Geometry based stochastic channel modeling89 cos(2+) 8 cos(2+8) h(t) . ...6 cos(2对1+0n) & Figure 4.8 SoS method of channel waveform generation. densityor.ateratively by the autocorrelation function(2002)ames K.Caver (2002)LHanzo and Keller eve the the simulated PDF of the random thesquare oot of e approximated tothe desired one ng the charact ristics of the The cut-off frequencies of in the digital domain. Cp3时pe line and low rm are fol in stages.The clear that the ethods filter gaus rly designed filters to te the channe waveform with the desired Doppler PSD. ane 0D the non-rational Dop mate the waveform with the non-rational Doppler PSD,the filter models have to include high-order filter approach beingsi compl ate e-consuming. the Dopple sing the rmeionedtri ben wielydtheting point of thenrionGeometry based stochastic channel modeling 89 cos(2 ) S 1 T1 f t C1 cos(2 ) S 1 T1 f t cos(2 ) S 2 T 2 tf C2 h(t) + Cn . . . . . . ( ) cos(2 ) n n S tf T Figure 4.8 SoS method of channel waveform generation. same variances are passed through identical lowpass filters to limit and reshape its spectrum. A Gaussian random process is completely characterized by its mean value and color, which can be described either by the power spectral density or, alternatively by the autocorrelation function Pätzold (2002)ames K. Caver (2002)L. Hanzo and Keller (2000)Stüber (2001). The purpose of filtering is to achieve the maximum possible resemblance of the simulated spectrum with the theoretical one Clarke (1968). These filters only limit and shape the spectrum but do not alter the PDF of the random process. However, these filters reduce the variances of the processes. The filter transfer function is the square root of the desired spectrum shape. The theoretical spectrum is U-shaped with limits equal to the maximum positive and negative Doppler shifts, which are equal to ν/λ, where ν is the velocity of the mobile unit and λ is the wavelength of the signal. It is practically not possible to shape the spectrum as the theoretical one, however it can be approximated to the desired one by controlling the characteristics of the shaping filter. The cut-off frequencies of these filters are equal to the maximum Doppler shift. These filters can be implemented in the analogue as well as in the digital domain. Digital implementation is flexible and gives very close approximation to the desired U-shaped spectrum. In practical digital implementations, the filters operate at a lower sampling frequency. In order to bring the sampling rate up to the value required by the signal representation, the spectrum shaping filters are followed by interpolators. The interpolation involves up sampling and lowpass filtering. It is efficient to perform interpolation in stages. Therefore, an overall interpolation factor is usually split into a number of cascaded stages to avoid large numbers of filter coefficients. It is clear that the filter methods filter Gaussian noise through properly designed filters to generate the channel waveform with the desired Doppler PSD, e.g., U-shape, flat shape, etc. The main limitation of this approach is that only the waveform with rational forms of the Doppler PSD can be produced exactly. However, as mentioned in Stüber (2001), the non-rational Doppler PSD is the typical form of Doppler PSD in reality. In order to approximate the waveform with the non-rational Doppler PSD, the filter models have to include high-order filters, which lead to this approach being significantly complicated and time-consuming. Moreover, the Doppler PSD obtained by using this approach is not band-limited since it is difficult to implement the filters with sharp stop-bands in practice. Although the filter method has the aforementioned limitations, it has been widely accepted as the starting point of the investigation of simulation models