Principles of Modern Radar - Volume 2 1891121537

784 CHAPTER 17 Advanced Processing Methods for Passive Bistatic Radar SystemsAs previously mentioned, in FUSC mode the variable pilots position is different for evenandodd-numbered OFDM symbols. However, frequency spacing among variable pilotswithin an OFDM symbol is constant and equal to 12f. Considering the alternate transmissionsof odd and even symbols and the relative displacement of the pilots subcarrierssets between consecutive symbols, the whole set A V of intrasymbol side peaks due tovariable pilots can be written asA V ={(n T U6 , i ); n ∈T S{((2n + 1) T U12 , 2i + 1 ); n ∈2T S[ ⌊1, ..., 6 T ⌋ ] }S− 1 ; i ∈ Z ∪T U[ ⌊1, ..., 6 T ⌋ ] }S− 1 ; i ∈ ZT U(17.32)Notice that the temporal separation, T U /6, between peaks corresponds to the inverse ofthe frequency displacement, 6f, between the pilots subcarriers sets exploited by odd andeven symbols. In Figure 17-21b, the first five intrasymbol side peaks due to variable pilotsare labeled with stars.Similarly the set B V of intersymbol side peaks caused by variable pilots is given byB V = {(2qT S , 0) ; q ∈ N} ∪{(qT S + T G + n T U6 , i )T S; n ∈{(qT S + T G + (2n + 1) T U12 , 2i + 1 ); n ∈2T S[ ⌊1, ..., 6 T ⌋ ]}S− 1 ; q ∈ N; i ∈ Z ∪T U[ ⌊1, ..., 6 T ⌋ ]}S− 1 ; q ∈ N; i ∈ ZT U(17.33)In Figure 17-21b, the first six intersymbol side peaks due to variable pilots are labeled withsquares. As expected, the first peak of this set appears at τ = T S + T G + T U /6 = 126.9 μs(T G = T U /8 in the considered example). Notice that the level of side peaks due to variablepilots is greater than the level of side peaks due to fixed pilots since a higher number ofsubcarriers is devoted to variable pilots.Obviously, side peak distributions are different for FUSC and PUSC transmissionmodes [15]. However, the obtained PSLR is comparable in the two cases. Specifically, thePSLR is dominated by the peak caused by the guard interval whose level has a theoreticalvalue equal to 20log 10 (T G /T U ) = –18 dB with respect to the main peak.Regarding the distribution of side peaks in the Doppler dimension, the first Dopplerside peak set (due to the preamble subcarriers allocation) appears at a Doppler frequencycorresponding to the inverse of the temporal separation between consecutive DL frames(1/T frame ). However, the preamble contribution to the AF of the whole DL frame canbe reasonably neglected. In any case, the single OFDM symbol corresponding to thepreamble might be left out of the integration time with a very small SNR degradation.Consequently, the first Doppler side peak set due to pilot tones appears at a Dopplerfrequency equal to f D = 1/2T S = 4.96 kHz. This Doppler frequency value correspondsto a bistatic velocity of about 765 km/h (in the worst case a 3.5 GHz carrier frequency).However, additional sidelobe structures appear at a Doppler frequency equal to 500 Hz(Figure 17-21). Such peaks are obviously because of the pulsed nature of the consideredsignals that consist of DL frames of duration T DL transmitted every T frame . The Dopplerambiguities result from the equivalent PRF = 1/T frame , which is not within the control ofthe radar designer. As an example, for the 2 ms frame duration considered in Figure 17-21,