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Global Positioning Systems, Inertial Navigation, and Integration, Mohinder S. Grewal, Lawrence R. Weill, Angus P. Andrews Copyright # 2001 John Wiley & Sons, Inc. Print ISBN 0-471-35032-X Electronic ISBN 0-471-20071-9 4 Receiver and Antenna Design 4.1 RECEIVER ARCHITECTURE Although there are many variations in GPS receiver design, all receivers must perform certain basic functions. We will now discuss these functions in detail, each of which appears as a block in the diagram of the generic receiver shown in Fig. 4.1. 4.1.1 Radio-Frequency Stages (Front End) The purpose of the receiver front end is to ®lter and amplify the incoming GPS signal. As was pointed out earlier, the GPS signal power available at the receiver antenna output terminals is extremely small and can easily be masked by interference from more powerful signals adjacent to the GPS passband. To make the signal usable for digital processing at a later stage, RF ampli®cation in the receiver front end provides as much as 35±55 dB of gain. Usually the front end will also contain passband ®lters to reduce out-of-band interference without degradation of the GPS signal waveform. The nominal bandwith of both the L1 and L2 GPS signals is 20 MHz (10 MHz on each side of the carrier), and sharp cutoff bandpass ®lters are required for out-of-band signal rejection. However, the small ratio of passband width to carrier frequency makes the design of such ®lters infeasible. Consequently, ®lters with wider skirts are commonly used as a ®rst stage of ®ltering, which also helps to prevent front-end overloading by strong interference, and the sharp cutoff ®lters are used later after downconversion to intermediate frequencies (IFs). 80 4.1 RECEIVER ARCHITECTURE 81 Antenna RF stage First IF stage Second Mixer First Mixer BPF Amp Second IF stage BPF Amp BPF LO Reference oscillator Amp A/D converter LO Frequency synthesizer Digitized IF signal Clocks Interrupts Code aquisition/tracking Carrier acquisition/tracking Message bit synchronization Navigation message demodulation Code/carrier pseudoranging Delta-range measurements H/W & S/W Signal Proccessing External inputs (INS, altimeter, Loran-C, clock aiding) Navigation processing (includes Kalman filtering) Navigation outputs (position, velocity, time, fault, detection/isolation) Fig. 4.1 Generic GPS receiver. 4.1.2 Frequency Downconversion and IF Ampli®cation After ampli®cation in the receiver front end, the GPS signal is converted to a lower frequency called an intermediate frequency for further ampli®cation and ®ltering. Downconversion accomplishes several objectives: 1. The total amount of signal ampli®cation needed by the receiver exceeds the amount that can be performed in the receiver front end at the GPS carrier frequency. Excessive ampli®cation can result in parasitic feedback oscillation, which is dif®cult to control. In addition, since sharp cutoff ®lters with a GPS signal bandwidth are not feasible at the L-band, excessive front-end gain makes the end-stage ampli®ers vulnerable to overloading by strong nearby out-of-band signals. By providing additional ampli®cation at an IF different from the received signal frequency, a large amount of gain can be realized without the tendency toward oscillation. 2. By converting the signal to a lower frequency, the signal bandwidth is unaffected, and the increased ratio of bandwidth to center frequency permits the design of sharp-cutoff bandpass ®lters. These ®lters can be placed ahead of the IF ampli®ers to prevent saturation by strong out-of-band signals. The ®ltering is often by means of surface acoustic wave (SAW) devices. 82 RECEIVER AND ANTENNA DESIGN 3. Conversion of the signal to a lower frequency makes the sampling of the signal required for digital processing much more feasible. Downconversion is accomplished by multiplying the GPS signal by a sinusoid called the local oscillator signal in a device called a mixer. The local oscillator frequency is either larger or smaller than the GPS carrier frequency by an amount equal to the IF. In either case the IF signal is the difference between the signal and local oscillator frequencies. Sum frequency components are also produced, but these are eliminated by a simple band-pass ®lter following the mixer. An incoming signal either above or below the local oscillator frequency by an amount equal to the IF will produce an IF signal, but only one of the two signals is desired. The other signal, called the image, can be eliminated by bandpass ®ltering of the desired signal prior to downconversion. However, since the frequency separation