As one of the most important and computationally-intensive parts in bioinformatics analysis, the Pair Hidden Markov Model (Pair-HMM) forward algorithm is widely recognized and has great potential. Therefore, it is important to accelerate the process of this algorithm. There are various approaches to accelerate Pair-HMM, especially the accelerators stemmed from the Field Programmable Gate Array (FPGA) due to the highly-customizable on-chip resources and deep pipeline potential available to the designer. In this paper, we focus on the FPGA-based accelerators for the Pair-HMM forward algorithm proposed in recent years. The non-cooperation structure, which was proposed in our previous work, is compared with the Systolic Array (SA) structure and PE ring structure in the structure characteristics, calculation mode, computational efficiency, and storage requirement. We build an analysis model to evaluate the performance of the ring structure and our non-cooperative structure. Furthermore, based on this, we provide a detailed analysis of the characteristics of structures of different accelerators and of the selection of a suitable structure for different scenarios. Based on the non-cooperative PE structure, we design a new chain topology for the accelerator. Experimental results show that our non-cooperation structure is superior to the other structures in performance and execution efficiency, and our new topology improves the performance of the accelerator. Finally, we propose some ideas about the improvement of the non-cooperative structure accelerator for future work.