# Simulation and Performance Evaluations of the New GPS L5 and L1 Signals

Authors: Tahir Saleem; Mohammad Usman; Atif Elahi; Noor Gul
Journal: Wireless Communications and Mobile Computing
 (2017)

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## Abstract

The Global Positioning System (GPS) signals are used for navigation and positioning purposes by a diverse set of users. As a part of GPS modernization effort L5 has been recently introduced for better accuracy and availability service. This paper intends to study and simulate the GPS L1/L5 signal in order to fulfill the following two objectives. The first aim is to point out some important features/differences between current L1 (whose characteristics have been fairly known and documented) and new L5 GPS signal for performance evaluation purpose. The second aim is to facilitate receiver development, which will be designed and assembled later for the actual acquisition of GPS data. Simulation has been carried out for evaluation of correlation properties and link budgeting for both L1 and L5 signals. The necessary programming is performed in Matlab.


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## Body

## 1. Introduction

The GPS (Global Positioning System) is satellite system operated by the United States of America (USA) defense department. Its services (Location, Navigation, and Time) can be accessed all the time by anyone having necessary GPS receiver. The GPS system has total 32 satellites out of which 24 satellites are operational. These operational satellites are arranged in 6 orbits. GPS satellites being connected to ground stations revolve around the earth with a distance of 20,000 km from the surface of earth.Initially GPS had started its operation with two signals L1 and L2. L1 is transmitted at 1575.42 MHz frequency and L2 at 1227.60 MHz. These GPS signals include two ranging codes. C/A (Carrier Acquisition) code and P (Y) or Precision code. The first code is used for civilian purpose, while the second one is restricted to military use only. These ranges codes are utilized for measurement of distance to the satellite as well as identifying uniquely the navigation message [1].Although the GPS system has almost reached its full operational capability, due to the increasing demand for better service and advances in technology, modernization and implementation of a new GPS system have recently started. The addition of L5 GPS signal is one of the modernization efforts being taken by US Department of Defense. L5 signal which is being transmitted on 1176.45 MHz frequency is also known as Safety of Life signal in the GPS community. With higher transmission power and improved signal design as compared to other GPS signals (L1 or L2) it is believed that L5 will enhance the existing performance of the GPS system. Due to wide bandwidth and comparatively longer spreading codes, the L5 signal is expected to give a high processing gain. For L5 signal transmission the Aeronautical Radio Navigation Service frequency band has been reserved which is easily accessible around the world. One of the unique features in proposed L5 signal is the inclusion of both separate carrier and quadrature data modulation component. Separate PN codes are used for the modulation of both components with PN chip clock rates of 10.23 Mcps and periods of 10230 chips or 1 ms [2–4].In this paper we tried to point out some important features like power levels, data encoding, correlation (auto and cross), and power budget analysis between L1 and L5 signal. Both L1 and L5 signals have been simulated and comparison is done on the basis of obtained results.


## 2. Performance Evaluation Parameters

### 2.1. Autocorrelation

In satellite navigation applications, autocorrelation function has great importance. It basically refers to the integration and multiplication of a signal with its delayed copy. The general formula for the autocorrelation function as given in [1, 5] can be written as(1)Rτ=limT→∞⁡12T∫-TTfitfit-τdt,where fi(t) represents signal with time t for ith satellite, T is time period, and τ is delay in time.The autocorrelation properties are utilized to detect a GPS signal in a noisy environment. The C/A codes of GPS signals exhibit greater autocorrelation peak and low cross-correlation. For better detection of a weak signal, it is necessary that autocorrelation peak of the weak signal must be greater than the cross-correlation peak of the strong signal. As C/A codes are near to orthogonal therefore cross-correlation value will approach to a smaller value. The autocorrelation function of a maximum length C/A code consists of an infinite sequence of triangular function, as shown in Figures1 and 2 for both L1 and L5, respectively. The peaks in the figures show high correlation value, which can be defined mathematically for L1 and L5 as follows:(2)R1τ=11,023TCA∫t=0t=1023fztfzt-τdt,R5τ=110,230TCA∫t=0t=10230fztfzt-τdt,where fz(t) is C/A code with time t for zth satellite, TCA is single C/A chipping period (L1 = 977.5 nSec and L5 = 97.75 nSec), and τ is delay in time.Figure 1
L1 autocorrelation function.Figure 2
L5 autocorrelation function.


