*3.3. Off-Line DSP Blocks*

The block diagram of the off-line DSP is illustrated in Figure 3a,e. In the Tx-side DSP, a QPSK symbol mapping and a raised-cosine (RC) filter with a roll-off factor of 0.01 are deployed, as shown in Figure 3a. Figure 3e depicts the four DSP options at the Rx side, verifying the validity of the J-DBN-based equalization schemes. Conventional, Opt. 1: the captured signal is offline, proposed by typical DSP steps including downconversion into baseband, resampling, Gram–Schmidt orthogonalization process (GSOP), followed by 53-tap CMA equalization. Then, the frequency offset noise can be mitigated via frequency offset estimation (FOE), and the phase offset problem can be solved after carrier phase recovery (CPR). Finally, a 37-tap DD-LMS equalizer is added to compensate for the remaining linear damage and I/Q imbalance before BER calculation.

We also compare the BER performance between the CMA equalizer, DBN-based equalizer, and J-DBN equalizer within these DSP steps. In Opt. 2, the adaptive DBN-1 equalizer adapts itself to compensate for the nonlinear distortion. It extracts the signal sequences' characteristics based on the BP algorithm and blind CMA algorithm. The scheme can reduce the sizeable residual error after convergence, which is suitable for the nonlinear channel balance. In Opt. 3, the blind DBN-2 equalizer optimizes the weight value and tap number based on the BP algorithm and DD-LMS equalizer. Moreover, the DBN-2 equalizer can utilize the weight value updated by the DBN-1 as the initial value. The scheme can further compensate for the remaining linear damage and nonlinear decision ability. In Opt. 4, the J-DBN equalizer combines two error cost functions, which is more helpful in handling the receiver sensitivity issue in THz-band wireless links and achieving a more accurate BER decision. Moreover, the J-DBN equalizer can be established via two steps. Firstly, it can be initialized with the aid of the training sequence, and then the weight value can be further optimized by employing the error function of CMA. Adopting our proposed J-DBN equalizer, both the lengths of the training data and the training time can be effectively reduced.

#### **4. Experimental Results and Discussion**

As we know, a well-designed equalizer is useful for resolving nonlinear issues and has been successfully applied in wireless communications. However, the selection of an error function is an important factor that affects the residual error of the blind equalizer; thus, the performance of the equalizer is different. In our experiment, we introduce some

equalizers in our proposed schemes and compare their performance, such as the typical CMA equalizer with taps and the DD-LMS equalizer.
