The ability to both spatially and spectrally demultiplex wireless transmitters enables communication networks with higher spectral and energy efficiency. In practice, demultiplexing requires sub-millisecond latency to map the dynamics of the user space in real-time. Here, we present a system architecture, referred to as k-space imaging, which channelizes the radio frequency signals both spatially and spectrally through optical beamforming, where the latency is limited only by the speed of light traversing the optical components of the receiver. In this architecture, a phased antenna array samples radio signals, which are then coupled into electro-optic modulators (EOM) that coherently up-convert these signals to the optical domain, preserving their relative phases. The received signals, now optical sidebands, are transmitted in optical fibers of varying path lengths, which act as true time delays that yield frequency-dependent optical phases. The output facets of the optical fibers form a two-dimensional optical phased array in an arrangement preserving the phases generated by the angle of arrival (AoA) and the time-delay phases. Directing the beams emanating from the fibers through an optical lens produces a two-dimensional Fourier transform of the optical field at the fiber array. Accordingly, the optical beam formed at the back focal plane of the lens is steered based upon the phases, providing the angle of arrival and instantaneous frequency measurement (IFM), with latency determined by the speed of light over the optical path length. We present a numerical evaluation and experimental demonstration of this passive AoA- and frequency-detection capability.

As mobile beam-bandwidth-product requirements accelerate, millimeter-wave (mmW) bands have been opened to telecommunications networks to enable wider channel bandwidths, while Massive Multiple-Input Multiple-Output (mMIMO) technology has been implemented to concurrently address multiple devices at the same frequency from a single base station. Such space-division multiplexing can be combined with spectral multiplexing to enable a very large number of concurrent users, but currently is implemented through computationally intensive digital beamforming networks. We show that a radio-frequency (RF) photonic receiver system, previously shown to be capable of sorting signals into respective spatial-spectral 'bins' is further capable, through an injection-locked tunable optical local oscillator (TOLO), of recovering the data upon each signal in the RF scene. The TOLO is combined in free-space with an up-converted optical sideband and the combined optical field impinges upon an array of photodetectors, each corresponding to separate points in k-space, defined by unique combinations of angle-of-arrival (AoA) and carrier frequency. Using this free-space LO insertion, we demonstrate simultaneous recovery of multiple spatially colocated data streams with resilience to interference.

Millimeter-wave (mmW) imaging receivers have demonstrated the ability to sense radio-frequency (RF) waves using traditional phased antenna array techniques, and, through a coherent photonic up-conversion process, image these waves using free-space optical systems. Building upon the idea of coherent up-conversion, k-space tomography extends the functionality of the millimeter-wave imaging receiver as a two-dimensional spatial processing unit to three-dimensional sensing with the addition of frequency detection. In this configuration, an arrayed waveguide grating, or temporal aperture, is implemented following the photonic up-conversion of RF signals received by the phased array. These waveguides of varying length add a spectral beam-forming network to the existing spatial beam-forming of the mmW-imaging receiver. The introduction of three-dimensional phase information to the imaging system disrupts the ability to directly image the RF signal distribution on a photo-detector array, requiring the application of tomographic algorithms to reconstruct the power distribution of the received signals. In order to receive and properly recover the spatial-spectral distribution of RF sources, the antenna array and temporal array must be sampled adequately to avoid introduction of grating artifacts into the system response. Grating lobes, an artifact of regular spacing of elements within a grating, restrict the alias-free field of regard for antenna arrays, or the free spectral range for time-delay based arrays, thus limiting the spatial-spectral monitoring of RF sources via the k-space imaging modality. To alleviate this constraint, we present a non-uniform log-periodic array sampling for the k-space tomographic time-delay based aperture, greatly increasing the free spectral range of the system while maintaining the number of existing channels.

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In this paper, we propose an architecture wherein the radio-frequency (RF) field at the antenna array is upconverted to an optical carrier and passed through an array of optical fibers, after which an analog Fourier transform is taken in a free-space optical processor. Through the use of multiple temporal dispersion projections, implemented through varied-length optical fiber segments, the locations of RF sources in three-dimensional space spanning angle-of-arrival (AoA) and instantaneous frequency may be determined on a millisecond time scale using commercial computing hardware after detection by a charge-coupled device (CCD) camera. We present a mathematical formulation of the problem, followed by simulated and experimental results showing three-dimensional spatial-spectral localization through the solution to a system of equations brought forth through the use of Fourier optics to process the RF field. I. INTRODUCTIONP ROVISIONS for future wireless networks are driven by the need for ever-increasing data rates [1]-[3]. To address this, emerging wireless networks are increasing their carrier frequencies to the millimeter-wave (mmW) regime, where the hardware requirements in terms of cost, size, weight and power (C-SWAP) to perform the digital beam-forming process become quite demanding. Digital beamforming, along with digital beamspace processing techniques such as BLAST and MUSIC, allow for angle-of-arrival (AoA) and frequency determination and are extensively implemented in the field [4]-[6]. However, digital beamforming techniques generally rely upon recording of high-frequency signals, implemented through high-speed analog-to-digital converters (ADCs). To handle today's broadband data streams, these ADCs have become quite expensive and power-hungry; techniques such as frontend downconversion reduce the required sample rates while introducing local oscillator (LO) synchronization error [7]. Further, performing direction-finding and frequency measurement requires either matrix inversions or fast Fourier transforms, with both operations becoming increasingly complex as array size increases. Additional techniques such as RF lenses alleviate the computational cost of the beamforming step, but are bulky due to their necessary RF wavelength-scale footprint, and can be lossy depending upon the material system [8], [9]. Array windowing or subarray processing offers a reduction in