# Comparison of L1 and L5 Bands GNSS Signals Acquisition

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## Abstract

**:**

## 1. Introduction

## 2. GNSS Signals and Acquisition

#### 2.1. GNSS Signals

#### 2.2. Acquisition of GNSS Signals

## 3. Assessment of Processing Time and Memory Requirements

#### 3.1. Acquisition of a Data Channel

#### 3.2. Acquisition of a Pilot Channel without Assistance

#### 3.2.1. Coherent Integration Only with Parallel Implementation

#### 3.2.2. Coherent Integration Only with Serial Implementation

#### 3.2.3. Coherent Integration only with Semi-Parallel Implementation

#### 3.2.4. Use of Non-Coherent Accumulation with Parallel Implementation

- The number of branches is ${N}_{\mathrm{S}}$ instead of ${N}_{\mathrm{D}}$.
- For a pilot channel, the coherent accumulations for the different delays start and finish at the same time, therefore the latency and the length of data needed is slightly reduced.

#### 3.2.5. Use of Non-Coherent Accumulation with Serial Implementation

#### 3.2.6. Use of Non-Coherent Accumulation with Semi-Parallel Implementation

#### 3.3. Acquisition of a Pilot Channel with Assistance

#### 3.3.1. Coherent Integration Only with Serial Implementation

#### 3.3.2. Coherent Integration Only with Semi-Parallel Implementation

#### 3.3.3. Use of Non-Coherent Accumulation with Serial Implementation

#### 3.3.4. Use of Non-Coherent Accumulation with Semi-Parallel Implementation

#### 3.4. Summary

## 4. Application to GPS and Galileo Signals

#### 4.1. Determination of the Integration Time

#### 4.2. Comparison of GPS L1 C/A and L5 Signals Acquisition

#### 4.2.1. Determination of Acquisition Parameters

#### 4.2.2. Determination of Ratio of Complexity for One Frequency Bin

#### 4.2.3. Determination of Ratio of Complexity for Multiple Frequency Bins

#### 4.2.4. Validation

#### 4.3. Comparison of Galileo E1 and E5 Signals Acquisition

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Overview of the considered parallel code search with long integration. Dashed blocks are optional.

**Figure 2.**Implementation of a data channel acquisition (timing diagram available in Figure 3).

**Figure 3.**Timing diagram of a data channel acquisition shown in Figure 2, with ${N}_{\mathrm{D}}=4$ for the illustration (in reality ${N}_{\mathrm{D}}=20$ for the GPS L1 C/A signal). Colors indicate different portions corresponding to the length of one data bit. Grey color indicates intermediate results (i.e., the value is not yet the final one).

**Figure 4.**Implementation of a pilot channel acquisition, with coherent integration only, in a parallel way (timing diagram available in Figure 5).

**Figure 5.**Timing diagram of the pilot channel acquisition shown in Figure 4, with ${N}_{\mathrm{S}}=4$ for the illustration.

**Figure 6.**Implementation of a pilot channel acquisition, without non-coherent accumulation, in a serial way (timing diagram available in Figure 7).

**Figure 7.**Timing diagram of the pilot channel acquisition shown in Figure 6, with ${N}_{\mathrm{S}}=4$ and $K=3$.

**Figure 8.**Implementation of a pilot channel acquisition, with non-coherent accumulation, in a parallel way (timing diagram available in Figure 5).

**Figure 9.**Implementation of a pilot channel acquisition, with non-coherent accumulation, in a serial way (timing diagram available in Figure 7).

**Figure 11.**Evaluation of the coherent integration time and number of non-coherent accumulations: (

**a**) When the coherent integration time is fixed, and the number of non-coherent accumulations is estimated; (

**b**) When there is coherent integration only, and the coherent integration time is estimated.

**Figure 12.**Ratio of complexity (product of processing time ratio and memory ratio) between the L5 and L1 C/A signals. (

**Left**) without assistance, (

**right**) with assistance. Solid curves do not consider the input memory, while dashed curves consider the input memory.

**Figure 13.**Number of frequency bins browsed (

**top**) and ratio (

**bottom**) of this over 100 simulations, for a sensitivity of −145 dBm without assistance.

**Figure 14.**Ratio of complexity (product of processing time ratio and memory ratio) between the E5 signal and the E1 signal with a sampling frequency of 4.096 MHz. (

**Left**) without assistance, (

**right**) with assistance. Solid curves do not consider the input memory, while dashed curves consider the input memory.

**Table 1.**Summary of the characteristics of the considered Global Navigation Satellite System (GNSS) signals. BPSK stand for Binary Phase Shift Keying, CBOC stands for Code Binary Offset Carrier.

System | L1 C/A | L5 | E1 | E5a | E5b | |||||
---|---|---|---|---|---|---|---|---|---|---|

Center frequency (MHz) | 1575.42 | 1176.45 | 1575.42 | 1176.45 | 1176.45 | |||||

Channel combination | - | Quadrature | Code multiplexing | Quadrature | Quadrature | |||||

Channel | Data | Data | Pilot | Data | Pilot | Data | Pilot | Data | Pilot | |

Bandwidth | 2.046 | 20.46 | 20.46 | 14.322 | 14.322 | 20.46 | 20.46 | 20.46 | 20.46 | |

Minimum bandwidth | 2.046 | 20.46 | 20.46 | 4.092 | 4.092 | 20.46 | 20.46 | 20.46 | 20.46 | |

Modulation | BPSK (1) | BPSK (10) | BPSK (10) | CBOC (6,1) | BPSK (10) | BPSK (10) | BPSK (10) | BPSK (10) | ||

Sub-carrier frequency (MHz) | - | - | - | 1.023 & 6.138 | 1.023 & 6.138 | - | - | - | - | |

Primary code | Chipping rate (Mchip/s) | 1.023 | 10.23 | 10.23 | 1.023 | 1.023 | 10.23 | 10.23 | 10.23 | 10.23 |

Length (chip) | 1023 | 10,230 | 10,230 | 4092 | 4092 | 10,230 | 10,230 | 10,230 | 10,230 | |

Length (ms) | 1 | 1 | 1 | 4 | 4 | 1 | 1 | 1 | 1 | |

Secondary code | Chipping rate (chip/s) | - | 1000 | 1000 | - | 250 | 1000 | 1000 | 1000 | 1000 |

Length (chip) | - | 10 | 20 | - | 25 | 20 | 100 | 4 | 100 | |

Length (ms) | - | 10 | 20 | - | 100 | 20 | 100 | 4 | 100 | |

Data rate | (symbol/s) | 50 | 100 | - | 250 | - | 50 | - | 250 | - |

(bit/s) | 50 | 50 | - | 125 | - | 25 | - | 125 | - | |

Minimum power received on Earth | (dBW) | −158.5 | −157 | −157 | −160 | −160 | −158 | −158 | −158 | −158 |