### 2.2. Power Budget Analysis

To check suitability of reflected L1 and L5 GPS signal with the aim of its utilization in remote sensing, power budget analysis is needed. Power budget analysis of reflected GPS signals has been elaborated in [6–8] where the reflected signals were used for passive imaging and target detection. The analysis is first accomplished for L1 and then for L5 signal.LetPt represent the power of transmitter (GPS satellite), Gt gain of transmitter, and σ target cross section, R1 shows range (distance) from GPS satellites to target, and R2 is range from target to receiver; then the received power can be calculated as [9](3)Pr=PtGt4πR124πR22∗σAef,where Aef represents receiving antenna effective area calculated by following mathematical formula when GPS signal wavelength and receiver gain is known:(4)Aef=λ2∗Gr4π. The receiver antenna SNR (Signal to Noise ratio) can be computed as(5)SNR=PtGtGrλ2σ4π3R12R22KTBn,where KTBn represent noise of receiver while λ is wavelength of GPS signal.Due to wide bandwidth, addition of Neuman-Hoffman codes in modulation, and comparatively longer spreading codes, the L5 signal is expected, given a high processing gain which is evident from Figure6. SNR comparison plots for L1 and L5 shown in Figures 5 and 6 are in Section 3.


### 2.3. Power Level

The L1 signal has a minimum signal strength of −158.5 dBW while L5 has −154.9 dBW. It means that L5 is 3.6 dB better level as compared to L1. Some other important difference parameters between L1 and L5 are summarized in Table1.Table 1
L1 and L5 comparison parameters.
Parameter L1 L5 Remarks Bandwidth 2 MHz 24 MHz The higher bandwidth of L5 can provide better accuracy in noisy environment Center frequency 1575.42 MHz 1176.45 MHz Secondary codes N/A Neuman-Hoffman (NH) codes The addition of NH codes in L5 signal:(1) Improved spectral line component spacing(2) Reduced effect of narrow band interference (3) Resulted in low cross-correlation(4) Provided better synchronization at bit level Chip rate 1.023 MHz 10.23 MHz Increasing chipping rate of L5: (1) provides greater bandwidth performance, (2) low signal distortion, (3) provides greater accuracy Data encoding No Improved data encoding with Parity & Cyclic Redundancy Check Greater signal and data integrity can be achieved with advanced methods of encoding


## 2.1. Autocorrelation

In satellite navigation applications, autocorrelation function has great importance. It basically refers to the integration and multiplication of a signal with its delayed copy. The general formula for the autocorrelation function as given in [1, 5] can be written as(1)Rτ=limT→∞⁡12T∫-TTfitfit-τdt,where fi(t) represents signal with time t for ith satellite, T is time period, and τ is delay in time.The autocorrelation properties are utilized to detect a GPS signal in a noisy environment. The C/A codes of GPS signals exhibit greater autocorrelation peak and low cross-correlation. For better detection of a weak signal, it is necessary that autocorrelation peak of the weak signal must be greater than the cross-correlation peak of the strong signal. As C/A codes are near to orthogonal therefore cross-correlation value will approach to a smaller value. The autocorrelation function of a maximum length C/A code consists of an infinite sequence of triangular function, as shown in Figures1 and 2 for both L1 and L5, respectively. The peaks in the figures show high correlation value, which can be defined mathematically for L1 and L5 as follows:(2)R1τ=11,023TCA∫t=0t=1023fztfzt-τdt,R5τ=110,230TCA∫t=0t=10230fztfzt-τdt,where fz(t) is C/A code with time t for zth satellite, TCA is single C/A chipping period (L1 = 977.5 nSec and L5 = 97.75 nSec), and τ is delay in time.Figure 1
L1 autocorrelation function.Figure 2
L5 autocorrelation function.


## 2.2. Power Budget Analysis

To check suitability of reflected L1 and L5 GPS signal with the aim of its utilization in remote sensing, power budget analysis is needed. Power budget analysis of reflected GPS signals has been elaborated in [6–8] where the reflected signals were used for passive imaging and target detection. The analysis is first accomplished for L1 and then for L5 signal.LetPt represent the power of transmitter (GPS satellite), Gt gain of transmitter, and σ target cross section, R1 shows range (distance) from GPS satellites to target, and R2 is range from target to receiver; then the received power can be calculated as [9](3)Pr=PtGt4πR124πR22∗σAef,where Aef represents receiving antenna effective area calculated by following mathematical formula when GPS signal wavelength and receiver gain is known:(4)Aef=λ2∗Gr4π. The receiver antenna SNR (Signal to Noise ratio) can be computed as(5)SNR=PtGtGrλ2σ4π3R12R22KTBn,where KTBn represent noise of receiver while λ is wavelength of GPS signal.Due to wide bandwidth, addition of Neuman-Hoffman codes in modulation, and comparatively longer spreading codes, the L5 signal is expected, given a high processing gain which is evident from Figure6. SNR comparison plots for L1 and L5 shown in Figures 5 and 6 are in Section 3.


