# Cognitive Interference Cancellation with Digital Channelizer for Satellite Communication
## 2 System Model  
In this study, a point-to-point satellite communication channel with an Earth station as well as a satellite and terminal station is considered as shown in Figure 2. In typical satellite communication, a satellite is not dedicated to a single link (or service), i.e., several links (or services) share a satellite for their own purposes. The total bandwidth of the satellite consists of several transponders, which are clusters including radio receivers, frequency translators, and transmitters. A satellite customer purchases a transponder, i.e., a dedicated block of bandwidth on a satellite for a period of time and provides a satellite communication service. To utilize the transponder, i.e., bandwidth, efficiently, a satellite employs a digital channelizer with many subchannels. With the digital channelizer, the transponder bandwidth and power can be finely controlled. For example, a carrier frequency of the transponder can be changed and the transmit power is also controlled using a switching and multiplexing functions of the channelizer. Figure 3 shows an operational example and overall functional diagram of a digital channelizer.  
In this work, we focus on a cognitive interference cancellation at a satellite by using a digital channelizer with \(N\) subchannels. Details on the digital channelizer and its implementation will be discussed in the next section. The signal received by the satellite as an input of the digital channelizer is given by  
\[y(Ni+k)=x(Ni+k)+s(Ni+k)+w(Ni+k),\ \ \ i=0,1,\cdots,\ \ k=0,\cdots,N-1, \tag{1}\]  
where \(x(\cdot)\), \(s(\cdot)\) and \(w(\cdot)\) are the desired wideband signal, CW tone interference, and additive white Gaussian noise (AWGN), respectively. Because we consider a 1024-subchannel channelizer, we make a block with 1024 samples. In Equation (1), \(i\) is a block index and \(k\) is the time domain sample index in the block. With the channelizer, the time-domain signal block, \([y(Ni),y(Ni+1),\cdots,y(Ni+N-1)]\), is transformed to the frequency-domain signal block, \([\bar{y}(Ni),\bar{y}(Ni+1),\cdots,\bar{y}(Ni+N-1)]\). Therefore, the output of the digital channelizer is expressed by  
\[\bar{y}(i,0) =\bar{y}(Ni)=\bar{x}(i,0)+\bar{w}(i,0)\] \[\bar{y}(i,1) =\bar{y}(Ni+1)=\bar{x}(i,1)+\bar{w}(i,1)\] \[\vdots \vdots \vdots\] \[\bar{y}(i,n) =\bar{y}(Ni+n)=\bar{x}(i,n)+\bar{s}(i,n)+\bar{w}(i,n)\] \[\vdots \vdots \vdots\] \[\bar{y}(i,N-1) =\bar{y}(Ni+N-1)=\bar{x}(i,N-1)+\bar{w}(i,N-1). \tag{2}\]  
In Equation (2), it is assumed that the frequency of the interference \(s(\cdot)\) is in the \(n\)-th subchannel. In the cognitive interference cancellation, the subchannel with the tone interference is identified and removed. After the cancellation, the satellite combines the uncorrupted subchannels and transmits (relays) the wideband signal to the receiver on Earth. As needed, switching and multiplexing functions, as well as power control are performed before transmission at the satellite.  
Figure 3: Functional block diagram and operational example of digital channelizer.  
Figure 2: Satellite communication channel with Earth and terminal stations, and satellite with a digital channelizer.