Photonic integrated circuit based compressive sensing radio frequency receiver using waveguide speckle.

A photonic integrated circuit (PIC) comprised of an 11 cm long multimode speckle waveguide, a 1 × 32 splitter, and a linear grating coupler array is fabricated and utilized to receive 2 GHz of radio-frequency (RF) signal bandwidth from 2.5 to 4.5 GHz using compressive sensing (CS). Incoming RF signals are modulated onto chirped optical pulses which are input to the multimode waveguide. The multimode waveguide produces the random projections needed for CS via optical speckle. The time-varying phase and amplitude of two test RF signals between 2.5 and 4.5 GHz are successfully recovered using the standard penalized l1-norm method. The PIC reduces the speckle mixer footprint compared with the previously demonstrated fiber system. Two new PIC structures, the "waveguide bus trombone flare" and the "matched 90 degree bus bend" are developed to support precise analog signal routing. The use of a passive PIC serves as an initial critical step towards the miniaturization of a compressive sensing RF receiver.

Demonstration of speckle-based compressive sensing system for recovering RF signals.

We demonstrate measurement of RF signals in the 2-19 GHz band using a photonic compressive sensing (CS) receiver. The RF is modulated onto chirped optical pulses that then propagate through a multimode fiber that produces the random projections needed for CS via optical speckle. Our system makes 16 independent measurements per optical pulse and we demonstrate several calibration techniques to obtain the CS measurement matrix from these measurements. Then a standard penalized l1 norm method recovers amplitude, phase, and frequency of single-tone and two-tone RF signals with about 100 MHz resolution in a single 4.5 ns pulse. A novel subspace method recovers the frequency to about 20 kHz resolution over 100 pulses in a 2.8 microsecond time window. These experiments use discrete fiber-coupled optical components, but all necessary functions can be realized in photonic and electronic integrated circuits.

Multimode waveguide speckle patterns for compressive sensing.

Compressive sensing (CS) of sparse gigahertz-band RF signals using microwave photonics may achieve better performances with smaller size, weight, and power than electronic CS or conventional Nyquist rate sampling. The critical element in a CS system is the device that produces the CS measurement matrix (MM). We show that passive speckle patterns in multimode waveguides potentially provide excellent MMs for CS. We measure and calculate the MM for a multimode fiber and perform simulations using this MM in a CS system. We show that the speckle MM exhibits the sharp phase transition and coherence properties needed for CS and that these properties are similar to those of a sub-Gaussian MM with the same mean and standard deviation. We calculate the MM for a multimode planar waveguide and find dimensions of the planar guide that give a speckle MM with a performance similar to that of the multimode fiber. The CS simulations show that all measured and calculated speckle MMs exhibit a robust performance with equal amplitude signals that are sparse in time, in frequency, and in wavelets (Haar wavelet transform). The planar waveguide results indicate a path to a microwave photonic integrated circuit for measuring sparse gigahertz-band RF signals using CS.

Compressive sensing of sparse radio frequency signals using optical mixing.

We demonstrate an optical mixing system for measuring properties of sparse radio frequency (RF) signals using compressive sensing (CS). Two types of sparse RF signals are investigated: (1) a signal that consists of a few 0.4 ns pulses in a 26.8 ns window and (2) a signal that consists of a few sinusoids at different frequencies. The RF is modulated onto the intensity of a repetitively pulsed, wavelength-chirped optical field, and time-wavelength-space mapping is used to map the optical field onto a 118-pixel, one-dimensional spatial light modulator (SLM). The SLM pixels are programmed with a pseudo-random bit sequence (PRBS) to form one row of the CS measurement matrix, and the optical throughput is integrated with a photodiode to obtain one value of the CS measurement vector. Then the PRBS is changed to form the second row of the mixing matrix and a second value of the measurement vector is obtained. This process is performed 118 times so that we can vary the dimensions of the CS measurement matrix from 1×118 to 118×118 (square). We use the penalized ℓ(1) norm method with stopping parameter λ (also called basis pursuit denoising) to recover pulsed or sinusoidal RF signals as a function of the small dimension of the measurement matrix and stopping parameter. For a square matrix, we also find that penalized ℓ(1) norm recovery performs better than conventional recovery using matrix inversion.

Phase ripple correction: theory and application.

Spectral phase ripple associated with novel dispersive devices can distort broadband optical signals. We present a digital postprocessing algorithm to correct for this distortion by exploiting the static deterministic nature of the ripple. This algorithm is demonstrated with empirical data for several systems employing chirped fiber Bragg gratings (CFBGs). We employ this technique in a photonic time-stretch system incorporating CFBGs, improving the signal fidelity by 9 dB. Simulations and experiments show that this algorithm, which can be reduced to a simple interpolation and matrix multiplication, also mitigates additive noise. We see that the act of distortion correction yields signal fidelity superior to that of an ideal dispersive element.