# A Low Complexity Reactive Tabu Search Based Constellation Constraints in Signal Detection
## 4 Simulation Results  
In this part, we will shown the advantages of CC-RTS algorithm in terms of computational complexity and BER performance. The algorithm may approach the original RTS algorithm in terms of BER performance with various MIMO configurations. Meanwhile the proposed algorithm may significantly reduce the detection complexity of the traditional RTS algorithm for massive MIMO systems. To evaluate the achievable performance of the proposed scheme, we present our results based on MATLAB simulations. We set up a simulation model with the following parameters: the system is a MIMO using QPSK modulation with \(4\times 4\), \(8\times 8\), \(16\times 16\), \(24\times 24\) MIMO antennas. We assume that the transmitted signal encounters independent Rayleigh Fading in the propagation channels. The transmitted \(\widehat{\mathbf{s}}\) are grouped into frames consisting of 100,000 symbol vectors, and 100,000 Monte Carlo simulation is carried to produce the results. In addition, the following RTS parameters are also used in the simulations: MMSE initial vector, initial tabu length is 3, and Iterations is 20. These parameters are shown in Table 3.  
**Performance**: In Figures 2 and 3, we present the simulated BER performance of the proposed CC-RTS algorithm with various selection of \(d_{th}\) with Rayleigh channel. Figure 2 shows that the \begin{table}
\begin{tabular}{l l} \hline \hline
**Input: \(\mathbf{r}\), \(\mathbf{H}\), \(d_{th}\)** \\
**Output: \(\widehat{\mathbf{s}}_{best}\)** \\
**Initialization:** \\ \(\widehat{\mathbf{s}}_{soft}\)\(\leftarrow\) the output of MMSE \\ \(\widehat{\mathbf{s}}\)\(\leftarrow\) corresponding hard decision of \(\widehat{\mathbf{s}}_{soft}\) \\ \(\widehat{\mathbf{s}}_{temp}\)\(\leftarrow\)\(\widehat{\mathbf{s}}\) \\ \(Item\)\(\leftarrow\) Number of iterations \\ Best-so-far \(\leftarrow||\mathbf{r}-\mathbf{H}\mathbf{s}_{temp}||^{2}\) \\ P \(\leftarrow\) the length of **tabulist** \\
**Constellation Constraints:** \\ \(\mathbf{\mathrm{for}}\ i\gets 1\) to \(N_{t}\) do \\ \(j\gets i_{th}\) element of \(\widehat{\mathbf{s}}_{soft}\) \\ \(\mathbf{\mathrm{if}}\ j\) is unreliable \\ \(\mathbf{\mathrm{s}}\mathbf{\mathrm{it}}_{i}\gets 1\) \\ \(\mathbf{\mathrm{else}}\) \\ \(\mathbf{\mathrm{s}}\mathbf{\mathrm{it}}_{i}\gets 0\) \\ \(\mathbf{\mathrm{end}}\) \\
**end for** \\
**CC-RTS:** \\ \(\mathbf{\mathrm{it}}=1\) \\ \(\mathbf{\mathrm{while}}\ \mathbf{\mathrm{it}}\leq Item\) \\ \(\mathbf{\mathrm{cat-matrix}}\leftarrow[]\) \\ \(\mathbf{\mathrm{generate}}\ \mathbf{\mathrm{tabulist}}\ \mathrm{according}\ \mathbf{\mathrm{P}}\) \\ \(\mathbf{\mathrm{for}}\ k\gets 1\) to \(N_{t}\) do \\ \(\mathbf{\mathrm{if}}\ \mathbf{\mathrm{s}}\mathbf{\mathrm{it}}_{k}==1\) \\ \(\mathbf{\mathrm{cat}}\leftarrow\) the candidates of \(k_{th}\) element of \(\mathbf{\mathrm{s}}_{temp}\) \\ \(\mathbf{\mathrm{cat-matrix}}\leftarrow[\mathbf{\mathrm{cat-matrix}};\mathbf{\mathrm{cat}}]\) \\ \(\mathbf{\mathrm{end}}\) \\ \(\mathbf{\mathrm{end}}\) \\ \(\mathbf{\mathrm{end}}\) \\ \(\mathbf{\mathrm{Using}}\ \mathbf{\mathrm{s}}\mathbf{\mathrm{ simplified}}\ \mathbf{\mathrm{cat-matrix}}\) to perform traditional RTS algorithm \\ \(\mathbf{\mathrm{it}}=\mathbf{\mathrm{it+1}}\) \\ \(\mathbf{\mathrm{end}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The proposed CC-RTS algorithm. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Modulation** & **Channels** & **Symbol Vectors** & **Initial Tabu Length** & **Iterations** \\ \hline QPSK & Rayleigh Fading Channel & 100,000 & 3 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters. variation of BER as a function of the \(d_{th}\), with \(N_{t}=N_{r}=\) 4, 8, 16, 24, respectively, and all the simulations are with SNR = 8 dB. It can be observed from Figure 2 that, depending on the choice of the value of \(d_{th}\), BER and \(d_{th}\) rendering correlation. Figure 3 shows the performances of the proposed CC-RTS and reference RTS, with \(N_{t}=N_{r}=\) 4, 8, 16, 24, and \(d_{th}=\)0.02.