Compressed Sensing

The modular ultra-wideband (UWB) pseudo noise (PN)-sequence sensor was introduced to showcase the capabilities of the EMS-developed integrated circuits (ICs) Xampling Generator 1 (XG1) and Xampling Frontend 1 (XF1) which were specifically designed to demonstrate the paradigm of compressive sampling implemented on real silicon hardware¹. The sensor system divides into two main units - modular multiple input and multiple output (MIMO) transceiver (TRx) frontend and corresponding data acquisition backend.

Wagner, Christoph W. and Semper, Sebastian and Römer, Florian and Schönfeld, Anna and Del Galdo, Giovanni.

We propose a compact hardware architecture for measuring sparse channel impulse responses (IR) by extending the M-Sequence ultra-wideband (UWB) measurement principle with the concept of compressed sensing. A channel is excited with a periodic M-sequence and its response signal is observed using a Random Demodulator (RD), which observes pseudo-random linear combinations of the response signal at a rate significantly lower than the measurement bandwidth. The excitation signal and the RD mixing signal are generated from compactly implementable Linear Feedback Shift registers (LFSR) and operated from a common clock. A linear model is derived that allows retrieving an IR from a set of observations using Sparse-Signal-Recovery (SSR).

When making use of the Compressed Sensing (CS) paradigm, one has to design the measurement process by means of a suitable compression step. Traditionally, the compression is modelled by means of a linear mapping acting on discretized version of the encountered signals, i.e. a usually complex-valued matrix ^{1 2 3}. Also, it has been an active field of research to apply CS as a data reduction scheme in radio channel sounding ⁴. Afterwards one is confronted with the problem to recover the parameters of interest, like time-of-flight, direction-of-arrival or Doppler-shifts from spectral-, spatial- and temporal measurements of a radio channel. In this context the iterative maximum-likelihood approach in ⁴ presents an optimization approach that is both computationally feasible and reproduces closely what is dictated by the Cramer-Rao-Lower-Bound (CRLB).

It has been shown¹ that Linear Feedback Shift Registers (LFSR) can serve as a Radar sensor by random demodulation that enables significantly lower data-rates than dictated by the Nyquist-Sampling Theorem. At the same time they can be implemented very efficiently in silicon, while still allowing high configurability. This makes this approach a prime candidate for a wide range of Radar and inspection applications, but it requires a thorough study of the resulting theoretically achieveable performance.