ICA-Based Super Resolution Pulse Compression Algorithm Incorporated by MUSIC Algorithm Tetsuhiro Okano, Shouhei Kidera and Tetsuo Kirimoto Graduate School of Informatics and Engineering, University of Electro-Communications, Tokyo, Japan e-mail : okano@secure.ee.uec.ac.jp Abstract—Pulse compression promises higher range resolu- tion in radar systems while avoiding high instantaneous power transmission. For super-high-resolution estimation of the time of arrival, multiple-signal classification (MUSIC) has been already proposed. However, this method suffers severely from accuracy distortion or low resolution when a number of highly correlated interference signals are mixed in the same range gate. As a solution to this problem, we propose a novel pulse compression algorithm by incorporating independent component analysis, which is a powerful tools for blind signal separation, into MUSIC. Numerical simulation shows that the proposed method achieves higher range resolution and accuracy than conventional MUSIC, particularly for lower signal-to-noise ratios. Key words—Independent component analysis (ICA), multiple- signal classification (MUSIC), radar pulse compression, time of arrival (TOA) estimation. I. I NTRODUCTION Pulse compression is commonly used in radar systems to obtain a sufficient range resolution while avoiding high peak transmission power. As the classical pulse compression scheme, cross-correlation algorithms [1], [2] have been in- tensively employed. However, such algorithms hardly sep- arate the target signal within the same range gate strictly determined by the transmission bandwidth. As a super-high- resolution technique to resolve the above difficulty, multiple- signal classification (MUSIC) [3], which is based on the resolution exploiting the eigenvectors of the noise subspace, has been proposed. However, its accuracy in estimating time of arrival (TOA) seriously degrades for lower signal-to-noise ratios (SNRs) or in the case that there are a number of highly correlated interference signals in the same range gate. To overcome the above problem, this paper proposes a novel pulse compression algorithm by incorporating independent component analysis (ICA) into MUSIC. ICA is one of the most useful tools for blind source separation, and requires only the statistical independence of the source signals for signal reconstruction [4]. In recent years, several ICA algorithms suitable for complex signals have been developed [5], [6], and successfully decomposed multiple deterministic signals as complex sinusoidal signals with different frequencies have been reported [7]. Such algorithms are also useful for pulse compression, because TOA estimation corresponds to the separation of the multiple complex sinusoidal signals in the frequency domain. As preprocessing for the proposed method, ICA is applied to observation signals to avoid resolution degradation due to coherent interference effects. Signal Generator s( t ) TOA Estimation x( t ) Transmitting & Receiving Antenna Transmitter Multiple-point scattering A/D Converter Receiver Duplexer Fig. 1. System model. In addition, to enhance the separation performance of com- plex sinusoidal signals at the frequency resolution, we intro- duce a novel ICA algorithm based on maximum likelihood criteria specified by a priori information of the probability density function (PDF) of complex sinusoidal signals. Numeri- cal simulations verify that the range resolution and accuracy of the proposed method are superior to those of the conventional MUSIC method. II. SYSTEM MODEL Figure 1 shows the system model. This paper assumes monostatic radar and multiple-point scattering. We consider a chirp-modulated transmitted signal, and the received signal is simply expressed as x(t)= L  i=1 a i s(t − τ i )+ n(t), (1) where a i is amplitude, τ i denotes each time of arrival, L is the number of signals, s(t) denotes the transmitted signal with chirp modulation, n(t) expresses a Gaussian white noise. We define the frequency transfer function as Z (nΔω) ≡ X (nΔω) S(nΔω) = L  i=1 a i exp(−jnΔωτ i )+ N (nΔω) S (nΔω) , (n =1, 2, ..., N ), (2) where X (ω), S(ω) and N (ω) are the Fourier transform of x(t), s(t) and n(t), N is the total number of frequency points, and Δω denotes the frequency sampling rate. III. CONVENTIONAL METHOD MUSIC has been proposed as a super-high-resolution method for TOA estimation. MUSIC positively employs eigen- vectors determined by the noise subspace decomposed from