## 6 Simulation Results  
Computer simulations were carried out to evaluate the proposed algorithm's performance in multipath scenarios. To this end, we draw the BER versus the signal-to-noise ratio (SNR) curves. We consider a \((3,6)\)-regular LDPC code of length 4000. The modulation format is B-PAM. In the distributed pilots, one pilot is inserted in every 20 successive symbols, while in the concentrated one a group of 100 pilots is inserted before and after the LDPC Packet. In a baseband communication system, pulse shaping was carried out using a raised cosine filter with a filter span of 10 per symbol, samples of 16 per symbol, i.e., dividing the symbol duration to 16 (16 possible _PE_s), and the roll-off factor of 0.5. We assumed that the symbol duration is much smaller than the coherent time of the channel; thus, no Doppler effect (otherwise, the baseband pulses will be broadened at the receiver, due to the Doppler effect). We also considered the transmitter and receiver filter delays in our simulations. Attenuation coefficients were randomly chosen from a set of 100 numbers in the range of \([0:99]\times\frac{1}{100}\). Please confirm this revision. To simplify the algorithm, we assume that LOSalways exists. The delay profile of the channel follows a Weibull distribution with a scale parameter of 1 and a shape parameter of 0.4. We consider code rate in the computation of noise variance at the receiver. We also set the minimum error packets to 100, detector iterations to 10, maximum number of decoder iterations to 200, and global iterations of the receiver to 5 and 30. We used lookup tables to compute the means of Gaussian likelihoods according to the explained instructions in this paper. Figures 2-5 show the simulation results for the distributed and concentrated pilots. The curve labelled by \"LDPC\" was obtained through pulse shaping, matched filtering and LDPC decoding in an AWGN channel. The name of the rest of the curves is based on their multipath numbers and global iterations of the receiver, e.g., 3-DD Glob. It. 5 represents joint detection and decoding in a scenario involving three unknown overlapping paths and 5 overall receiver iterations. The relative solution is obtained through 200 iterations of the decoder and single iteration of the receiver where the observations are computed by \(\exp\left\{-\frac{(\eta_{2}-\alpha_{2})^{2}}{2\sigma^{2}}\right\}\). \(\sigma^{2}\) is inversely proportional to the average power of the received signal. The relative solution can be used to compare the performance of various algorithms in the multipath scenario. The more an algorithm outperforms the relative solution, the more accurate it is. As the receiver lacks knowledge of the channel parameters, previous methods have been unable to track them, requiring changes to existing algorithms. In response, we present a relative solution that establishes an upper bound for system performance. For simplicity, the simulation assumes that only the number of interfering paths remains fixed at each time epoch. The results indicate that the performances of distributed and concentrated pilots are nearly identical under the same conditions. In the scenario with two overlapping paths, the proposed algorithm experiences a degradation of 0.6 dB compared with LDPC, and in the scenario with three overlapping paths, this degradation increases to 1 dB. However, in every case, the proposed algorithm outperforms the relative solution by 0.2 dB. Although the difference between 5 and 30 iterations of the receiver is negligible for two overlapping paths, as the number of unknown paths increases, the difference becomes more significant. Figure 2: 2-JDD in the distributed pilots, including the lower and upper bounds (LDPC and relative solution). Figure 4: 2-JDD in the concentrated pilots, including the lower and upper bounds (LDPC and relative solution). Figure 3: 3-JDD in the distributed pilots pilots, including the lower and upper bounds (LDPC and relative solution).