Method for compressive sensing , reconstruction, and estimation of ultra-wideband channels

A method for compressive sensing (CS), reconstruction and estimation of ultra-wideband channels of a UWB transmission, comprising the steps of:

• building an IR-UWB channel dictionary matrix related to antenna angles of transmission and antenna angles of arrival associated with an IR-UWB signal transmitted over the IR-UWB channel;
• using the IR-UWB channel dictionary matrix in conjunction with a measurement basis to perform an action selected from the action groups consisting of reconstructing the IR-UWB signal and estimating the channel of the IR-UWB signal;
• when the action group performed is the IR-UWB reconstruction, the step of using the IR-UWB channel dictionary matrix includes the steps of:
• (a) combining a measurement matrix Φ with the channel dictionary matrix Ψ;
• (b) measuring the IR-UWB signal using the measurement and channel dictionary matrix combination, thereby producing an output stream of signal measurements;
• (c) executing a CS algorithm on the signal measurements using the measurement and channel dictionary matrix combination, the CS algorithm producing a CS algorithm output;
• and
• (d) combining the CS algorithm output with the channel dictionary matrix, thereby reconstructing the IR-UWB signal.