# Deep-Unfolded Tikhonov-Regularized Conjugate Gradient Algorithm for MIMO Detection
## 5 Simulation Results  
Within this section, several MIMO layouts over different channel conditions and modulation orders are discussed to demonstrate the performance of the proposed DU-TCG detection method. In particular, the simulation results highlight the detection performance improvement of the DU-TCG over well-known approaches such as the MMSE, CG, and LCG. Unless otherwise stated, BPSK modulation is used for the sake of simplicity, as it allows a straightforward evaluation of the behavior of the algorithm and a demonstration of its core performance. Bit error rate (BER) and normalized mean square error (NMSE) metrics are employed to illustrate the superiority of the proposed method over the discussed other methods. Figure 4 compares the BER performance of the proposed DU-TCG method with other methods, namely MMSE, CG, LCG, and ideal ML detector over a Rayleigh fading channel for a BPSK modulated 10 \(\times\) 10 MIMO system. Figure 4 shows that although the ML detector offers the lowest bit error rates, the proposed DU-TCG can perform better than other gradient-based techniques such as CG, and LCG and traditional MMSE, which makes it a promising candidate for practical applications. The proposed DU-TCG method has approximately 4 dB SNR gain over CG and LCG methods at BER values of 10\({}^{-3}\). In Figure 4, all methods except ML have poor BER performance at low SNR values as expected. Unlike ML, iterative methods are more affected by low SNR values during the initial iterations, leading to suboptimal results. Figure 5 shows that the proposed DU-TCG method outperforms CG and LCG for different number of layers in the 10 \(\times\) 10 MIMO layout. As shown in Figure 5, DU-TCG exhibits better BER performance with both 5 and 15 layers, compared to the CG and LCG methods. Although the performance of the CG and LCG improves when the number of layers is increased by 3 times, DU-TCG still outperforms these methods. However, as the complexity of the system is directly related by the number of layers, the results show that DU-TCG is a better candidate in terms of system cost. Besides the conventional MIMO scheme and channel models discussed above, in Figure 6, we also compare the performance of DU-TCG with Kronecker, TDL-A, and TDL-E channel models for the 32 \(\times\) 64 MIMO scheme with BPSK modulation. Since the channel conditions are challenging, 15 layers are used here in the training process. Figure 4: BER performance for a 10 \(\times\) 10 MIMO system. For Kronecker, TDL-A, and TDL-E channel models, both the proposed DU-TCG and existing LCG methods do not have a sufficient detection performance. However, DU-TCG still outperforms the LCG for all three channel models. DU-TCG has employed the benefit of Tikhonov regularization's superiority for the ill-posed problems, and DU-TCG's sophisticated regularization mechanism significantly improves the detection process compared to the LCG method. Figure 7 presents the BER performance of CG, LCG, and the proposed DU-TCG methods for BPSK and QAM16 modulation types for a 32 \(\times\) 128 MIMO layout in TDL-A channel. It is well known that the performance of iterative detection methods increases significantly when the number of receiving antennas is much greater than the number of transmitting antennas, and this effect is reflected in our simulation results using the DU-TCG, LCG, and CG methods. Figure 7 shows the results of the system with such a MIMO structure. The detection performance of LCG is close to DU-TCG for lower-order modu  
Figure 5: BER performance for different number of layers: (**a**) 5 layers; (**b**) 15 layers. Figure 6: BER performance over different channel models: Kronecker, TDL-A, and TDL-E.  
lations in a difficult channel condition such as TDL-A, while DU-TCG outperforms LCG for a higher-order modulation. The figure demonstrates that the BER of DU-TCG is up to 1.2 times better than LCG when using BPSK modulation under TDL-A fading and up to 8.3 times better when using 16-QAM modulation.