(dBm) | −128.5 | −127 | −127 | −130 | −130 | −128 | −128 | −128 | −128 |

Implementation | Processing Time of One Frequency Bin ${\mathit{T}}_{\mathit{F}\mathit{B}}$ (Clock Cycle) | Memory (bit) | Figure | |
---|---|---|---|---|

Data | Parallel NC | ${N}_{\mathrm{P}}\left[\left(K+1\right)2{N}_{\mathrm{D}}+1\right]+{N}_{\mathrm{Z}}\left[\left(K+1\right){N}_{\mathrm{D}}\right]+2L$ | ${N}_{\mathrm{D}}{N}_{\mathrm{P}}\left[3{B}_{\mathrm{R}}+3\u23a1{\mathrm{log}}_{2}\left({N}_{\mathrm{D}}\right)\u23a4+\u23a1{\mathrm{log}}_{2}\left(K\right)\u23a4\right]$ | 2, 3 |

Pilot | Parallel C | ${N}_{\mathrm{P}}\left(2K{N}_{\mathrm{S}}+3\right)+{N}_{\mathrm{Z}}\left(K{N}_{\mathrm{S}}+1\right)+2L$ | ${N}_{\mathrm{S}}2{N}_{\mathrm{P}}\left({B}_{\mathrm{R}}+\u23a1{\mathrm{log}}_{2}\left(K{N}_{\mathrm{S}}\right)\u23a4\right)$ | 4, 5 |

Parallel NC | ${N}_{\mathrm{P}}\left(2K{N}_{\mathrm{S}}+3\right)+{N}_{\mathrm{Z}}\left(K{N}_{\mathrm{S}}+1\right)+2L$ | ${N}_{\mathrm{S}}{N}_{\mathrm{P}}\left[3{B}_{\mathrm{R}}+3\u23a1{\mathrm{log}}_{2}\left(K{N}_{\mathrm{S}}/{N}_{\mathrm{NC}}\right)\u23a4+\u23a1{\mathrm{log}}_{2}\left({N}_{\mathrm{NC}}\right)\u23a4\right]$ | 5, 8 | |

Serial C | ${N}_{\mathrm{P}}\left(2K{N}_{\mathrm{S}}^{2}+3\right)+{N}_{\mathrm{Z}}\left(K{N}_{\mathrm{S}}^{2}+1\right)+2L$ | $2{N}_{\mathrm{P}}\left({B}_{\mathrm{R}}+\u23a1{\mathrm{log}}_{2}\left(K{N}_{\mathrm{S}}\right)\u23a4\right)$ | 6, 7 * | |

Serial C with assistance | ${N}_{\mathrm{P}}\left(2K{N}_{\mathrm{S}}{N}_{\mathrm{SCB}}+3\right)+{N}_{\mathrm{Z}}\left(K{N}_{\mathrm{S}}{N}_{\mathrm{SCB}}+1\right)+2L$ | $2{N}_{\mathrm{P}}\left({B}_{\mathrm{R}}+\u23a1{\mathrm{log}}_{2}\left(K{N}_{\mathrm{S}}\right)\u23a4\right)$ | 6, 7 * | |

Serial NC | ${N}_{\mathrm{P}}\left(2K{N}_{\mathrm{S}}^{2}+3\right)+{N}_{\mathrm{Z}}\left(K{N}_{\mathrm{S}}^{2}+1\right)+2L$ | ${N}_{\mathrm{P}}\left[3{B}_{\mathrm{R}}+3\u23a1{\mathrm{log}}_{2}\left(K{N}_{\mathrm{S}}/{N}_{\mathrm{NC}}\right)\u23a4+\u23a1{\mathrm{log}}_{2}\left({N}_{\mathrm{NC}}\right)\u23a4\right]$ | 7 *, 9 | |

Serial NC with assistance | ${N}_{\mathrm{P}}\left(2K{N}_{\mathrm{S}}{N}_{\mathrm{SCB}}+3\right)+{N}_{\mathrm{Z}}\left(K{N}_{\mathrm{S}}{N}_{\mathrm{SCB}}+1\right)+2L$ | ${N}_{\mathrm{P}}\left[3{B}_{\mathrm{R}}+3\u23a1{\mathrm{log}}_{2}\left(K{N}_{\mathrm{S}}/{N}_{\mathrm{NC}}\right)\u23a4+\u23a1{\mathrm{log}}_{2}\left({N}_{\mathrm{NC}}\right)\u23a4\right]$ | 7 *, 9 | |

Semi-parallel C | ${N}_{\mathrm{P}}\left(2K{N}_{\mathrm{S}}\u23a1\frac{{N}_{\mathrm{S}}}{{N}_{\mathrm{A}}}\u23a4+3\right)+{N}_{\mathrm{Z}}\left(K{N}_{\mathrm{S}}\u23a1\frac{{N}_{\mathrm{S}}}{{N}_{\mathrm{A}}}\u23a4+1\right)+2L$ | ${N}_{\mathrm{A}}2{N}_{\mathrm{P}}\left({B}_{\mathrm{R}}+\u23a1{\mathrm{log}}_{2}\left(K{N}_{\mathrm{S}}\right)\u23a4\right)$ | ||

Semi-parallel C with assistance | $\begin{array}{l}{N}_{\mathrm{P}}\left(2K{N}_{\mathrm{S}}\u23a1\frac{{N}_{\mathrm{S}}{N}_{\mathrm{SCB}}}{{N}_{\mathrm{A}}}\u23a4+3\right)\\ +{N}_{\mathrm{Z}}\left(K{N}_{\mathrm{S}}\u23a1\frac{{N}_{\mathrm{S}}{N}_{\mathrm{SCB}}}{{N}_{\mathrm{A}}}\u23a4+1\right)+2L\end{array}$ | ${N}_{\mathrm{A}}2{N}_{\mathrm{P}}\left({B}_{\mathrm{R}}+\u23a1{\mathrm{log}}_{2}\left(K{N}_{\mathrm{S}}\right)\u23a4\right)$ | ||

Semi-parallel NC | ${N}_{\mathrm{P}}\left(2K{N}_{\mathrm{S}}\u23a1\frac{{N}_{\mathrm{S}}}{{N}_{\mathrm{A}}}\u23a4+3\right)+{N}_{\mathrm{Z}}\left(K{N}_{\mathrm{S}}\u23a1\frac{{N}_{\mathrm{S}}}{{N}_{\mathrm{A}}}\u23a4+1\right)+2L$ | ${N}_{\mathrm{A}}{N}_{\mathrm{P}}\left[3{B}_{\mathrm{R}}+3\u23a1{\mathrm{log}}_{2}\left(K{N}_{\mathrm{S}}/{N}_{\mathrm{NC}}\right)\u23a4+\u23a1{\mathrm{log}}_{2}\left({N}_{\mathrm{NC}}\right)\u23a4\right]$ | ||

