GPS World, January 2017

3 21 tracking and the computation of range measurements The pre detection integration interval applicable to the tracking channel is illustrated in the figure By parallelizing this beamforming process multiple beams can be formed simultaneously for each tracking channel as shown in Figure 1 Next consider 1 N duty cycling applied to the tracking channel described above where N is the number of antenna elements This can be implemented as sample gating as illustrated in FIGURE 4 It should be clear that this duty cycling negates the N fold S N 0 advantage of traditional beamforming In other words in the absence of multipath the carrier to noise density ratio C N 0 measured by the duty cycled tracking channel that has formed a beam towards the received signal will equal the mean C N 0 values measured by N single element tracking channels each connected to the individual sample streams However it should be clear that the spatial gain pattern of the CRPA specific to the set of phase shifts applied to the elements is unaffected by the duty cycling process This means that such a system would have the same multipath rejection properties of the non duty cycled case because the multipath is still attenuated relative to the direct signal Consider now the case where each phase aligned sample stream is sequentially selected for 1 N of the integration interval as illustrated in FIGURE 5 This is essentially identical to an N to 1 switch connected to the input of the tracking channel Clearly since no coherent combination of sample streams is taking place C N 0 measured by this tracking channel will equal the mean C N 0 values of the individual sample streams the same as that for 1 N duty cycling as depicted in Figure 4 Consider only a GNSS signals carrier signal buried 58 GPS WORLD WWW GPSWORLD COM JANUARY 2017 3 21 within the uncorrelated thermal noise For the relatively short duration of an integration interval the carrier signals within the phase aligned sample streams can be assumed to be time invariant that is each given cycle is the same as the ones before and after it Therefore whether all N sample streams are summed over a 1 N integration interval duty cycling or integrating 1 N of each sample stream over the entire integration interval the processing gain remains the same Under the assumption of time invariance the beam gain also remains unchanged Therefore it can be said that these two processes are equal It is stressed that this equality holds true only for time invariant signals For example the multipath rejection ability discussed previously is retained for N to 1 switching However there is no rejection capability for non time invariant signals such as broadband noise Rather than performing phase alignment prior to N to 1 switching it could be built into the switching process itself This is conceptually illustrated in FIGURE 6 It is clear that phase shifting can be applied to either the incoming sample stream or the local replica to yield the same result Hence the phase rotations illustrated in Figure 6 can also be implemented by adding appropriate phase offsets to the phase accumulation register of the tracking channels carrier numerically controlled oscillator NCO This is also known as phase bumping the carrier NCO illustrated in Figure 2 The two compelling advantages of NCO phase bumping over phase rotating the switched sample stream are 1 the resolution of a phase offset that can be applied to the carrier NCO is 1 2 K cycles where K represents the number of bits comprising the NCO phase register Typically K can range between 20 and 64 bits resulting Phase shifters Summation of switched phase shifted sample streams Integration interval Switching index 0 Element 0 Reference Element 1 Element 2 Element 3 Phase shifts Switched and phase shifted sample streams Integration interval Switching index 0 Element 0 Reference Element 1 Element 2 Element 3 FIGURE 5 Illustration of 1 N duty cycling replaced by N to 1 switching FIGURE 6 Illustration of N to 1 switching with phase shifts applied at switch state transitions