of the desired and image signals is twice the IF, the ®ltering becomes dif®cult if a single downconversion to a low IF is attempted. For this reason downconversion is often accomplished in more than one stage, with a relatively high ®rst IF (30±100 MHz) to permit image rejection. Whether it is single stage or multistage, downconversion typically provides a ®nal IF that is low enough to be digitally sampled at feasible sampling rates without frequency aliasing. In low-cost receivers typical ®nal IFs range from 4 to 20 MHz with bandwidths that have been ®ltered down to several MHz. This permits a relatively low digital sampling rate and at the same time keeps the lower edge of the signal spectrum well above 0 Hz to prevent spectral foldover. However, for adequate image rejection either multistage downconversion or a special single-stage image rejection mixer is required. In more advanced receivers there is a trend toward single conversion to a signal at a relatively high IF (30±100 MHz), because advances in technology permit sampling and digitizing even at these high frequencies. Signal-to-Noise Ratio An important aspect of receiver design is the calculation of signal quality as measured by the signal-to-noise ratio (SNR) in the receiver IF bandwith. Typical IF bandwidths range from about 2 MHz in low-cost receivers to the full GPS signal bandwidth of 20 MHz in high-end units, and the dominant type of noise is the thermal noise in the ®rst RF ampli®er stage of the receiver front end (or the antenna preampli®er if it is used). The noise power in this bandwidth is given by N ˆ kTe B 4:1† where k ˆ 1:3806  10 23 J=K, B is the bandwidth in Hz, and Te is the effective noise temperature in degrees Kelvin. The effective noise temperature is a function of sky noise, antenna noise temperature, line losses, receiver noise temperature, and ambient temperature. A typical effective noise temperature for a GPS receiver is 513 K, resulting in a noise power of about 138:5 dBW in a 2-MHz bandwidth and 128:5 dBW in a 20-MHz bandwidth. The SNR is de®ned as the ratio of signal power to noise power in the IF bandwidth, or the difference of these powers when 4.1 RECEIVER ARCHITECTURE 83 expressed in decibels. Using 154:6 dBW for the received signal power obtained in Section 3.3, the SNR in a 20-MHz bandwidth is seen to be 154:6 128:5† ˆ 26:1 dB. Although the GPS signal has a 20-MHz bandwidth, about 90% of the C=A-code power lies in a 2-MHz bandwith, so there is only about 0.5 dB loss in signal power. Consequently the SNR in a 2-MHz bandwidth is 154:6 0:5† 138:5† ˆ 16:6 dB. In either case it is evident that the signal is completely masked by noise. Further processing to elevate the signal above the noise will be discussed subsequently. 4.1.3 Digitization In modern GPS receivers digital signal processing is used to track the GPS signal, make pseudorange and Doppler measurements, and demodulate the 50-bps data stream. For this purpose the signal is sampled and digitized by an analog-to-digital converter (ADC). In most receivers the ®nal IF signal is sampled, but in some the ®nal IF signal is converted down to an analog baseband signal prior to sampling. The sampling rate must be chosen so that there is no spectral aliasing of the sampled signal; this generally will be several times the ®nal IF bandwidth (2±20 MHz). Most low-cost receivers use 1-bit quantization of the digitized samples, which not only is a very low cost method of analog-to-digital conversion, but has the additional advantage that its performance is insensitive to changes in voltage levels. Thus, the receiver needs no automatic gain control (AGC). At ®rst glance it would appear that 1-bit quantization would introduce severe signal distortion. However, the noise, which is Gaussian and typically much larger than the signal at this stage, introduces a dithering effect that, when statistically averaged, results in an essentially linear signal component. One-bit quantization does introduce some loss in SNR, typically about 2 dB, but in low-cost receivers this is an acceptable trade-off. A major disadvantage of 1-bit quantization is that it exhibits a capture effect in the presence of strong interfering signals and is therefore quite susceptible to jamming. Typical high-end receivers use anywhere from 1.5-bit (three-level) to 3-bit (eightlevel) sample quantization. Three-bit quantization essentially eliminates the SNR degradation found in 1-bit quantization and materially improves performance in the presence of jamming signals. However, to gain the advantages of multibit quantization, the ADC input signal level must exactly match the ADC dynamic range. Thus the receiver must have AGC to keep the ADC input level constant. Some military receivers use even more than 3-bit quantization to extend the dynamic range so that jamming signals are less likely to saturate the ADC. 4.1.4 Baseband Signal Processing Baseband signal processing refers to a collection of high-speed real-time algorithms implemented in dedicated hardware and controlled by software that acquire and track the GPS signal, extract the 50-bps navigation data, and provide measurements of code and carrier pseudoranges and Doppler. 