Semi-parallel NC with assistance | $\begin{array}{l}{N}_{\mathrm{P}}\left(2K{N}_{\mathrm{S}}\u23a1\frac{{N}_{\mathrm{S}}{N}_{\mathrm{SCB}}}{{N}_{\mathrm{A}}}\u23a4+3\right)\\ +{N}_{\mathrm{Z}}\left(K{N}_{\mathrm{S}}\u23a1\frac{{N}_{\mathrm{S}}{N}_{\mathrm{SCB}}}{{N}_{\mathrm{A}}}\u23a4+1\right)+2L\end{array}$ | ${N}_{\mathrm{A}}{N}_{\mathrm{P}}\left[3{B}_{\mathrm{R}}+3\u23a1{\mathrm{log}}_{2}\left(K{N}_{\mathrm{S}}/{N}_{\mathrm{NC}}\right)\u23a4+\u23a1{\mathrm{log}}_{2}\left({N}_{\mathrm{NC}}\right)\u23a4\right]$ |

**Table 3.**Parameters independent of the integration time selected for Global Positioning System (GPS) signals.

Signal | ${\mathit{f}}_{\mathbf{S}}$ | ${\mathit{N}}_{\mathbf{P}}$ | ${\mathit{N}}_{\mathbf{FFT}}$ | ${\mathit{N}}_{\mathbf{Z}}$ | ${\mathit{N}}_{\mathbf{D}}$ | ${\mathit{N}}_{\mathbf{S}}$ | ${\mathit{B}}_{\mathbf{R}}$ |
---|---|---|---|---|---|---|---|

L1 C/A | 2.048 MHz | 2048 | 4096 | 0 | 20 | - | 16 |

L5 | 20.48 MHz | 20,480 | 65,536 | 24,576 | - | 20 | 16 |

**Table 4.**Search space and statistical parameters for ${P}_{\mathrm{FA},\mathrm{G}}={10}^{-3}$ and ${P}_{\mathrm{D}}=0.9$ for different contexts with GPS signals.

Context | Signal | ${\mathit{T}}_{\mathbf{C}}$ | ${\mathit{N}}_{\mathbf{FB}}$ | ${\mathit{N}}_{\mathbf{CB}}$ | ${\mathit{N}}_{\mathbf{CELL}}$ | ${\mathit{P}}_{\mathbf{FA},\mathbf{C}}$ | $\mathit{S}\mathit{N}\mathit{R}$ |
---|---|---|---|---|---|---|---|

no assistance | L1 C/A | 20 ms | 300 | 2048 | 614,400 | 1.63 × 10^{−9} | 17.15 dB |

L5 | 20 ms | 225 | 409,600 | 92,160,000 | 1.09 × 10^{−11} | 18.04 dB | |

L5 | unlimited | 225 | 409,600 | 92,160,000 | 1.09 × 10^{−11} | 18.04 dB | |

assistance | L1 C/A | 20 ms | 16 | 2048 | 32,768 | 3.05 × 10^{−8} | 16.52 dB |

L5 | 20 ms | 12 | 20,480 | 245,760 | 4.07 × 10^{−9} | 16.96 dB | |

L5 | unlimited | 12 | 20,480 | 245,760 | 4.07 × 10^{−9} | 16.96 dB |

**Table 5.**Total integration time ${T}_{\mathrm{IT}}={T}_{\mathrm{C}}\times {N}_{\mathrm{NC}}$ as function of the sensitivity and context with GPS signals, for average losses. Note that the sensitivities given are for the L1 C/A signal; those of L5 are 1.5 dB higher.

Context | Signal | ${\mathit{T}}_{\mathbf{C}}$ | −140 dBm | −145 dBm | −150 dBm | −155 dBm | −160 dBm |
---|---|---|---|---|---|---|---|

no assistance | L1 C/A | 20 ms | 20 × 1 = 20 | 20 × 4 = 80 | 20 × 23 = 460 | 20 × 170 = 3400 | 20 × 1536 = 30,720 |

L5 | 20 ms | 20 × 1 = 20 | 20 × 3 = 60 | 20 × 16 = 320 | 20 × 111 = 2220 | 20 × 963 = 19,260 | |

L5 | unlimited | 15 × 1 = 15 | 47 × 1 = 47 | 146 × 1 = 146 | 462 × 1 = 462 | 1460 × 1 = 1460 | |

assistance | L1 C/A | 20 ms | 20 × 1 = 20 | 20 × 4 = 80 | 20 × 20 = 400 | 20 × 147 = 2940 | 20 × 1328 = 26,560 |

L5 | 20 ms | 20 × 1 = 20 | 20 × 3 = 60 | 20 × 13 = 260 | 20 × 86 = 1720 | 20 × 751 = 15,020 | |

L5 | unlimited | 12 × 1 = 12 | 38 × 1 = 38 | 120 × 1 = 120 | 377 × 1 = 377 | 1191 × 1 = 1191 |

**Table 6.**Total integration time ${T}_{\mathrm{IT}}={T}_{\mathrm{C}}\times {N}_{\mathrm{NC}}$ as function of the sensitivity and context with GPS signals, for worst losses. Note that the sensitivities given are for the L1 C/A signal; those of L5 are 1.5 dB higher.

Context | Signal | ${\mathit{T}}_{\mathbf{C}}$ | −140 dBm | −145 dBm | −150 dBm | −155 dBm | −160 dBm |
---|---|---|---|---|---|---|---|

no assistance | L1 C/A | 20 ms | 20 × 2 = 40 | 20 × 9 = 180 | 20 × 59 = 1180 | 20 × 495 = 9900 | 20 × 4670 = 93,400 |

L5 | 20 ms | 20 × 2 = 40 | 20 × 7 = 140 | 20 × 40 = 800 | 20 × 315 = 6300 | 20 × 2906 = 58,120 | |

L5 | unlimited | 26 × 1 = 26 | 82 × 1 = 82 | 258 × 1 = 258 | 814 × 1 = 814 | 2573 × 1 = 2573 | |

assistance | L1 C/A | 20 ms | 20 × 2 = 40 | 20 × 8 = 160 | 20 × 51 = 1020 | 20 × 428 = 8560 | 20 × 4040 = 80,800 |

L5 | 20 ms | 20 × 2 = 40 | 20 × 5 = 100 | 20 × 31 = 620 | 20 × 246 = 4920 | 20 × 2266 = 45,320 | |

L5 | unlimited | 21 × 1 = 21 | 67 × 1 = 67 | 210 × 1 = 210 | 664 × 1 = 664 | 2099 × 1 = 2099 |

**Table 7.**Ratio of total integration time (%) for different comparisons with GPS signals. Top value is for average losses, and bottom value is for worst losses. Note that the sensitivities given are for the L1 C/A signal; those of L5 are 1.5 dB higher.

