# Assessing the Spoofing Threat: Development of a Portable GPS Civilian Spoofer

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8 from packing 32 samples of quantized carrier replicas over a ±-khz range of Doppler frequency offsets and 2π radians of carrier phase. This is another way of saying that the information content of the quantized sampled carrier replicas is low, which is to be expected. Figure 8 illustrates this concept by showing a case with a sampling frequency f s = 5.74 MHz, an intermediate frequency f IF =.45 MHz, and a Doppler frequency range of ±khz. This Doppler frequency range covers the expected range of Doppler shifts seen by a terrestrial GPS receiver, with 5 khz of margin for receiver clock rate error. The sampling and intermediate frequencies are typical for civil GPS applications. Over the interval shown in Fig. 8, the total number of cycles for the two signals, whose initial phases are aligned, differs by less than /8 of a cycle. When sampled and 2-bit quantized into the sign (s) and magnitude (m) bits that run along the bottom of each frame, the resultant carrier replicas have the same sign-bit history and only different magnitude bits. This indicates that the sampled carrier replicas covering a reasonable Doppler shift frequency range are primarily a function of the initial phase offset for each 32-bit word. This observation remains true whenever f IF < f s and f D,mabs << f IF, where f D,mabs is the maximum absolute value of the Doppler frequency shift s m s m Maximum Minimum Doppler Shift = = + KHz Hz Minimum Maximum Doppler Shift = + = KHzHz Bit Number in Word Fig. 8. Two-bit quantization of the local carrier replica at the maximum and minimum Doppler frequency shifts. The low information content of the sampled carrier replicas makes them amenable to tabular storage and efficient retrieval. Two tables are required, one each for the sign and magnitude bits. Let i f {,,, N f } and i θ {,,, N θ } represent the respective indices into the frequency and phase dimensions of the tables. For each carrier replica segment (typically -ms long), a single frequency index is calculated as ( ) fd f D,min i f = round N f (6) f D,max f D,min where f D is the exact desired frequency and f D,min and f D,max are the minimum and maximum Doppler frequency shifts. The phase index i θ is different for each of the 32- bit words that are strung together to compose the carrier replica segment. Let τ k be the time offset of the midpoint of the kth word in the segment relative to the time of the first sample in the segment. The phase at the midpoint of the kth word is calculated as θ mid,k = mod [2π(f IF + f D )τ k + θ ] (7) where θ is the phase of the first sample in the segment, and the modulo operation is modulo 2π. Finally, the phase index of the kth word is calculated as ( ) θmid,k i θk = round 2π N θ (8) To meet precision requirements, the number of indices into the frequency and phase dimensions of the tables were set respectively to N f = 32 and N θ = 256. With this table size, the table-generated carrier replicas are not significantly different from carrier replicas generated by applying the exact phase and frequency values using doubleprecision computations. The sign and magnitude tables occupy a total of 64 kb in on-chip memory. B.4 Data Bit Predictor The GPS L navigation data bit sequence {d n,j, d n,j+, } required by the nth spoofer channel is most easily generated in one of two ways. The simplest approach is to pass data bits to the spoofer channels as soon as they can be reliably read off the incoming GPS signals. Naturally, this approach results in a delay in the arrival time of the spoofing data bit as compared to that of the true data bit at the target receiver s antenna. The delay is most conveniently made an integer number of -ms C/A code intervals. Clearly, such a delay is undesirable in a spoofer because a target receiver could be designed to watch for such a delay and thereby detect a spoofing attack. The second approach is to predict the data bits based on knowledge of the bit structure and a recent bit observation interval. This is the function of the receiver-spoofer s data bit predictor. This method relies on the fact that the GPS navigation message has a 2.5-minute period and remains nearly perfectly predictable for a period of two hours. In fact, the almanac component of the 2.5-minute data block is refreshed by the GPS Control Segment only once per day, and the remaining data the individual satellite 8

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### PCM Encoding and Decoding:

PCM Encoding and Decoding: Aim: Introduction to PCM encoding and decoding. Introduction: PCM Encoding: The input to the PCM ENCODER module is an analog message. This must be constrained to a defined bandwidth