84 RECEIVER AND ANTENNA DESIGN Carrier Tracking Tracking of the carrier phase and frequency is accomplished by using feedback control of a numerically controlled oscillator (NCO) to frequency shift the signal to precisely zero frequency and phase. Because the shift to zero frequency results in spectral foldover of the signal sidebands, both in-phase (I ) and a quadrature (Q) baseband signal components are formed in order to prevent signal information loss. The I component is generated by multiplying the digitized IF by the NCO output and the Q component is formed by ®rst introducing a 90 phase lag in the NCO output before multiplication. Feedback is accomplished by using the measured baseband phase to control the NCO so that this phase is driven toward zero. When this occurs, signal power is entirely in the I component, and the Q component contains only noise. However, both components are necessary both in order to measure the phase error for feedback and to provide full signal information during acquisition when phase lock has not yet been achieved. The baseband phase ybaseband is de®ned by ybaseband ˆ atan2 I ; Q† 4:2† where atan2 is the four-quadrant arctangent function. The phase needed for feedback is recovered from I and Q after despreading of the signal. When phase lock has been achieved, the output of the NCO will match the incoming IF signal in both frequency and phase but will generally have much less noise due to low-pass ®ltering used in the feedback loop. Comparing the NCO phase to a reference derived from the receiver reference oscillator provides the phase measurements needed for carrier phase pseudoranging. Additionally, the cycles of the NCO output can be accumulated to provide the raw data for Doppler, delta-range, and integrated Doppler measurements. Code Tracking and Signal Spectral Despreading The digitized IF signal, which has a wide bandwidth due to the C=A- (or P-) code modulation, is completely obscured by noise. The signal power is raised above the noise power by despreading, in which the digitized IF signal is multiplied by a receiver-generated replica of the code precisely time aligned with the code on the received signal. Typically the individual baseband I and Q signals from the controlled NCO mixer are despread in parallel, as previously shown in Fig. 3.13. The despreading process removes the code from the signal, thus concentrating the full signal power into the approximately 50-Hz baseband bandwidth of the data modulation. Subsequent ®ltering (usually in the form of integration) can now be employed to dramatically raise the SNR to values permitting observation and measurement of the signal. As an example, recall that in a GPS receiver a typical SNR in a 2-MHz IF bandwidth is 16:6 dB. After despreading and 50-Hz low-pass ®ltering the total signal power is still about the same, but the bandwidth of the noise has been reduced from 2 MHz to about 50 Hz, which increases the SNR by the ratio 2  106 =50, or 46 dB. The resulting SNR is therefore 16:6 ‡ 46:0 ˆ 29:4 dB. 4.2 4.2 4.2.1 RECEIVER DESIGN CHOICES 85 RECEIVER DESIGN CHOICES Number of Channels and Sequencing Rate GPS receivers must observe the signal from at least four satellites to obtain threedimensional position and velocity estimates. If the user altitude is known, three satellites will suf®ce. There are several choices as to how the signal observations from a multiplicity of satellites can be implemented. In early designs, reduction of hardware cost and complexity required that the number of processing channels be kept at a minimum, often being smaller than the number of satellites observed. In this case, each channel must sequentially observe more than one satellite. As a result of improved lower cost technology, most modern GPS receivers have a suf®cient number of channels to permit one satellite to be continuously observed on each channel. 