# Hybrid FSK-FDM Scheme for Data Rate Enhancement in Dual-Function Radar and Communication
## 3 Proposed Transmit Signalling Strategy for Information Embedding  
Binary information is embedded in radar signals in the form of waveform numbers and frequencies. These signals are sent from a DFRC transmitter and received by both a radar and communication receiver. The data is then extracted from the signal, allowing the radar receiver to determine the objects' direction and velocity. Two bits of information are mapped during each radar transmit pulse, whereas two frequencies are used in this technique to represent either binary 0 or binary 1, as shown in Figure 1.  
The two frequencies are selected from a pool of available frequencies, depending on the information the transmitter wants to communicate. The communication receiver then decodes the frequencies and extracts the binary information from the signal. Similarly, the two waveforms represent binary 0 or binary 1. This information mapping is performed through FSK. This method is based on the fact that different frequencies can be easily distinguished and used to represent different binary values. In FSK, two different frequencies are assigned to represent the binary digit 0 and digit 1. The transmitter then sends these frequencies, one after the other. The receiver decodes the frequencies to extracts the binary data from the signal. Thus, employing FSK modulation, two bits can be represented by distinct frequencies and waveforms, as shown in Table 1.  
Each communication symbol encodes two bits of information using a waveform and frequency combination. Consider the random bits pattern shown in Table 2. By mapping each bit pattern to a specific waveform and frequency combination, it is possible to construct two distinct symbols that can be sent over a communication channel. These symbols can then be decoded back to the corresponding bit pattern on the receiver side. The pattern selector selects a suitable combination of waveform and frequency to be transmitted.  
For example, for \(B_{l}(t)=00\), the joint waveform and frequency (JWF) combination of \(\xi_{00}(t)\) has been selected from the lookup table. Moreover, multiple JWF combinations are added to make a composite signal using FDM. This signal is then transmitted from the DFRC transmitter as shown in Figure 2. Next, the modulated symbols are added together to achieve a double data rate using the FDM technique. The composite signal is received by the communication receiver, where the JWF symbols are separated via a frequency demodulator. The pattern selector then decodes these JWF combinations into the corresponding bit patterns. These bit patterns can then be converted back to the symbols originally sent by the transmitter. The symbols are then converted to binary data, which can be used for further processing. The mathematical description of a composite signal is given as:  
\[\mathbf{x}_{fdm}(t)=\sum_{j=1}^{J}\mathbf{m}_{j}(t,\tau) \tag{2}\]  
where, \(\mathbf{m}_{j}\), \(j=1,...,J\) is the JWF symbol added together to double the data rate in the proposed scheme. The overall form of the JWF sample with allocated power can be written as  
\[\mathbf{m}_{i,j}(t)=\sqrt{\frac{M_{T}}{L_{B}}}(t)\xi_{i,f_{j}}(t) \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline... & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 &... \\ \hline  & \(\xi_{01}(t)\) & & \(\xi_{11}(t)\) & & \(\xi_{10}(t)\) & & \(\xi_{00}(t)\) & \\ \hline \end{tabular}
\end{table}
Table 2: Random information bit mapping to a JWF combination.  
Figure 1: The proposed information embedding methodology at the DFRC transmitter.  
The nomograph of the proposed FDM-based composite signals with linear adder is shown in Figure 2.  
Note that all waveforms must be mutually orthogonal for improved communication with less inter-waveform interference.