1 Computer simulation of weather radar signals Sutanay Choudhury , Nitin Bharadwaj Department of Electrical & Computer Engineering Colorado State University Abstract: Computer simulation is largely used in radar signal analysis. This present work treats the simulation of precipitation echoes in weather radar application. where two different approaches are used for simulating weather radar signals. These simulated signals offer great potential for estimating spectral moment and various polarimetric variables .One of the methods uses a time domain approach while the other uses the frequency domain approach. We show that the simulated signals reflect the desired properties. Both the simulation algorithms are based on a macroscopic model, i.e. a random processes with an assigned power spectrum. 1.Introduction : Weather radar signals are a composite of echoes from a very large number of individual hydrometeors or from refractive index irregularities in clear air. The conventional single-polarized Doppler radar uses the measurement of radar reflectiviy, radial velocity, and storm structure to infer some aspects of hydrometeor types and amounts. With the advent of dual-polarized radar techniques it is generally possible to achieve significantly higher accuracy. From simulation point of view, this implies the generation of two pseudorandom sequences with an assigned autocorrelation function and an assigned cross correlation. Computer simulation of the precipitation echo is necessary to study signal processing and data extraction .By means of a signal simulator it is possible to evaluate the effectiveness of a signal processing algorithm in a controlled environment. The weather echoes contribute to produce a complex voltage V=I+jQ. A rain signal simulator shall provide in phase and in quadrature components of the channel in horizontal polarization, (I H , Q H ), and of the channel in the vertical polarization, (I V , Q V ) with correct marginal and joint densities. As the rain echo is assumed to be a stationary Gaussian process it follows that it is completely characterized by its covariance matrix and it is sufficient to simulate correctly the autocovariance and mutual covariance between the H and the V. The parameters involved in the selection of the generation method are-N P , Z, Z DR , and the shape of the autocorrelation coefficient at lag k,ρ(k), k>1. In this project two methods are considered: the first, called the FCG (Fast Convolution Generator) uses a fast convolution in the frequency domain, while the other creates the spectral components (Fourier harmonics) of the sequence. 2. Time series with an assigned polarization using FCG : The weather echo, supposed stationary is characterized by the power spectral density given by ( 29         - - = 2 2 2 2 exp 2 1 ) ( f D f y f f f S σ πσ And a autocorrelation function as follows, ), 1 ( ) ( ) ( * + = k y k Ey n R n, k integers, Where f D is the Doppler frequency and σ f is the spectral width. The relationship between σ f and velocity spread σ V of the radial speed of hydrometeors is λ σ σ v f 2 = , Where λ is the radar wavelength. The purpose of the generator is to generate a complex random signal having the properties (1) and (2). This is equivalent, as regard s the spectral properties, to generate a time series with an autocorrelation coefficient equal to ( 29 [ ] [ ] S D S f nT f j nT n π πσ ρ 2 exp 2 exp ) ( 2 ⋅ - = Where T S is the pulse repetition period. An FIR filter is used to implement the FCG.The underlying principle is based upon the “coloration “ of a white spectrum by linear filtering. Complex Gaussian white noise (S x (f)=1) is colored by an FIR filter. The output time series obtained from this filter in the frequency domain is ( 29 ( 29 ( 29 f X f H f Y ⋅ =