4.2.1.1 Receivers with Channel Time Sharing Single-Channel Receivers In a single-channel receiver, all processing, such as acquisition, data demodulation, and code and carrier tracking, is performed by a single channel in which the signals from all observed satellites are time shared. Although this reduces hardware complexity, the software required to manage the time-sharing process can be quite complex, and there are also severe performance penalties. The process of acquiring satellites can be very slow and requires a juggling act to track already-acquired satellites while trying to acquire others. The process is quite tricky when receiving ephemeris data from a satellite, since about 30 s of continuous reception is required. During this time the signals from other satellites are eclipsed, and resumption of reliable tracking can be dif®cult. After all satellites have been acquired and their ephemeris data stored, two basic techniques can be used to track the satellite signals in a single-channel receiver. In slow-sequencing designs the signal from each satellite is observed for a duration (dwell time) on the order of 1 s. Since a minimum of four satellites must typically be observed, the signal from each satellite is eclipsed for an appreciable length of time. For this reason, extra time must be allowed for signal reacquisition at the beginning of each dwell interval. Continually having to reacquire the signal generally results in less reliable operation, since the probability of losing a signal is considerably greater as compared to the case of continuous tracking. This is especially critical in the presence of dynamics, in which unpredictable user platform motion can take place during signal eclipse. Generally the positioning and velocity accuracy is also degraded in the presence of dynamics. If a single-channel receiver does not have to accurately measure velocity, tracking can be accomplished with only a frequency-lock loop (FLL) for carrier tracking. Since a FLL typically has a wider pull-in range and a shorter pull-in time than a phase-lock loop (PLL), reacquisition of the signal is relatively fast and the sequencing dwell time can be as small as 0.25 s per satellite. Because loss of phase lock is not an issue, this type of receiver is also more robust in the presence of dynamics. On the other hand, if accurate velocity determination is required, a PLL 86 RECEIVER AND ANTENNA DESIGN must be used and the extra time required for phase lock during signal reacquisition pushes the dwell time up to about 1±1.5 s per satellite, with an increased probability of reacquisition failure due to dynamics. A single-channel receiver requires relatively complex software for managing the satellite time-sharing process. A typical design employs only one pseudonoise (PN) code generator and one PPL in hardware. Typical tasks that the software must perform during the dwell period for a speci®c satellite are as follows: 1. Select the PN code corresponding to the satellite observed. 2. Compute the current state of the code at the start of the dwell based on the state at the end of the last dwell, the signal Doppler, and the eclipse time since the last dwell. 3. Load the code state into the code generator hardware. 4. Compute the initial Doppler frequency of the FLL=PLL reference. 5. Load the Doppler frequency into the FLL=PLL hardware. 6. Initiate the reacquisition process by turning on the code and carrier tracking loops. 7. Determine when reacquisition (code=frequency=phase lock) has occurred. 8. Measure pseudorange=carrier phase=carrier phase rate during the remainder of the dwell. In addition to these tasks, the software must be capable of ignoring measurements from a satellite if the signal is momentarily lost and must permanently remove the satellite from the sequencing cycle when its signal becomes unusable, such as when the satellite elevation angle is below the mask angle. The software must also have the capability of acquiring new satellites and obtaining their ephemeris data as their signals become available while at the same time not losing the satellites already being tracked. A satellite whose ephemeris data is being recorded must have a much longer dwell time (about 30 s) than the dwell times of other satellites that are only being tracked, which causes a much longer eclipse time for the latter. The software must therefore modify the calculations listed above to take this into account. Because current technology makes the hardware costs of a multichannel receiver almost as small as that for a single channel, the single-channel approach has been almost entirely abandoned in modern designs. Another method of time sharing that can be used in single-channel receivers is multiplexing, in which the dwell time is much shorter, typically 5±10 ms per