# Efficient Low-Complexity Turbo-Hadamard Code in UAV Anti-Jamming Communications
## 1 Introduction  
Unmanned aerial vehicles (UAVs) have been applied extensively in a wide range of scenarios during the past decade [1; 2; 3; 4; 5; 6], as they represent a promising avenue of research, providing flexible deployment and on-demand mobility in a cost-effective way. In particular, UAVs are playing increasingly crucial roles in applications in which human lives would otherwise be endangered. As for military applications, UAVs become indispensable in reconnaissance [1], surveillance [2] and strikes [3]; meanwhile, UAVs are essential in disaster relief [4], remote sensing [5] and weather forecasting [6] in civil scenarios. The performance of UAVs depends heavily on the quality of wireless communication links between UAVs. However, UAVs' wireless communication links are vulnerable to jamming due to their exposed nature [7]. As a result, anti-jamming performance has become an important design metric for the wireless communication systems of UAVs. However, most existing research contributions on UAVs have focused on the analysis and improvement of their links and quality of servicen conditions without jamming [8; 9; 10; 11]. The quality of those wireless links can be particularly worsened in the complex electromagnetic environment of the battlefield. Hence, anti-jamming in UAV communications has attracted substantial research interest. At present, the frequency hopping (FH) spread spectrum technique works well in combating jamming. The FH system gains its anti-jamming performance through frequency domain diversity. The frequency bin selection mechanism of the FH communication system is pseudo-randomly varied, which produces outstanding anti-jamming performance [12]. With the development of different methods of jamming, the application of the FH scheme alone can not guarantee the quality of UAV communications links in the face of maliciousjamming. Therefore, it is worthwhile to consider the use of advanced waveform design methods, such as interleaving, channel coding and efficient modulation techniques [13]. The channel coding scheme has been demonstrated to be essential in FH systems due to the high coding gain it has demonstrated. Substantial research has been conducted with the aim of applying various coding algorithm to FH communication systems in diverse UAV scenarios. Reed-Solomon (RS) codes, convolutional codes, turbo codes and low-density parity check (LDPC) codes are widely studied in FH systems [13; 14; 15; 16; 17]. Those codes demonstrate a considerable coding gain against noise. However, since the code rates of those codes are not low enough, they cannot be used to combat malicious jamming with high power, which can cause the received symbols to be entirely suppressed by powerful interference, meaning that the receiver cannot succeed in decoding the message at all.As a result, it has become critical to combine low-rate codes with FH communication systems in UAVs for the purpose of anti-jamming. Hadamard codes are one kind of low-rate code, which can be decoded with a rather low complexity, employing prior information by means of maximum posterior (MAP) decoding rules [18]. Meanwhile, turbo codes have been proven to achieve coding gains close to the Shannon limit [19], and have been demonstrated to combat jamming effectively due to the characteristics of their interleaving-coded bit sequence. As a consequence, a hybrid concatenation of convolutional codes and Hadamard codes called the turbo-Hadamard code was proposed in [20], featuring a low rate and anti-jamming capability. This proposed code can be treated as an approximately random code which is proven to be a \"good code\" when the code length becomes \(\infty\). Low-rate codes have been employed when the complexity is acceptable in 6G UAV scenarios [21]. However, the high complexity of the decoding of turbo-Hadamard codes is one obstacle to its implementation on the platform of limited UAVs. Moreover, turbo-Hadamard codes exhibit great efficiency losses due to their trellis structure with short information bits.