Spatial Processing with Lens Antenna Arrays for Direction-of-arrivalestimation

In this paper, spatial processing with lens antennas arrays for direction-of-arrival (DOA) estimation is considered. In this approach, when using the Multiple Signal Classification (MUSIC) algorithm, the dimension is reduced by the front end which performs spatial processing, resulting in increased computational speed and decreased computational load. As a specific example, simulations of a 33-element lens array with DOA estimation for 7 simultaneous sources shows that the computational load is reduced to 68% of that for a 33-element linear uniform array. In this paper, we consider the case of narrowband uncorrelated signals, and uniform spacing of receivers on the lens image surface, but the analysis can be extended to broadband non-uniform scenarios. INTRODUCTION Direction-of-arrival (DOA) estimation is one of the main function requirements for direction-finding smart antennas in futuregeneration mobile communication systems [1]. This paper investigates the possibility of improving the resolution, while at the same time reducing the computational load for DOA estimation by using a lens antenna array front end in place of a more standard uniform antenna array. Discrete lens arrays (DLAs), Fig.1, are beam-forming multi-beam arrays which are implemented with 3 antenna arrays: the source-side array, the image-side array, and the receiver array. The first two arrays are fabricated on Fig. 1. Sketch of a discrete lens antenna array. In reception, the source-side antenna elements receive the incident waves, and transmit it through variable delay lines to the image-side elements. The delay lines are designed to provide focusing onto receiver antennas positioned on the focal surface. These signals are A-to-D sampled and input to the DOA algorithm. the same single or multi-layer substrate, while the third array is conformal at a distance determined by the focal-length-todiameter (F/D) of the particular design. The source-side array samples the input wavefront, as in any two-dimensional array. Each antenna in this array transmits the received signals to the image-side antenna elements through waveguides (usually microstrip or CPW) of varying length across the array. This produces a spatial Fourier transform of the source space on the image (focal) surface of the DLA, and this image is sampled by the receiver elements. In contrast to dielectric lenses, DLAs can be fabricated using standard PCB technology, they can be designed to have good scanning properties for large angles [2] and low losses with no additional anti-reflection coatings, polarization is an additional design parameter, and active circuitry that provides gain can be integrated in the lens itself. Active DLAs for half-duplex [3], [4] and full-duplex [5] active transmit/receive arrays have been demonstrated over the past few years. In these arrays, power amplifiers and lownoise amplifiers are integrated in each array element, allowing for increased effective radiated power (ERP) in transmission and increased dynamic range in reception. More recently, the LMS adaptive algorithm applied to a DLA showed significant reduction of adaptation weights for non-optimal solutions [6]. A 10-GHz DLA was also integrated with an analog optical processor for broadband adaptive independent-component analysis. [7]. In this paper, the Multiple Signal Classification (MUSIC) algorithm is applied to the signals received at the image (Fourier transform) surface of a DLA. The lens transforms the element-space (the output of the source-side array) to beam-space (the output of the receivers that sample the image) with equal or reduced dimension, allowing for reduced computational load. In addition, it is expected that the estimation bias may be decreased when applying MUSIC in beam-space, thereby improving the resolution. To evaluate the performance of a lens-array system and compare it to a uniform linear array, two parameters are calculated: the root-mean-square error (RMSE) and the resolution signal-to-noise (SNR) threshold (probability of resolving a source). In this paper, narrowband signals and uniform sampling of the DLA image are considered in the modelling. However, these are not fundamental limitations, as has been shown in [8], where an extension of MUSIC to broadband non-uniform arrays is presented. In the next section, the framework and notation for the simulations are presented; in particular, the narrowband signal model, the source-direction matrix for arbitrary arrays, and a brief overview of the MUSIC algorithm are presented. In Section III, the spatial pre-processing by DLAs as applied to MUSIC is developed, and in Section IV, the simulation results are discussed. SIGNAL AND ANTENNA ARRAY MODELS In simulations presented in this paper, all M antenna elements are assumed to be uniform directional patterns and mutual coupling between elements is not taken into account. The signal and noise models are narrowband, and the P signals incident on the array from P different sources are assumed to be uncorrelated. The sources are assumed to be in the far field of the array, producing incident plane waves at angles ( 1; 1); : : : ; ( P ; P ), centered around a frequency !0. Narrowband signal model For the narrowband problem, it is convenient to use models of signal and noise in time-domain. Using complex envelope representation, the (M 1)-vector of array-output signals can be expressed by