Reactively Controlled Adaptive Arrays – a Key Technologyfor Achieving the Wireless Ad-hoc Community Network

This paper overviews our recent research on adaptive beamforming of reactively controlled array as a nonlinear spatial filter with variable parameters, which forms both beam and nulls. The learning rate schedule is examined with respect to output SINR, convergence, stability, misadjustment, noise effect etc. Our theoretic study, simulation results and performance analysis show that such kind of arrays can be controlled effectively and has strong potential for use in the wireless ad-hoc community networks. Further development is described. INTRODUCTION The reactively controlled arrays were first investigated in [1] and [2]. In [1] the direction of maximum gain was controlled by varying the load reactances of a moderate number of dipoles (resonance mode) and an optimum seeking univariate search procedure was applied; in [2] the experimental results and theory were presented for reactively steered adaptive array in a power inversion mode. However, these papers fail to meet the demand for adaptively canceling interferences and reducing an additive noise. The electronically steerable passive array radiator (ESPAR) antenna [3] is one kind of parasitic elements based a single-port output antenna with several variable reactances. It performs analog aerial beamforming, which provides a dramatically simplified architecture that results in significantly lower power dissipation and fabrication cost in comparison with digital beamforming antennas. In [6] it was shown that by applying compact adaptive ESPAR antennas to portable mobile user terminals can enlarge the capacity of Wireless Ad-hoc Community Networks (WACNet), reduce consumption of power etc. Such a network can be considered as a means of linking portable user terminals that meet temporarily in locations where the connection to a network infrastructure is difficult. One example of effective application of the reactively controlled adaptive arrays to a WACNet is the Contiguous Communication Network on Ubiquitous Transmission [7]. In reactively controlled adaptive array none of the signals on its passive elements can be observed. This fact and one that is more important – the nonlinear dependence of the output of the antenna on adjustable reactances – makes the problem substantially new and not resolvable by means of conventional adaptive array beamforming techniques. The essence of beamforming functionality in the reactively controlled antenna is complex weighting in each branch of the array and adaptive optimization of the weights via adjustable reactances [4],[5]. In this paper minimization of the objective function is performed via a stochastic descent technique in accordance with stochastic approximation (SA) theory [8]. Finally, by using cyclostationary features of the SOI [9], a blind algorithm is proposed. ESPAR ANTENNA CONFIGURATION AND FORMULATION An (M+1) – element ESPAR antenna with M=6 is depicted in Fig. 1. The 0-th element is an active radiator located at the center of a circular ground plane. It is a λ/4 monopole (where λ is the wavelength) and is connected to the RF receiver in a coaxial fashion. The remaining M elements of λ/4 monopoles are passive radiators surrounding the active radiator symmetrically with radius R=λ/4 of the circle. These M elements are loaded with varactors having appropriate reactances. Thus adjusting the values of the reactances can change the radiation patterns of the antenna. A key role is played by the RF current weight vector [5] which does not have independent components but is an unconventional one – wuc. It depends nonlinearly by reactance vector x and adaptive beamforming of the reactively controlled antenna must be considered as a nonlinear spatial filter that has variable parameters. The output of the ESPAR antenna can be expressed as the model Fig. 1. A 7-element adaptive ESPAR antenna ) ( ν ) ( ) ( ) ( 1 t t s t y p P p p H uc + ∑ = = θ a w (1) where ) (t s p , p=1,...,P is the waveform of the p-th user terminal; ) ( p θ a is the steering vector in the direction p θ ; ) ( ν t is a complex valued additive Gaussian noise (AGN) and the weight vector uc w was mentioned above. OBJECTIVE FUNCTION The output of the antenna is not linearly connected by the adjustable reactances. The character of this nonlinearity has not been studied until now. That is why the model is considered and evaluated numerically instead of presenting an analytical solution of optimal adaptive beamforming. Let us turn to the measures as mean squared error (MSE) or normalized MSE (NMSE) of the output waveform y(t) relative to the desired waveform d(t) 2 1 ) , ( yd d y NMSE ρ − = (2) where yd ρ is the cross-correlation coefficient. Let us have the N-dimensional vectors d(n) and y(n) that are discretetime samples of the desired signal d(t) and the output signal y(t). Then the following objective function has to be minimized: = = ) , ( ) ( d y x NMSE J N 2 2 2 2 ) ( ) ( ) ( ) ( ) ( ) ( 1 n n n n n n H H