# Superimposed Perfect Binary Array-Aided Channel Estimation for OTFS Systems
## 1 Introduction  
As one of the most widely adopted multicarrier modulation systems, orthogonal frequency-division multiplexing (OFDM) offers the advantages of anti-frequency selectivity and high spectral efficiency (SE). In high-mobility scenarios, however, time-varying channels with high Doppler spread severely affect OFDM performance [1, 2, 3]. Hence, in [4, 5], [PERSON] et al. derived orthogonal time-frequency space (OTFS) modulation, which can address the above limitations. Unlike classic OFDM, by mapping data symbols into the delay-Doppler (DD) domain instead of the time-frequency (TF) domain [6], OTFS converts doubly selective channels into stable and sparse channels in the DD domain. In this way, all transmitted symbols experience near-constant channel gain [7, 8]. Therefore, at the receiver side, the complexity of channel estimation and data detection is reduced. Furthermore, OTFS is compatible with existing multicarrier modulations through pre- and post-processing modules [9, 10, 11]. Accurate channel estimation at the receiver is a precondition for OTFS data detection. The current channel estimation methods can be roughly divided into three categories. The first category uses the entire OTFS frame as the pilot for channel estimation, and the estimated information is used for data detection in next frame, which can be represented by the method of [12]. However, the performance of these methods may be degraded because the channel estimation easily becomes outdated in the following frame for rapidly time-varying channels. The second category is the embedded pilot (EP) channel estimation method proposed in [13]. By embedding a single pilot symbol in the DD domain and setting an appropriatethreshold for its response, high-precision channel estimation is achieved. In [14; 15; 16], the EP concept was redesigned to improve the channel estimation performance. However, guard symbols are always needed in this channel estimation category to avoid interference between pilot and data symbols, which results in SE loss. The third category is the superimposed pilot (SP)-based channel estimation method proposed in [17; 18]. In this method, the pilot symbols are superimposed onto the data symbols, and the guard symbols in the second category are no longer needed. This mitigates the SE loss. In the method of [17], the complex channel gains were estimated by treating the data as interference; in addition, iteration between channel estimation and data detection was adopted to prevent performance degradation at high SNRs. However, the delay-Doppler taps of the channel must be estimated by means of an additional non-superimposed EP frame for the following SP-aided frames, as they can only estimate the complex channel gains in this method. In rapidly delay-Doppler varying communication scenarios, this SP method exhibits lower adaptability when compared to that of the EP method. As an alternative approach, [PERSON]. [18] proposed a method that utilized the whole frame for data transmission, and a single pilot symbol was superimposed onto the data symbol. This pilot design is similar to the EP method in the second category. In [18], no dedicated DD domain grids were occupied for channel estimation; however, since pilot and data symbols were superimposed, the interference between them was unavoidable. As a result, an iterative process must be adopted to mitigate this interference. In this paper, we propose an OTFS channel estimation method based on the superimposed perfect binary array (SPBA). The main contributions of this paper are as follows:  
1. In the proposed SPBA method, the whole OTFS frame is used for data transmission, while a perfect binary array (PBA) that plays the role of the pilot is superimposed on data symbols in the DD domain, resulting in higher SE when compared to that of the EP scheme in [11].