Adaptive Waveform Design for Target Enumeration in Cognitive Radar Joseph Tabrikian Department of Electrical and Computer Engineering Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel Email: joseph@ee.bgu.ac.il Abstract—In this paper, the problem of sequential waveform design for target enumeration for cognitive multiple-input single- output (MISO) radar is investigated. In the proposed technique, the transmit spatial waveform is adaptively determined at each step based on observations in the previous steps. The waveform is determined to minimize an approximated lower bound on the average sample number (ASN) required to achieve given error rates. The algorithm is tested via simulations and shown to exhibit superior performance compared to orthogonal waveform transmission. I. I NTRODUCTION Cognitive radar is an emerging technology proposed in [1] and has been investigated in several works. A cognitive radar system adaptively interrogates the radar environment based on previous observations, side information, and task priorities. It adaptively illuminates the environment in a closed loop manner in order to optimize some predefined objective functions. In [2] an adaptive technique for waveform design for target local- ization was proposed. This technique is based on minimizing performance lower bounds on the target parameters and it was shown to automatically focus the transmit beam towards the targets directions in a very low signal-to-noise ratio (SNR). In [3], two adaptive waveform design techniques using sequential hypothesis testing for target classification was proposed. In [4] the problem of adaptive waveform design for sequential target detection with subspace interference was investigated. In the last two works, the Kullback-Leibler divergence (KLD) was used as a criterion for adaptive waveform design. Multiple-input multiple-output (MIMO) radar [5]-[7], has attracted the attention of many researchers in the last decade. One of the main directions of research within the topic of MIMO radar is waveform design, which has been intensively investigated in the recent years. Waveform optimization for MIMO radar target localization using the Cramér-Rao bound (CRB), was studied in [8]. In [9], [10] waveform design based on mutual information and minimum mean-square-error (MMSE) was considered and it was shown that by using optimized waveforms, better detection performance can be ob- tained. In [11] sequential Bayesian inference was investigated using adaptive polarized waveform design for target tracking. In this paper, an adaptive spatial waveform design tech- nique for target enumeration is proposed. A multiple-input single-output radar is considered. At each step, the posterior probabilities for the different hypotheses which are charac- terized by the number of targets, are computed. The spatial waveform for the next transmit pulse is designed in order to minimize an approximated lower bound on the average sample number (ASN). The paper is organized as follows. The next section presents the signal model and the problem statement. In Sec- tion III the criterion for waveform optimization is stated and an adaptive waveform design scheme is presented. Section IV derives an algorithm based on Bayesian information criterion (BIC) for target enumeration and computation of the posterior probabilities. In Section V, the performance of the proposed adaptive waveform design technique is evaluated and compared to fixed, orthogonal waveform transmission. II. SIGNAL MODEL Consider a mono-static radar consisting of a transmit array of N T transmitters and a single receiving element. The received signal model for a given range-Doppler cell in the presence of M targets can be expressed as [5], [6] x k,l = s T k,l M X m=1 α m a T (θ m )+v k,l , k =1, 2,..., l =1,...,L (1) where x k,l ∈ C, v k,l ∈ C, and s k,l ∈ C N T are the received signal, the additive noise, and the transmit signal vector at the lth snapshot of the kth step, and L denotes the number of snapshots at each step. The parameters α m and θ m denote the complex attenuation and direction of the mth target, respectively, and a T (·) ∈ C N T is the transmit array steering vector where the array origin is set to the location of the receiving element. We assume that {v k,l } are independent and identically distributed (i.i.d.) complex circularly symmetric Gaussian random variables with zero mean and variance σ 2 . We will assume that the number of targets at the considered range-Doppler cell, M , is smaller than the number of transmit array elements, N T . This assumption is required also in non- parametric source enumeration methods, which are based on identification of the noise subspace whose size is given by M - N T . The sufficient statistic for estimating the target param- eters at the kth step is given by correlating the received signal with transmit signal. Let A T 4 =[a T (θ 1 ),..., a T (θ M )], α 4 = [α 1 ,...,α M ] T , and R s k 4 =  1 L ∑ L l=1 s k,l s H k,l  * . Then, the data model for the sufficient statistic, y 4 = R -1/2 s k 1 L ∑ L l=1 s * k,l x k,l , is given by [6] y k = R 1/2 s k A T α + w k , k =1, 2, .... (2) 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) 978-1-4673-3146-3/13/$31.00 ©2013IEEE 69