satellite. Because the eclipse time is so short, the satellites do not need to be reacquired at each dwell. However, a price is paid in that the effective SNR is signi®cantly reduced in proportion to the number of satellites being tracked. Resistance to jamming is also degraded by values of 7 dB or more. Additionally, the process of acquiring new satellites without disruption is made more demanding because the acquisition search must be broken into numerous short time intervals. Due to the rapidity with which satellites are sequenced, a common practice with a two-channel receiver is to use a 4.2 RECEIVER DESIGN CHOICES 87 full complement of PN code generators that run all the time, so that high-speed multiplexing of a single code generator can be avoided. Two-Channel Receivers The use of two channels permits the second channel to be a ``roving'' channel, in which new satellites can be acquired and ephemeris data collected while on the ®rst channel satellites can be tracked without slowdown in position=velocity updates. However, the satellites must still be time shared on the ®rst channel. Thus the software must still perform the functions listed above and in addition must be capable of inserting=deleting satellites from the sequencing cycle. As with single-channel designs, either slow sequencing or multiplexing may be used. Receivers with Three to Five Channels In either slow-sequencing or multiplexed receivers, additional channels will generally permit better accuracy and jamming immunity as well as more robust performance in the presence of dynamics. A major breakthrough in receiver performance occurs with ®ve or more channels, because four satellites can be simultaneously tracked without the need for time sharing. The ®fth channel can be used to acquire a new satellite and collect its ephemeris data before using it to replace one of the satellites being tracked on the other four channels. Multichannel All-in-View Receivers The universal trend in receiver design is to use enough channels to receive all satellites that are visible. In most cases eight or fewer useful satellites are visible at any given time; for this reason modern receivers typically have no more than 10±12 channels, with perhaps several channels being used for acquisition of new satellites and the remainder for tracking. Position=velocity accuracy is materially improved because satellites do not have to be continually reacquired as is the case with slow sequencing, there is no reduction in effective SNR found in multiplexing designs, and the use of more than the minimum number of satellites results in an overdetermined solution. In addition, software design is much simpler because each channel has its own tracking hardware that tracks only one satellite and does not have to be time shared. 4.2.2 L2 Capability GPS receivers that can utilize the L2 frequency (1227.60 MHz) gain several advantages over L1 -only receivers. Currently the L2 carrier is modulated only with a military-encrypted P-code, called the Y-code, and the 50-bps data stream. Because of the encryption, civilians are denied the use of the P-code. However, it is still possible to recover the L2 carrier, which can provide signi®cant performance gains in certain applications. Dual-Frequency Ionospheric Correction Because the pseudorange error caused by the ionosphere is inversely proportional to the square of frequency, it 88 RECEIVER AND ANTENNA DESIGN can be calculated in military receivers by comparing the P-code pseudorange measurements obtained on the L1 and L2 frequencies. After subtraction of the calculated error from the pseudorange measurements, the residual error due to the ionosphere is typically no more than a few meters as compared to an uncorrected error of 5±30 m. Although civilians do not have access to the P-code, in differential positioning applications the L2 carrier phase can be extracted without decryption, and the ionospheric error can then be estimated by comparing the L1 and L2 phase measurements. Improved Carrier Phase Ambiguity Resolution in High-Accuracy Differential Positioning High-precision receivers, such as those used in surveying, use carrier phase measurements to obtain very precise pseudoranges. However, the periodic nature of the carrier makes the measurements highly ambiguous. Therefore, solution of the positioning equations yields a grid of possible positions separated by distances on the order of one to four carrier wavelengths, depending on geometry. Removal of the ambiguity is accomplished by using additional information in the form of code pseudorange measurements, changes in satellite geometry, or the use of more satellites than is necessary. In general, ambiguity resolution becomes less dif®cult as the frequency of the carrier decreases. By using both the L1 and L2 carriers, a virtual carrier frequency of L1 L2 ˆ 1575:42 1227:60 ˆ 347:82 MHz can be obtained, which has a wavelength of about 86 cm as compared to the 19 cm wavelength of the L1 carrier. Ambiguity resolution can therefore be made faster and more reliable by using the difference frequency. 