# SDR Proof-of-Concept of Full-Duplex Jamming for Enhanced Physical Layer Security
## 2 Background
### Self-Interference Cancellation  
There are three different categories of SI cancellation mechanisms [38], namely passive suppression, analog cancellation and finally digital cancellation. Passive suppression is based on attenuating the SI signal by physically separating/changing somehow the transmitter antenna and the receiver antenna of the device. The analog SI cancellation is performed before the signal goes into the analog-to-digital converter (ADC) (e.g., by using a noise canceling integrated circuit). Digital SI cancellation works after the signal goes into  
Figure 2: Adapted scrambled coding for secrecy with a hidden key (SCS-HK) scheme.  
the ADC and takes advantage of the knowledge of the interfering signal for the purpose of canceling it, and will be the focus of our work.  
There are adaptive SI cancellation algorithms which iteratively adjust the coefficients of the signal in a way to predict the desired one. The least mean square (LMS), normalized least mean square (NLMS), recursive least squares (RLS) and QR decomposition recursive least squares (QRD-RLS) are state-of-the-art examples of such [34; 35; 39]. These algorithms operate with a given target/reference signal \(d(n)\) and the input signal \(x(n)\). The filter transfer function \(H(z)\) outputs \(y(n)\), which considers the statistics of \(x(n)\) and \(d(n)\) in order for the output signal \(y(n)\) to approximate the target/reference signal \(d(n)\). That is, after \(x(n)\) is filtered, \(y(n)\) is produced, which is an estimate of the target signal \(d(n)\) with some error of \(e(n)\).  
The LMS algorithm [34; 39] is based on the concept of the adaptive finite impulse filter (FIR) Wiener filtering, however, instead of using auto-correlation and cross-correlation operations to estimate the signal, it uses the steepest descent method to estimate the gradient vector and constantly update the filter taps' weights to converge to the optimum filter weight vector while minimizing the mean square error (to converge to the minimum mean squared error).  
The NLMS [39] is a version slightly modified of the LMS which corrects the gradient noise amplification problem caused by the weight's adjustment being directly proportional to the input \(x(n)\).  
While LMS aims to reduce the mean squared error between the estimated signal and the desired one, RLS tries to recursively find the taps' weights using the least squares method [35; 39]. Therefore, the LMS input signal needs to be stochastic, while the RLS works better for a deterministic environment (i.e., there is no randomness on the input signal or the input signal has slowly time-varying randomness).  
QRD-RLS is based on the previous one, but uses the QR decomposition [35], to explore the good numerical properties (raised when the algorithms are numerically implemented, i.e., due to inaccuracy of the ADC), thus achieving a numerically more stable algorithm.  
Finally, since the self-interference is canceled prior to decoding, [PERSON] and [PERSON] are free to use any selection of waveforms or modulation, including multi-carrier waveforms such as OFDM.