## 2.3. Power Level

The L1 signal has a minimum signal strength of −158.5 dBW while L5 has −154.9 dBW. It means that L5 is 3.6 dB better level as compared to L1. Some other important difference parameters between L1 and L5 are summarized in Table1.Table 1
L1 and L5 comparison parameters.
Parameter L1 L5 Remarks Bandwidth 2 MHz 24 MHz The higher bandwidth of L5 can provide better accuracy in noisy environment Center frequency 1575.42 MHz 1176.45 MHz Secondary codes N/A Neuman-Hoffman (NH) codes The addition of NH codes in L5 signal:(1) Improved spectral line component spacing(2) Reduced effect of narrow band interference (3) Resulted in low cross-correlation(4) Provided better synchronization at bit level Chip rate 1.023 MHz 10.23 MHz Increasing chipping rate of L5: (1) provides greater bandwidth performance, (2) low signal distortion, (3) provides greater accuracy Data encoding No Improved data encoding with Parity & Cyclic Redundancy Check Greater signal and data integrity can be achieved with advanced methods of encoding


## 3. Results and Simulation

Simulation is carried out in Matlab environment, for the autocorrelation of one set of C/A code for a satellite broadcasting L1 signal, and the result is plotted in Figure3. The amplitude peak value around 1500 in the diagram represents autocorrelation of C/A code.Figure 3
The autocorrelation of L1 signal.Similarly Figure4 depicts the autocorrelation of the simulated L5 signal with autocorrelation value more than 4000. It is evident from the diagram that L5 autocorrelation value is greater than L1. Hence L5 provides better detection capability as compared to L1 signal. The secondary peaks in Figure 3 of the autocorrelation are significantly less than higher peak. Both Figures 3 and 4 clearly show that the cross-correlation values are very small, which enables the GPS satellites to broadcast signals simultaneously at the same frequency using different C/A codes. From both figures it is evident that the secondary peaks in the autocorrelation diagram are significantly lower than the higher peak. This higher peak value helps the receiver in acquisition and tracking of the GPS signal.Figure 4
The autocorrelation of L5 signal.Figure 5
SNR versus range plot without processing gain.Figure 6
SNR versus range plot with processing gain.The simulation result of SNR versus range for reflected L1 and L5 GPS signals shown in Figure5 was carried out for 0 to 1000 m range with target cross section of 10 m2. SNR is calculated for different values of the range. At a range of 100 m SNR values of L1 and L5 signals are, respectively, −50 dB and −30 dB, which are very low and detection of target is almost impossible in both cases. It is evident from Figure 5 that the SNR is very poor even at short distances; hence tracking of the GPS signals is almost impossible.For further SNR improvement the GPS signals were correlated for a longer period of time consequently better processing gain was achieved. The simulation results of SNR with processing gain of 43 dB for GPS L1 and around 50 dB for L5 are shown in Figure6. It is worth mentioning that the L5 reflected GPS has 7 dB more processing gain when compared with L1 signal.Since correlation peaks of L5 signal are much larger than L1 signal, as shown in Figures3 and 4, it can be deduced that L5 signals have improved signal reliability and are more resistant to false acquisition problems. Moreover from the results it can be observed that, for same acquisition time, noise floor of L5 signal is lower than L1 and therefore acquisition peaks are more prominent. This low noise floor decreases, susceptibility to wave form distortion, and offers better accuracy and processing gain than L1 signal.


## 4. Conclusion

In this paper performance evaluation for the newly introduced L5 and L1 GPS signals have been performed. Different evaluation parameters are considered and analyzed. Among these parameters simulation is carried out for correlation and power budget analysis. The results are recorded above. From the results it can be deduced that L5 has superior detection characteristics as compared to L1 due to greater bandwidth, high correlation peaks, and better SNR. Hence better results can be achieved with L5 GPS signal as compared to L1 signal.



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*Source: 7492703-2017-01-17.xml*