Comparison | Fixed Element | −140 dBm | −145 dBm | −150 dBm | −155 dBm | −160 dBm |
---|---|---|---|---|---|---|

Impact of using L5: L5 verses L1 C/A with ${T}_{\mathrm{C}}=20$ ms | no assistance | 100 | 75 | 70 | 65 | 63 |

100 | 78 | 68 | 64 | 62 | ||

assistance | 100 | 65 | 65 | 59 | 57 | |

100 | 61 | 61 | 57 | 56 | ||

Impact of ${T}_{\mathrm{C}}$: Unlimited verses 20 ms with L5 signal | no assistance | 75 | 78 | 46 | 21 | 8 |

65 | 59 | 32 | 13 | 4 | ||

assistance | 60 | 63 | 46 | 22 | 8 | |

53 | 67 | 34 | 13 | 5 | ||

Impact of assistance: Assistance verses no assistance | L1 signal | 100 | 100 | 87 | 86 | 86 |

100 | 89 | 86 | 86 | 87 | ||

L5 signal (${T}_{\mathrm{C}}=20$ ms) | 100 | 100 | 81 | 77 | 78 | |

100 | 71 | 78 | 78 | 78 | ||

L5 signal (${T}_{\mathrm{C}}$ unlimited) | 80 | 81 | 82 | 82 | 82 | |

81 | 82 | 81 | 82 | 82 |

**Table 8.**Processing time (clock cycle) and memory requirements (bit) of the different implementations for a sensitivity of −150 dBm with average losses. Ratios are computed with the values of the L1 C/A signal.

Implementation | $\mathit{K}$ | ${\mathit{N}}_{\mathbf{NC}}$ | ${\mathit{N}}_{\mathbf{A}}$ | ${\mathit{B}}_{\mathbf{C}}$ | ${\mathit{B}}_{\mathbf{NC}}$ | ${\mathit{T}}_{\mathbf{FB}}$ | Ratio of ${\mathit{T}}_{\mathbf{FB}}$ | $\mathit{M}$ | Ratio of $\mathit{M}$ | Product of Ratios |
---|---|---|---|---|---|---|---|---|---|---|

L1 C/A Parallel NC | 23 | 23 | 20 | 21 | 26 | 1,968,128 | 2,785,280 | |||

L5 Parallel NC | 16 | 16 | 20 | 21 | 25 | 21,057,536 | 10.7 | 27,443,200 | 9.9 | 105.4 |

L5 Semi-parallel NC | 16 | 16 | 10 | 21 | 25 | 42,029,056 | 21.4 | 13,751,600 | 4.9 | 105.2 |

L5 Semi-parallel NC | 16 | 16 | 9 | 21 | 25 | 63,000,576 | 32.0 | 12,349,440 | 4.4 | 141.9 |

L5 Semi-parallel NC | 16 | 16 | 8 | 21 | 25 | 63,000,576 | 32.0 | 10,977,280 | 3.9 | 126.2 |

L5 Semi-parallel NC | 16 | 16 | 7 | 21 | 25 | 63,000,576 | 32.0 | 9,605,120 | 3.4 | 110.4 |

L5 Semi-parallel NC | 16 | 16 | 6 | 21 | 25 | 83,972,096 | 42.7 | 8,232,960 | 3.0 | 126.1 |

L5 Semi-parallel NC | 16 | 16 | 5 | 21 | 25 | 83,972,096 | 42.7 | 6,860,800 | 2.5 | 105.1 |

L5 Semi-parallel NC | 16 | 16 | 4 | 21 | 25 | 104,943,616 | 53.3 | 5,488,640 | 2.0 | 105.1 |

L5 Semi-parallel NC | 16 | 16 | 3 | 21 | 25 | 146,886,656 | 74.6 | 4,116,480 | 1.5 | 110.3 |

L5 Semi-parallel NC | 16 | 16 | 2 | 21 | 25 | 209,801,216 | 106.6 | 2,744,320 | 1.0 | 105.0 |

L5 Serial NC | 16 | 16 | 1 | 21 | 25 | 419,516,416 | 213.2 | 1,372,160 | 0.5 | 105.0 |

L5 Parallel C | 7.30 | 1 | 20 | 24 | - | 9,654,272 | 4.9 | 19,660,800 | 7.1 | 34.6 |

L5 Semi-parallel C | 7.30 | 1 | 10 | 24 | - | 19,222,528 | 9.8 | 9,830,400 | 3.5 | 34.5 |

L5 Semi-parallel C | 7.30 | 1 | 9 | 24 | - | 28,790,784 | 14.6 | 8,847,360 | 3.2 | 46.5 |

L5 Semi-parallel C | 7.30 | 1 | 8 | 24 | - | 28,790,784 | 14.6 | 7,864,320 | 2.8 | 41.3 |

L5 Semi-parallel C | 7.30 | 1 | 7 | 24 | - | 28,790,784 | 14.6 | 6,881,280 | 2.5 | 36.1 |

L5 Semi-parallel C | 7.30 | 1 | 6 | 24 | - | 38,359,040 | 19.5 | 5,898,240 | 2.1 | 41.3 |

L5 Semi-parallel C | 7.30 | 1 | 5 | 24 | - | 38,359,040 | 19.5 | 4,915,200 | 1.8 | 34.4 |

L5 Semi-parallel C | 7.30 | 1 | 4 | 24 | - | 47,927,296 | 24.4 | 3,932,160 | 1.4 | 34.4 |

L5 Semi-parallel C | 7.30 | 1 | 3 | 24 | - | 67,063,808 | 34.1 | 2,949,120 | 1.1 | 36.1 |

L5 Semi-parallel C | 7.30 | 1 | 2 | 24 | - | 95,768,576 | 48.7 | 1,966,080 | 0.7 | 34.3 |

L5 Serial C | 7.30 | 1 | 1 | 24 | - | 191,451,136 | 97.3 | 983,040 | 0.4 | 34.3 |

L1 C/A Parallel + assist. | 20 | 20 | 20 | 21 | 26 | 1,722,368 | 2,785,280 | 1.0 | ||

L5 Serial NC + assist. | 13 | 13 | 1 | 21 | 25 | 21,057,536 | 12.2 | 1,372,160 | 0.5 | 6.0 |

L5 Serial C + assist. | 6.00 | 1 | 1 | 23 | - | 7,950,336 | 4.6 | 942,080 | 0.3 | 1.6 |

**Table 9.**Memory requirements (bit) of the different implementations for a sensitivity of −150 dBm with average losses, considering the input memory. Ratios are computed with the values of the L1 C/A signal.

