# Research on Tracking Technique Based on BPSK-CSK Signals
## 2 Materials and Methods  
### Fundamentals of BPSK-CSK Signaling Theory  
CSK Modulation and Demodulation  
The CSK modulation technique is essentially a spread spectrum modulation; only the phase of the pseudo-code is cyclically shifted according to the different data sent to obtain a new code, which overcomes the limitation of the spreading gain on the data rate and improves the information transmission rate without changing the signal bandwidth, amplitude, and other parameters. Therefore, each cyclically shifted pseudocode can represent a CSK symbol. The receiving end identifies the pseudocode phase of a CSK symbol by demodulation, which means that the data coming from the sending end can be obtained [1].  
CSK uses M orthogonal signals to transmit \(U=\log_{2}(M)\) bits. The special feature of CSK modulation is that the symbols of each set of input bits are obtained from different cyclic shifts of a single elementary PRN sequence. In addition, each cyclic shift consists of an integer number of code slices and is assumed to be a full-cycle version of the basic pseudocode.  
Figure 1 shows the CSK modulation flow. The phase of the pseudo-code for direct sequence spread spectrum modulation is always kept constant, i.e., only the pseudo-code with phase 0 is used for the direct sequence spread spectrum, while in CSK modulation,  
the basic pseudo-code generates M cyclically shifted pseudo-codes through the code slice delayer. In addition, the data stream with U bits in a group corresponds to one CSK symbol, which is mapped to obtain the corresponding CSK cyclically shifted sequence, thus generating one CSK symbol, which is finally transmitted through carrier modulation.  
From the principle of CSK modulation, different pseudo-code phases represent different data. At the receiver side, it is only necessary to demodulate the pseudo-code phases, and then by searching the reflective table, you can know the modulated data in the pseudo-code period. Commonly used CSK demodulation methods are matched filter demodulation and FFT demodulation. Through demodulation, the correlation value between the received signal and each CSK cyclic code word can be obtained, and the cyclic code word with the largest correlation value is selected as the demodulated output.  
The principle of matched filtering is to match correlate CSK symbols through a filter bank and select the CSK cyclic code word corresponding to the maximum value of the matched filter output as the demodulation of the transmitted symbols.  
Matched filter demodulation is performed using two matched filter banks, in-phase and quadrature, where the input IF signal is mixed with the locally generated in-phase and quadrature carriers, respectively, and the mixed results are fed into the filter banks for matched correlation. Each filter bank contains M filters, and the cyclic shift sequences used by the filters are matched and correlated with the received signals. Finally, the correlation output is obtained by integrating and summing. Due to the good autocorrelation of the pseudocode, if the received CSK symbols are aligned with a certain cyclic shift sequence, the correlation output of that filter will have a significant peak, and the outputs of the other filters will be noise.  
When the number M of CSK modulation is increased, the number of matched filter banks is also increased, and the complexity of demodulation will be further increased. In order to reduce the complexity of CSK demodulation, FFT-based demodulation can be used, and its demodulation principle is consistent with the principle of parallel code phase capture of satellite navigation signals. Figure 2 shows the principle diagram of CSK demodulation based on FFT.