4.2.3 Code Selections: C=A, P, or Codeless All GPS receivers are designed to use the C=A-code, since it is the only code accessible to civilians and is used by the military for initial signal acquisition. Most military receivers also have P-code capability to take advantage of the improved performance it offers. On the other hand, commercial receivers seldom have P-code capability because the government does not make the needed decryption equipment available to the civil sector. Some receivers, notably those used for precision differential positioning application, also incorporate a codeless mode that permits recovery of the L2 carrier without knowledge of the code waveform. The C=A-Code The C=A-code, with its 1.023-MHz chipping rate and 1-ms period, has a bandwidth that permits a reasonably small pseudorange error due to thermal noise. The code is easily generated by a few relatively small shift registers. Because the C=A-code has only 1023 chips per period, it is relatively easy to acquire. In military receivers direct acquisition of the P-code would be extremely dif®cult and time consuming. For this reason these receivers ®rst acquire the C=Acode on the L1 frequency, allowing the 50-bps data stream to be recovered. The data contains a hand-over word that tells the military receiver a range in which to search for the P-code. 4.2 RECEIVER DESIGN CHOICES 89 The P-Code The unencrypted P-code has a 10.23-MHz chipping rate and is known to both civilian and military users. It has a very long period of one week. The Y-code is produced by biphase modulation of the P-code by an encrypting code known as the W-code. The W-code has a slower chipping rate than the P-code; there are precisely 20 P-code chips per W-code chip. Normally the W-code is known only to military users who can use decryption to recover the P-code, so that the civilian community is denied the full use of the L2 signal. However, as will be indicated shortly, useful information can still be extracted from the L2 signal in civilian receivers without the need for decryption. Advantages of the P-code include the following: Improved Navigation Accuracy. Because the P-code has 10 times the chipping rate of the C=A-code, its spectrum occupies a larger portion of the full 20MHz GPS signal bandwidth. Consequently, military receivers can typically obtain three times better pseudoranging accuracy than that obtained with the C=A-code. Improved Jamming Immunity. The wider bandwidth of the P-code gives about 40 dB suppression of narrow-band jamming signals as compared to about 30 dB for the C=A-code, which is of obvious importance in military applications. Better Multipath Rejection. In the absence of special multipath mitigation techniques, the P-code provides signi®cantly smaller pseudorange errors in the presence of multipath as compared to the C=A-code. Because the P-code correlation function is approximately one-tenth as wide as that of the C=Acode, there is less opportunity for a delayed-path component of the receivergenerated signal correlation function to cause range error by overlap with the direct-path component. Codeless Techniques Commercial receivers can recover the L2 carrier without knowledge of the code modulation simply by squaring the received signal waveform or by taking its absolute value. Because the a priori SNR is so small, the SNR of the recovered carrier will be reduced by as much as 33 dB because the squaring of the signal greatly increases the noise power relative to that of the signal. However, the squared signal has extremely small bandwidth (limited only by Doppler variations), so that narrow-band ®ltering can make up the difference. 4.2.4 Access to SA Signals Selective Availability (SA) refers to errors that may be intentionally introduced into the satellite signals by the military to prevent full-accuracy capability by the civilian community. SA was suspended on May 1, 2000 but can be turned on again at the discretion of the DoD. The errors appear to be random, have a zero long-term average value, and typically have a standard deviation of 30 m. Instantaneous position errors of 50±100 m occur fairly often and are magni®ed by large position