Implementation | ${\mathit{T}}_{\mathbf{IT}}$ | Input Memory (bit) | Total Memory (bit) | Memory Ratio | Product of Ratios |
---|---|---|---|---|---|

L1 C/A Parallel NC | 460 | 942,080 | 3,727,360 | ||

L5 Parallel NC | 320 | 6,553,600 | 33,996,800 | 9.1 | 97.6 |

L5 Semi-parallel NC | 320 | 6,553,600 | 20,275,200 | 5.4 | 116.2 |

L5 Semi-parallel NC | 320 | 6,553,600 | 18,903,040 | 5.1 | 162.3 |

L5 Semi-parallel NC | 320 | 6,553,600 | 17,530,880 | 4.7 | 150.6 |

L5 Semi-parallel NC | 320 | 6,553,600 | 16,158,720 | 4.3 | 138.8 |

L5 Semi-parallel NC | 320 | 6,553,600 | 14,786,560 | 4.0 | 169.3 |

L5 Semi-parallel NC | 320 | 6,553,600 | 13,414,400 | 3.6 | 153.6 |

L5 Semi-parallel NC | 320 | 6,553,600 | 12,042,240 | 3.2 | 172.3 |

L5 Semi-parallel NC | 320 | 6,553,600 | 10,670,080 | 2.9 | 213.6 |

L5 Semi-parallel NC | 320 | 6,553,600 | 9,297,920 | 2.5 | 265.9 |

L5 Serial NC | 320 | 6,553,600 | 7,925,760 | 2.1 | 453.2 |

L5 Parallel C | 146 | 2,990,080 | 22,650,880 | 6.1 | 29.8 |

L5 Semi-parallel C | 146 | 2,990,080 | 12,820,480 | 3.4 | 33.6 |

L5 Semi-parallel C | 146 | 2,990,080 | 11,837,440 | 3.2 | 46.5 |

L5 Semi-parallel C | 146 | 2,990,080 | 10,854,400 | 2.9 | 42.6 |

L5 Semi-parallel C | 146 | 2,990,080 | 9,871,360 | 2.6 | 38.7 |

L5 Semi-parallel C | 146 | 2,990,080 | 8,888,320 | 2.4 | 46.5 |

L5 Semi-parallel C | 146 | 2,990,080 | 7,905,280 | 2.1 | 41.3 |

L5 Semi-parallel C | 146 | 2,990,080 | 6,922,240 | 1.9 | 45.2 |

L5 Semi-parallel C | 146 | 2,990,080 | 5,939,200 | 1.6 | 54.3 |

L5 Semi-parallel C | 146 | 2,990,080 | 4,956,160 | 1.3 | 64.7 |

L5 Serial C | 146 | 2,990,080 | 3,973,120 | 1.1 | 103.7 |

L1 C/A Parallel + assist. | 400 | 819,200 | 3,604,480 | ||

L5 Serial NC + assist. | 260 | 5,324,800 | 6,696,960 | 1.9 | 22.7 |

L5 Serial C + assist. | 120 | 2,457,600 | 3,399,680 | 0.9 | 4.4 |

**Table 10.**Ratio of complexity (product of processing time ratio and memory ratio) between the L5 and L1 C/A signals. Top rows do not consider the input memory, while bottom rows consider the input memory.

Sensitivity | Parallel without Assistance | Serial with Assistance | ||||||
---|---|---|---|---|---|---|---|---|

Non-Coherent | Coherent Only | Non-Coherent | Coherent Only | |||||

Average | Worst | Average | Worst | Average | Worst | Average | Worst | |

−140 dBm | 84.2 | 109.3 | 40.9 | 47.4 | 4.2 | 5.5 | 1.7 | 1.9 |

−145 dBm | 97.6 | 111.1 | 52.1 | 45.6 | 4.9 | 6.3 | 2.1 | 2.1 |

−150 dBm | 105.4 | 106.8 | 34.6 | 25.0 | 6.0 | 6.2 | 1.6 | 1.1 |

−155 dBm | 102.4 | 101.6 | 15.3 | 9.5 | 5.9 | 5.9 | 0.7 | 0.4 |

−160 dBm | 98.9 | 98.2 | 5.6 | 3.2 | 5.7 | 5.8 | 0.3 | 0.2 |

−140 dBm | 84.2 | 109.3 | 41.0 | 47.4 | 5.5 | 8.6 | 2.1 | 2.8 |

−145 dBm | 96.2 | 108.3 | 51.7 | 43.8 | 8.8 | 14.0 | 3.7 | 4.6 |

−150 dBm | 97.6 | 90.9 | 29.8 | 17.0 | 22.7 | 35.4 | 4.4 | 3.5 |

−155 dBm | 78.0 | 69.4 | 6.6 | 2.1 | 49.3 | 58.7 | 2.0 | 0.9 |

−160 dBm | 64.5 | 62.5 | 0.6 | 0.2 | 62.4 | 63.5 | 0.3 | 0.1 |

Sensitivity | Parallel without Assistance | Serial with Assistance | ||||||
---|---|---|---|---|---|---|---|---|

Non-Coherent | Coherent Only | Non-Coherent | Coherent Only | |||||

Average | Worst | Average | Worst | Average | Worst | Average | Worst | |

−140 dBm | 0.8 | 0.8 | 0.6 | 1.0 | 0.8 | 0.8 | 0.5 | 0.8 |

−145 dBm | 0.8 | 0.8 | 1.8 | 3.1 | 0.8 | 0.8 | 1.4 | 2.5 |

−150 dBm | 0.8 | 0.8 | 5.5 | 9.7 | 0.8 | 0.8 | 4.5 | 7.9 |

−155 dBm | 0.8 | 0.8 | 17.3 | 30.5 | 0.8 | 0.8 | 14.1 | 24.9 |

−160 dBm | 0.8 | 0.8 | 54.8 | 96.5 | 0.8 | 0.8 | 44.7 | 78.7 |

Sensitivity | Parallel without Assistance | Serial with Assistance | ||||||
---|---|---|---|---|---|---|---|---|

