## 1 Introduction
Then, the output of the first detector, which contains 1D interference, is supplied to the second detector to detect the 0/1 bits and recover the original data. In the serial detection, because the 2D target is analyzed into two 1D targets, we can easily use the conventional Viterbi algorithm (VA). In addition, to use the 1D VA for the 2D target, we use the intertrack-interference (ITI)/ISI estimator to remove the interference from neighboring tracks. The ITI and ISI are the parts of 2D interference in BPMR systems, as in Figure 2.  
When removing ITI/ISI, the received signal rests the 1D interference on the main track. Therefore, we can apply the 1D VA on the main track to restore the original data. In [23; 24], [PERSON] and [PERSON] proposed the ITI/ISI estimator for BPMR and HDS systems, respectively. The authors used the extended trellis to predict the ITI/ISI. The ITI/ISI estimator based on extended trellis achieved high BER performance for both BPMR and HDS systems. However, their model obtained very high complexity. To avoid using the extended trellis, [PERSON] and [PERSON] introduced a multilayered 2D GPR target [25]. In [25], the authors used  
Figure 1: Isolated patterns. Figure 2: ITI and ISI of 2D interference. three equalizers and targets. The first target was designed following the 1D form. With a 1D target, we can use the 1D VA for detection. In the second and third targets, a 2D form is exploited. Then, the output from 1D VA detection was used to predict ITI/ISI in the second and third targets. Serial targets and detection methods have also been applied to the HDS system by [PERSON] and [PERSON] [26]. As mentioned above, the serial structure in their study used the VA to detect the received signal. Therefore, to develop serial detection, in the present study, we propose a new detection algorithm based on the maximum a posteriori (MAP) algorithm to improve the BER performance in HDS systems. After distortion by the 2D interference in the HDS system, the received signal is converted by an equalizer into the desired target signal. The 2D target is analyzed into two serial targets: a 1D horizontal target and a 1D vertical target. The parameters of the horizontal and vertical targets are supplied to the first and second detectors, respectively. Based on the output of the equalizer, symbol information is estimated by the first detector. Dissimilar to the VA, which creates a hard output signal, the MAP algorithm creates a soft output signal. Therefore, the MAP algorithm can improve the BER performance of serial detection. Then, these values were supplied for the second detection step to restore the original bit. In the second detector, the algorithm is then modified to extract information from these symbols and supply it to the trellis. Symbol information is detected in the bit data during the second detector, and the original signal (bit information) is recovered. The bit information is also used to create a priori information about the symbol (probability of the symbols) and feedback for the first detection. This helps in creating an iterative algorithm for our proposed detection. The simulation results show that the proposed algorithm outperforms existing detection methods and significantly improves the BER performance of HDS systems. The remainder of this paper is organized as follows: In Section 2, we provide a brief review of the literature on MAP detection. Section 3 presents the proposed model using a MAP-based detection algorithm. Section 4 presents the simulation results and a performance evaluation of the proposed algorithm. Finally, in Section 5, we provide concluding remarks and discuss the implications of our study for the field of HDS.