Random sequence encoded waveforms for covert asynchronous communications and radar

Clutter-Masked Waveform Design for LPI/LPD Radarcom Signal Encoding

“…In [ 5 ], we selected Weibull-distributed random process with probability density function (PDF) , where λ is the scale parameter and k is the shape parameter. Assuming that the shape parameter k is selected arbitrarily and is known to the authorized platforms only, we proposed to encode communication data using the scale parameter λ .…”

“…For simplicity, we formulate that correctly recovering an estimate of λ by an authorized receiver achieves our goal of the communication data reception. An authorized receiver can perform this estimation using a simple expression [ 5 , 17 ]: where is mathematical expectation of the vector containing estimates of the received signal’s OFDM sub-carrier amplitudes, and Γ is the gamma function. In contrast, an unauthorized interceptor without the knowledge of k will need to perform estimation of that parameter first, which requires solving a non-linear equation that is highly susceptible to disturbances, such as additive noise: where is the estimate of the m th OFDM sub-carrier amplitude.…”

“…In Case 2, the return is the sum of independent random variables C and N . In the actual system implementation, the received signal is recorded in terms of its magnitude samples [ 5 ]. Owing to the independence of C and N , we then formulate the expression for their joint PDF, expressed via their individual pdf’s: where the sign denotes convolution.…”

“…An OFDM signal with 32 sub-carriers was generated for each bit using (1) with formed as per (11). Upon reception, a friendly platform used FFT to reconstruct the sub-carrier coefficients using FFT and extracting the magnitude estimates only, via the process explained in [ 5 ]. Once these estimates were obtained, the value of the k th bit was estimated using the vector and the estimate of its corresponding b -parameter as: …”

“…In our previous work, we investigated the performance of the random sequence encoding (RSE) method of waveform design, where the transmissions could be derived from a clutter model [ 5 ]. This was achieved via a novel algorithm in which the communication data are encoded as a parameter of a particular random distribution, whereas the radarcom signal is then created using samples of the thus distributed random process.…”