Non-Coherent | Coherent Only | Non-Coherent | Coherent Only | |||||

Average | Worst | Average | Worst | Average | Worst | Average | Worst | |

−140 dBm | 63.1 | 81.9 | 23.0 | 46.2 | 3.2 | 4.1 | 0.8 | 1.5 |

−145 dBm | 73.2 | 83.3 | 91.8 | 140.4 | 3.7 | 4.7 | 3.0 | 5.3 |

−150 dBm | 79.1 | 80.1 | 189.6 | 242.3 | 4.5 | 4.6 | 7.0 | 8.9 |

−155 dBm | 76.8 | 76.2 | 264.4 | 289.9 | 4.4 | 4.4 | 10.2 | 11.2 |

−160 dBm | 74.2 | 73.7 | 303.9 | 313.5 | 4.3 | 4.3 | 11.7 | 12.2 |

−140 dBm | 63.1 | 81.9 | 23.1 | 46.2 | 4.1 | 6.5 | 1.0 | 2.2 |

−145 dBm | 72.1 | 81.2 | 91.1 | 134.8 | 6.6 | 10.5 | 5.3 | 11.6 |

−150 dBm | 73.2 | 68.2 | 163.2 | 164.3 | 17.0 | 26.5 | 19.6 | 27.5 |

−155 dBm | 58.5 | 52.0 | 113.9 | 65.6 | 37.0 | 44.0 | 28.3 | 22.1 |

−160 dBm | 48.4 | 46.9 | 32.8 | 16.6 | 46.8 | 47.6 | 14.2 | 8.6 |

**Table 13.**Theoretical and average of the measured number of frequency bins and their ratio between L5 and L1.

Signals | No Assistance | Assistance | |||||
---|---|---|---|---|---|---|---|

−140 dBm | −145 dBm | −150 dBm | −140 dBm | −145 dBm | −150 dBm | ||

Number of frequency bins in the search space | L1 C/A | 301 | 301 | 301 | 17 | 17 | 17 |

L5 NC | 225 | 225 | 225 | 13 | 13 | 13 | |

L5 C | 169 | 529 | 1643 | 7 | 23 | 73 | |

Number of frequency bins searched until detection | L1 C/A | 135.5 | 146.9 | 139.9 | 7.3 | 7.0 | 7.9 |

L5 NC | 100.5 | 109.4 | 104.3 | 5.1 | 4.9 | 5.6 | |

L5 C | 75.4 | 256.6 | 711.0 | 3.2 | 10.1 | 35.7 | |

Ratio of number of frequency bin in the search space | L5 NC verses L1 C/A | 0.75 | 0.75 | 0.75 | 0.76 | 0.76 | 0.76 |

L5 C verses L1 C/A | 0.56 | 1.76 | 5.46 | 0.41 | 1.35 | 4.29 | |

Ratio of number of frequency bins searched until detection | L5 NC verses L1 C/A | 0.74 | 0.74 | 0.75 | 0.70 | 0.71 | 0.71 |

L5 C verses L1 C/A | 0.56 | 1.75 | 5.08 | 0.43 | 1.44 | 4.52 |

Signal | ${\mathit{f}}_{\mathbf{S}}$ | ${\mathit{N}}_{\mathbf{P}}$ | ${\mathit{N}}_{\mathbf{FFT}}$ | ${\mathit{N}}_{\mathbf{Z}}$ | ${\mathit{N}}_{\mathbf{D}}$ | ${\mathit{N}}_{\mathbf{S}}$ | ${\mathit{B}}_{\mathbf{R}}$ |
---|---|---|---|---|---|---|---|

E1 | 4.096 MHz | 16,384 | 32,768 | 0 | - | 25 | 16 |

E1 | 6.144 MHz | 24,576 | 65,536 | 16,384 | - | 25 | 16 |

E5a | 20.48 MHz | 20,480 | 65,536 | 24,576 | - | 100 | 16 |

**Table 15.**Search space and statistical parameters for ${P}_{\mathrm{FA},\mathrm{G}}={10}^{-3}$ and ${P}_{\mathrm{D}}=0.9$ for different contexts with Galileo signals. The same values are considered for unlimited ${T}_{\mathrm{C}}$.

Context | Signal | ${\mathit{T}}_{\mathbf{C}}$ | ${\mathit{N}}_{\mathbf{FB}}$ | ${\mathit{N}}_{\mathbf{CB}}$ | ${\mathit{N}}_{\mathbf{CELL}}$ | ${\mathit{P}}_{\mathbf{FA},\mathbf{C}}$ | $\mathit{S}\mathit{N}\mathit{R}$ |
---|---|---|---|---|---|---|---|

no assistance | E1 (4.096) | 100 ms | 1200 | 409,600 | 491,520,000 | 2.04 × 10^{−12} | 18.30 dB |

E1 (6.144) | 100 ms | 1200 | 614,400 | 737,280,000 | 1.36 × 10^{−12} | 18.35 dB | |

E5 | 100 ms | 900 | 2,048,000 | 1,843,200,000 | 5.40 × 10^{−13} | 18.49 dB | |

assistance | E1 (4.096) | 100 ms | 32 | 16,384 | 524,288 | 1.91 × 10^{−9} | 17.12 dB |

E1 (6.144) | 100 ms | 32 | 24,576 | 786,432 | 1.27 × 10^{−9} | 17.20 dB | |

E5 | 100 ms | 24 | 20,480 | 491,520 | 2.04 × 10^{−9} | 17.10 dB |

**Table 16.**Total integration time ${T}_{\mathrm{IT}}={T}_{\mathrm{C}}\times {N}_{\mathrm{NC}}$ as function of the sensitivity and context with Galileo signals, for average losses. Note that the sensitivities given are for the L1 C/A signal; those of E1 are 1.5 dB lower and those of E5 are 0.5 dB higher.

Context | Signal | ${\mathit{T}}_{\mathbf{C}}$ | −140 dBm | −145 dBm | −150 dBm | −155 dBm | −160 dBm |
---|---|---|---|---|---|---|---|

no assistance | E1 (4.096) | 100 ms | 100 × 1 = 100 | 100 × 1 = 100 | 100 × 5 = 500 | 100 × 24 = 2400 | 100 × 179 = 17,900 |

E1 (6.144) | 100 ms | 100 × 1 = 100 | 100 × 1 = 100 | 100 × 5 = 500 | 100 × 25 = 2500 | 100 × 182 = 18,200 | |

E5 | 100 ms | 100 × 1 = 100 | 100 × 1 = 100 | 100 × 3 = 300 | 100 × 13 = 1300 | 100 × 82 = 8200 | |

E1 (4.096) | unlimited | 100 × 1 = 100 | 100 × 1 = 100 | 400 × 1 = 400 | 1000 × 1 = 1000 | 3100 × 1 = 3100 | |

E1 (6.144) | unlimited | 100 × 1 = 100 | 100 × 1 = 100 | 400 × 1 = 400 | 1000 × 1 = 1000 | 3100 × 1 = 3100 | |

E5 | unlimited | 100 × 1 = 100 | 100 × 1 = 100 | 300 × 1 = 300 | 700 × 1 = 700 | 2100 × 1 = 2100 | |

assistance | E1 (4.096) | 100 ms | 100 × 1 = 100 | 100 × 1 = 100 | 100 × 4 = 400 | 100 × 19 = 1900 | 100 × 137 = 13,700 |

E1 (6.144) | 100 ms | 100 × 1 = 100 | 100 × 1 = 100 | 100 × 4 = 400 | 100 × 19 = 1900 | 100 × 139 = 13,900 | |

