performance of TS algorithms for a \(32\times 32\) MIMO system with 4-QAM.