Position, Navigation, and Timing Technologies in the 21st Century. Группа авторов

bias. Since the chip interval is known and the PN offset can be decoded by the receiver, only δt_s needs to be estimated.

      It is worth noting that the cdma2000 standard requires the BTS’s clock to be synchronized with GPS to within 10 μs, which translates to a range of approximately 3 km (the average cell size) [51]. Note that a PN offset of 1 (i.e. 64 chips) is enough to prevent significant interference from different BTSs. This translates to more than 15 km between BTSs. Subtracting 6 km from this value due to worst‐case synchronization with GPS (i.e. 3 km for each BTS), BTSs at 9 km or more from the serving BTS could cause interference (assuming all BTSs suffer from the worst‐case synchronizations). But 9 km is larger than the maximum distance for receiving cellular CDMA signals for ground receivers. Therefore, this synchronization requirement is enough to prevent severe interference between the short codes transmitted from different BTSs and maintains the CDMA system’s capability to perform soft hand‐offs [47]. The clock bias of the BTS can therefore be neglected for communication purposes. However, ignoring δt_s in navigation applications can be disastrous, and it is therefore crucial for the receiver to know the BTS’s clock bias. The estimation of δt_s can be accomplished via the frameworks discussed in Section 38.4.

      38.5.1.6 Received Signal Model

      Assuming the transmitted signal to have propagated through an additive white Gaussian noise channel with a power spectral density of , a model of the received discrete‐time signal r[m] after radio frequency (RF) front‐end processing: down‐mixing, a quadrature approach to bandpass sampling [52], and quantization can be expressed as

(38.5)

where t_s(t_m) ≜ δt_TOF + Δ(t_k − δt_TOF) is the PN code phase of the BTS, t_m = mT_s is the sample time expressed in receiver time, T_s is the sampling period, δt_TOF is the time of flight (TOF) from the BTS to the receiver, θ is the beat carrier phase of the received signal, and n[m] = n_I[m] + jn_Q[m] with n_I and n_Q being independent and identically distributed Gaussian random sequences with zero mean and variance . The receiver presented in Section 38.5.2 will operate on the samples of r[m] in Eq. (38.5).

      38.5.2 CDMA Receiver Architecture

      This section details the architecture of a cellular CDMA navigation receiver, which consists of three main stages: signal acquisition, tracking, and message decoding [18]. The receiver utilizes the pilot signal to detect the presence of a CDMA signal and then tracks it. Section 38.5.2.1 describes the correlation process in the receiver. Sections 38.5.2.2 and 38.5.2.3 discuss the acquisition and tracking stages, respectively. Section 38.5.2.4 details decoding the sync and paging channel messages.

      38.5.2.1 Correlation Function

      Given samples of the baseband signal exiting the RF front‐end defined in Eq. (38.5), the cellular CDMA receiver first wipes off the residual carrier phase and match‐filters the resulting signal. The output of the matched filter can be expressed as

(38.6)

where is the beat carrier phase estimate, and h is a pulse shaping filter, which is a discrete‐time version of the one used to shape the spectrum of the transmitted signal, with a finite‐impulse response (FIR) given in Table 38.3. The samples m′ of the FIR in Table 38.3 are spaced by .

Table 38.3 FIR of the pulse shaping filter used in cdma2000 [50]

      Source: 3GPP2, “Physical layer standard for cdma2000 spread spectrum systems (C.S0002‐E),” 3rd Generation Partnership Project 2 (3GPP2), TS C.S0002‐E, June 2011. Reproduced with permission of 3CPP2.

m′	h[m′]	m′	h[m′]	m′	h[m′]
0, 47	−0.02528832	8, 39	0.03707116	16, 31	−0.01283966
1, 46	−0.03416793	9, 38	−0.02199807	17, 30	−0.14347703
2, 45	−0.03575232	10, 37	−0.06071628	18, 29	−0.21182909
3, 44	−0.01673370	11, 36	−0.05117866	19, 28	−0.14051313
4, 43	0.02160251	12, 35	0.00787453	20, 27	0.09460192
5, 42	0.06493849	13, 34	0.08436873	21, 26	0.44138714
6, 41	0.09100214	14, 33	0.12686931	22, 25	0.78587564
7, 40	0.08189497	15, 32	0.09452834