E5 | 100 ms | 100 × 1 = 100 | 100 × 1 = 100 | 100 × 2 = 200 | 100 × 9 = 900 | 100 × 59 = 5900 | |

E1 (4.096) | unlimited | 28 × 1 = 28 | 80 × 1 = 80 | 248 × 1 = 248 | 776 × 1 = 776 | 2452 × 1 = 2452 | |

E1 (6.144) | unlimited | 28 × 1 = 28 | 80 × 1 = 80 | 252 × 1 = 252 | 788 × 1 = 788 | 2488 × 1 = 2488 | |

E5 | unlimited | 16 × 1 = 16 | 49 × 1 = 49 | 154 × 1 = 154 | 487 × 1 = 487 | 1540 × 1 = 1540 |

**Table 17.**Total integration time ${T}_{\mathrm{IT}}={T}_{\mathrm{C}}\times {N}_{\mathrm{NC}}$ as function of the sensitivity and context with Galileo signals, for worst losses. Note that the sensitivities given are for the L1 C/A signal; those of E1 are 1.5 dB lower and those of E5 are 0.5 dB higher.

Context | Signal | ${\mathit{T}}_{\mathbf{C}}$ | −140 dBm | −145 dBm | −150 dBm | −155 dBm | −160 dBm |
---|---|---|---|---|---|---|---|

no assistance | E1 (4.096) | 100 ms | 100 × 1 = 100 | 100 × 2 = 200 | 100 × 10 = 1000 | 100 × 63 = 6300 | 100 × 520 = 52,000 |

E1 (6.144) | 100 ms | 100 × 1 = 100 | 100 × 2 = 200 | 100 × 10 = 1000 | 100 × 64 = 6400 | 100 × 526 = 52,600 | |

E5 | 100 ms | 100 × 1 = 100 | 100 × 2 = 200 | 100 × 6 = 600 | 100 × 30 = 3000 | 100 × 228 = 22,800 | |

E1 (4.096) | unlimited | 100 × 1 = 100 | 200 × 1 = 200 | 600 × 1 = 600 | 1800 × 1 = 1800 | 5400 × 1 = 5400 | |

E1 (6.144) | unlimited | 100 × 1 = 100 | 200 × 1 = 200 | 600 × 1 = 600 | 1800 × 1 = 1800 | 5500 × 1 = 5500 | |

E5 | unlimited | 100 × 1 = 100 | 200 × 1 = 200 | 400 × 1 = 400 | 1200 × 1 = 1200 | 3600 × 1 = 3600 | |

assistance | E1 (4.096) | 100 ms | 100 × 1 = 100 | 100 × 2 = 200 | 100 × 8 = 800 | 100 × 48 = 4800 | 100 × 396 = 39,600 |

E1 (6.144) | 100 ms | 100 × 1 = 100 | 100 × 2 = 200 | 100 × 8 = 800 | 100 × 49 = 4900 | 100 × 404 = 40,400 | |

E5 | 100 ms | 100 × 1 = 100 | 100 × 1 = 100 | 100 × 4 = 400 | 100 × 22 = 2200 | 100 × 166 = 16,600 | |

E1 (4.096) | unlimited | 44 × 1 = 44 | 140 × 1 = 140 | 432 × 1 = 432 | 1368 × 1 = 1368 | 4316 × 1 = 4316 | |

E1 (6.144) | unlimited | 44 × 1 = 44 | 140 × 1 = 140 | 440 × 1 = 440 | 1388 × 1 = 1388 | 4384 × 1 = 4384 | |

E5 | unlimited | 28 × 1 = 28 | 86 × 1 = 86 | 272 × 1 = 272 | 858 × 1 = 858 | 2713 × 1 = 2713 |

**Table 18.**Ratio of total integration time (%) for different comparisons with Galileo signals. Top value is for average losses, and bottom value is for worst losses. Note that the sensitivities given are for the L1 C/A signal; those of E1 are 1.5 dB lower and those of E5 are 0.5 dB higher.

Comparison | Fixed Element | −140 dBm | −145 dBm | −150 dBm | −155 dBm | −160 dBm |
---|---|---|---|---|---|---|

Impact of using E5: E5 verses E1 4.096 | ${T}_{\mathrm{C}}=100$ ms (no assistance) | 100 | 100 | 60 | 54 | 46 |

100 | 100 | 60 | 48 | 44 | ||

${T}_{\mathrm{C}}$ unlimited (no assistance) | 100 | 100 | 75 | 70 | 68 | |

100 | 100 | 67 | 67 | 67 | ||

${T}_{\mathrm{C}}=100$ ms (assistance) | 100 | 100 | 50 | 47 | 43 | |

100 | 50 | 50 | 46 | 42 | ||

${T}_{\mathrm{C}}$ unlimited(assistance) | 57 | 61 | 62 | 63 | 63 | |

64 | 61 | 63 | 63 | 63 | ||

Impact of ${T}_{\mathrm{C}}$: Unlimited verses 100 ms | E1 signal 4.096 (no assistance) | 100 | 100 | 80 | 42 | 17 |

100 | 100 | 60 | 29 | 10 | ||

E1 signal 6.144 (no assistance) | 100 | 100 | 80 | 40 | 17 | |

100 | 100 | 60 | 28 | 10 | ||

E5 signal (no assistance) | 100 | 100 | 100 | 54 | 26 | |

100 | 100 | 67 | 40 | 16 | ||

E1 signal 4.096 (assistance) | 28 | 80 | 62 | 41 | 18 | |

44 | 70 | 54 | 29 | 11 | ||

E1 signal 6.144 (assistance) | 28 | 80 | 63 | 41 | 18 | |

44 | 70 | 55 | 28 | 11 | ||

E5 signal (assistance) | 16 | 49 | 77 | 54 | 26 | |

28 | 86 | 68 | 39 | 16 | ||

Impact of assistance: Assistance verses no assistance | E1 signal 4.096 (${T}_{\mathrm{C}}=100$ ms) | 100 | 100 | 80 | 79 | 77 |

100 | 100 | 80 | 76 | 76 | ||

E1 signal 6.144 (${T}_{\mathrm{C}}=100$ ms) | 100 | 100 | 80 | 76 | 76 | |

100 | 100 | 80 | 77 | 77 | ||

E5 signal (${T}_{\mathrm{C}}=100$ ms) | 100 | 100 | 67 | 69 | 72 | |

100 | 50 | 67 | 73 | 73 | ||

E1 signal 4.096 (${T}_{\mathrm{C}}$ unlimited) | 28 | 80 | 62 | 78 | 79 | |

44 | 70 | 72 | 76 | 80 | ||

E1 signal 6.144 (${T}_{\mathrm{C}}$ unlimited) | 28 | 80 | 63 | 79 | 80 | |

44 | 70 | 73 | 77 | 80 | ||

E5 signal (${T}_{\mathrm{C}}$ unlimited) | 16 | 49 | 51 | 70 | 73 | |

28 | 43 | 68 | 72 | 75 |

**Table 19.**Ratio of complexity (product of processing time ratio and memory ratio) between the E1 signal with a sampling frequency of 6.144 MHz and the E1 signal with a sampling frequency of 4.096 MHz. Top rows do not consider the input memory, while bottom rows consider the input memory.

