Regarding the calculation correction of the article "Starting from the sensitivity of GPS receivers"
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After the last article " Starting from the Sensitivity of GPS Receivers " was published , readers reminded me and the author recalculated and found that there was a step in the unit calculation that caused an error in the calculation of the GPS signal limit SNR (from this I can see that my junior high school physics teacher was right and told me to use physical units when calculating), resulting in the wrong conclusion that the limit sensitivity of GPS L1 C/A was -169dBm. After recalculation, the corrected limit sensitivity is -199.7dBm.
We now display the manuscript of the calculation at that time and publish the complete calculation process. We apologize for the misleading information to readers. Thank you for the enthusiastic readers who left us a message and pointed out the error!
The above picture is the author's manuscript on 2020-05-03
The following is the process of recalculating the derivation
I would like to explain here that this is just my calculation method. The common receiver sensitivity formula I use does not include the last item, the spread spectrum gain Gp=43. If this value is not entered, the theoretical minimum sensitivity is S= -174+63+2- 47.7= -156.7dBm. This does not seem to be the limit value, because many manufacturers can achieve a sensitivity far lower than this.
The lowest sensitivity of the consumer electronics GPS L1 C/A chip is -167dBm, which is a huge gap from the theoretical value of -199.7dBm. Due to the author's limited ability, if there are any errors or inappropriateness in this algorithm, I sincerely hope that readers will criticize and correct it.
After the last article was published, we were fortunate to receive corrections from enthusiastic reader Ba Xiaohui from the Institute of Microelectronics, Chinese Academy of Sciences. We also communicated with Ba and obtained some opinions for your reference and discussion:
The formula in the article is correct. It's just that my understanding of the last item, which is GP, is different from the author's. Different manufacturers have different GPs, which leads to different sensitivity. Taking L1C/A signal as an example, some manufacturers use 20ms cumulative value for tracking. 20ms is because the message rate is 50bps, but some manufacturers may use 40ms or even 100ms cumulative value for tracking (the message can be stripped). The latter has a higher GP and higher sensitivity.
Shannon’s theorem is not very relevant. Shannon’s theorem describes the maximum channel capacity in distortion-free transmission. The current problem is not distortion-free transmission, but stable tracking. It is okay if the demodulated bit error rate is very high.
Mr. Ba understands the sensitivity limit as such a problem. If the satellite and the receiver are not moving, the loop dynamics are very small, and the gain can be increased by coherent accumulation for a long time. I believe that there are receivers that exceed -167dBm, which should not be a problem. But in reality, the satellite is moving, and the receiver is also moving. When the accumulation time exceeds a certain level, the dynamics are difficult to guarantee, which limits the accumulation time. The sensitivity can only be fixed at a number in the end, unless there is external assistance (such as inertial navigation), but let's not talk about external assistance here.
The above are the opinions of enthusiastic readers and are for reference only.
When I was writing my previous article, I found some information about the GPS receiver sensitivity formula. Since it is different from the common formula I use, I did not mention it. Since this is a discussion, I will share it with you and readers can take what they need.
The following is from Li Jie, Multi-mode Multi-frequency GNSS Receiver RF Front-end Chip System Design, School of Microelectronics, Shanghai Jiao Tong University, 2009: P46
The following is a white paper article GPS Receiver Testing on the National Instruments official website about the GPS receiver sensitivity formula.
This is a rare opportunity for us to receive comments and discussions from enthusiastic readers, and we are deeply grateful for this. We hope that you will continue to care about us, participate in topic discussions, and share your insights.
Historical articles :
Starting from GPS receiver sensitivity
Keywords:
GNSS, GPS, GSS7000, NF, RX sensitivity, receive sensitivity, Process Gain, spread spectrum system, spread spectrum gain, Shannon theorem
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千斤顶
impressive. I have learned a lot. Thanks for sharing.