## 5 Experimental Tests
### Transmission Parameters of UAC Channel  
The multipath propagation phenomenon's intensity can be expressed with two basic transmission parameters of the communication channel, namely, the delay spread and the coherence bandwidth. In order to estimate these parameters, the Time-Varying Impulse Response (TVIR) was measured by the correlation method with the use of a Pseudo-Random Binary Sequence (PRBS) signal, based on an m-sequence of rank 8. The carrier frequency \(f_{c}\) and the sampling frequency \(f_{s}\) in each case were equal to 30 kHz and 200 kHz, respectively. The impulse response was measured using a PRBS signal of 5 different bandwidths, corresponding to the communication signal's bandwidths. For measured bandpass impulse responses, its complex baseband equivalent \(h(t,\tau)\) was calculated, defined in a window of observation time \(t\), and delay \(\tau\). A maximum value of delay t is a duration of a single realization of TVIR. It is equal to a single-probe sequence duration, that is, \(T_{s}=\frac{R_{s}L}{f_{s}}=102.3\) ms, where \(L=2^{8}-1\) denotes the number of m-sequence bits and \(R\) denotes the upsampling factor, which is equal to \(\frac{f_{s}}{B}\), where \(B\) is the bandwidth of the PRBS signal. The probe sequence was repeated numerous times, which allowed the capture of up to 48 realizations of the impulse response. Thus, \(h(t,\tau)\) is a discrete-time function defined in the \(\tau\) domain with a resolution equal to \(1/f_{s}\), and in the \(t\) domain with a resolution equal to probe signal duration \(T_{s}\). TVIR is a basis for calculating the Time-Varying Transfer Function (TVTF) \(H(t,f)\) with the use of Fourier transform. The autocorrelation function of TVIF is called the Space-Time-Frequency Correlation Function (STFCF) \(R_{h}(\Delta t,\Delta f)\). It is a basis for calculating the 2-dimensional Scattering Function (SF) in the manner described by Equation (3):  
\[S(\
u,\tau)=\int_{\Delta t}\int_{\Delta f}R_{h}(\Delta t,\Delta f)e^{-j2\pi( \
u\Delta t-\tau\Delta f)}d\Delta td\Delta f \tag{3}\]  
where \(\Delta t\) and \(\Delta f\) are time and frequency differences, respectively, \(\
u\) is the Doppler spread, \(\tau\) is the delay, and \(R_{h}(\Delta t,\Delta f)\) is the STFCF of the channel. The integral of \(S(\
u,t)\) over \(\
u\) gives the Power Delay Profile (PDP) \(P(\tau)\). Based on PDP, the delay spread is obtained as a maximum delay spread \(\tau_{M}\) measured at a threshold level of 0.1 of a maximum value of \(P(\tau)\), and as root-mean-square (rms) value \(\tau_{rms}\):  
\[\tau_{rms}=\sqrt{\tau^{2}-\tau_{m}^{2}} \tag{4}\]  
where:  
\[\tau^{2}=\frac{\sum_{k}P(\tau_{k})\tau_{k}^{2}}{\sum_{k}P(\tau_{k})},\quad \tau_{m}^{2}=\frac{\sum_{k}P(\tau_{k})\tau_{k}}{\sum_{k}P(\tau_{k})}\]  
Averaging \(R(\Delta t,\Delta f)\) over the \(\Delta t\) domain gives the Space-Frequency Correlation Function (SFCF) \(R(\Delta f)\). The coherence bandwidth \(B_{c}\) is calculated as the width of \(R(\Delta f)\) at a threshold level \(T_{r}\) equal to 0.5 and 0.7 [20]. Figures 11-15 show the modules of TVIRs, PDPs, and SFCFs estimated based on measurements performed by PRBS signals of different bandwidths. It can be clearly seen in the plots of modules of TVIRs and PDPs that the relative intensity of multipath propagation increases with the increased signal bandwidth. The shape of the SFCF also changes as the probe signal bandwidth increases. The transmission parameters of a measured UAC channel are shown in Table 9. The values vary depending on the bandwidth of the measurement signal. The maximum delay spread, estimated on the basis of TVIR measured with a sequence of duration 255 ms, is equal to about 62 ms, and this is almost twice as long as the one estimated from the measurement with a signal with a bandwidth of 8 kHz. The rms values of the delay spread differ even more. The value estimated in the  
case of the 1 kHz measurement signal is four times larger than the one estimated based on the results of measurements performed at a bandwidth of 8 kHz.