Sensitivity | Parallel without Assistance | Serial with Assistance | ||||||
---|---|---|---|---|---|---|---|---|

Non-Coherent | Coherent Only | Non-Coherent | Coherent Only | |||||

Average | Worst | Average | Worst | Average | Worst | Average | Worst | |

−140 dBm | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 |

−145 dBm | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 |

−150 dBm | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.1 |

−155 dBm | 2.8 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 |

−160 dBm | 3.0 | 3.0 | 3.0 | 3.1 | 3.0 | 2.8 | 3.0 | 3.0 |

−140 dBm | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.4 |

−145 dBm | 3.0 | 2.9 | 3.0 | 3.2 | 3.0 | 3.8 | 3.0 | 3.8 |

−150 dBm | 3.0 | 3.1 | 3.0 | 3.2 | 3.0 | 4.8 | 3.1 | 4.5 |

−155 dBm | 2.9 | 4.3 | 3.0 | 3.5 | 3.0 | 7.2 | 3.1 | 5.0 |

−160 dBm | 3.0 | 7.5 | 3.0 | 4.0 | 3.0 | 8.7 | 3.1 | 5.3 |

**Table 20.**Ratio of complexity (product of processing time ratio and memory ratio) between the E5 signal and the E1 signal with a sampling frequency of 4.096 MHz. Top rows do not consider the input memory, while bottom rows consider the input memory.

Sensitivity | Parallel without Assistance | Serial with Assistance | ||||||
---|---|---|---|---|---|---|---|---|

Non-Coherent | Coherent Only | Non-Coherent | Coherent Only | |||||

Average | Worst | Average | Worst | Average | Worst | Average | Worst | |

−140 dBm | 41.9 | 41.9 | 41.9 | 41.9 | 10.5 | 10.5 | 5.4 | 6.2 |

−145 dBm | 41.9 | 42.0 | 41.9 | 42.6 | 10.5 | 10.8 | 6.1 | 6.3 |

−150 dBm | 43.3 | 43.5 | 32.3 | 27.6 | 10.9 | 10.9 | 6.7 | 6.8 |

−155 dBm | 41.6 | 44.2 | 30.2 | 28.7 | 10.9 | 11.0 | 6.5 | 6.5 |

−160 dBm | 44.3 | 44.0 | 29.1 | 27.6 | 10.9 | 11.2 | 6.5 | 6.5 |

−140 dBm | 41.8 | 41.8 | 41.8 | 41.8 | 18.4 | 18.4 | 6.3 | 9.1 |

−145 dBm | 41.8 | 41.2 | 41.2 | 45.5 | 18.4 | 18.4 | 8.8 | 12.7 |

−150 dBm | 41.8 | 42.3 | 31.5 | 28.6 | 16.0 | 28.0 | 11.7 | 19.0 |

−155 dBm | 35.4 | 42.5 | 28.4 | 30.3 | 17.4 | 40.7 | 13.9 | 23.5 |

−160 dBm | 23.4 | 46.9 | 25.1 | 29.5 | 16.4 | 45.8 | 15.0 | 26.2 |

Sensitivity | Parallel without Assistance | Serial with Assistance | ||||||
---|---|---|---|---|---|---|---|---|

Non-Coherent | Coherent Only | Non-Coherent | Coherent Only | |||||

Average | Worst | Average | Worst | Average | Worst | Average | Worst | |

−140 dBm | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | 0.4 | 0.5 |

−145 dBm | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | 0.5 | 0.5 |

−150 dBm | 0.8 | 0.8 | 0.6 | 0.5 | 0.8 | 0.8 | 0.5 | 0.5 |

−155 dBm | 0.8 | 0.8 | 0.5 | 0.5 | 0.8 | 0.8 | 0.5 | 0.5 |

−160 dBm | 0.8 | 0.8 | 0.5 | 0.5 | 0.8 | 0.8 | 0.5 | 0.5 |

Sensitivity | Parallel without Assistance | Serial with Assistance | ||||||
---|---|---|---|---|---|---|---|---|

Non-Coherent | Coherent Only | Non-Coherent | Coherent Only | |||||

Average | Worst | Average | Worst | Average | Worst | Average | Worst | |

−140 dBm | 31.4 | 31.4 | 31.4 | 31.4 | 7.9 | 7.9 | 2.3 | 2.9 |

−145 dBm | 31.4 | 31.5 | 31.4 | 32.0 | 7.9 | 8.1 | 2.8 | 2.9 |

−150 dBm | 32.5 | 32.6 | 18.2 | 13.8 | 8.1 | 8.2 | 3.1 | 3.2 |

−155 dBm | 31.2 | 33.2 | 15.9 | 14.4 | 8.2 | 8.2 | 3.1 | 3.1 |

−160 dBm | 33.3 | 33.0 | 14.8 | 13.8 | 8.2 | 8.4 | 3.1 | 3.1 |

−140 dBm | 31.4 | 31.4 | 31.3 | 31.3 | 13.8 | 13.8 | 2.7 | 4.4 |

−145 dBm | 31.4 | 30.9 | 31.3 | 34.1 | 13.8 | 13.8 | 4.0 | 5.9 |

−150 dBm | 31.3 | 31.8 | 17.7 | 14.3 | 12.0 | 21.0 | 5.4 | 9.0 |

−155 dBm | 26.5 | 31.9 | 14.9 | 15.1 | 13.0 | 30.5 | 6.5 | 11.1 |

−160 dBm | 17.5 | 35.2 | 12.8 | 14.8 | 12.3 | 34.4 | 7.1 | 12.3 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Leclère, J.; Landry, R., Jr.; Botteron, C.
Comparison of L1 and L5 Bands GNSS Signals Acquisition. *Sensors* **2018**, *18*, 2779.
https://doi.org/10.3390/s18092779

**AMA Style**

Leclère J, Landry R Jr., Botteron C.
Comparison of L1 and L5 Bands GNSS Signals Acquisition. *Sensors*. 2018; 18(9):2779.
https://doi.org/10.3390/s18092779

**Chicago/Turabian Style**

Leclère, Jérôme, René Landry, Jr., and Cyril Botteron.
2018. "Comparison of L1 and L5 Bands GNSS Signals Acquisition" *Sensors* 18, no. 9: 2779.
https://doi.org/10.3390/s18092779