I thought FT8, JT65, JT9, etc, were the best low noise schemes because of the very narrow bandwidth, which means you can use very narrow filters and get rid of almost all the noise.
GPS Signals also come below the noise floor. They also have a correlation receiver type. The descriptions of it, that I found, did not brought me insight how it really works on the modulation level. I only understood that upper layer, there it receives from the 4 or more satellites their precise realtime and precise in space position, albeit the last digits of these numbers are enciphered for intentionally reducing the precision on non-military receivers.
It's like all of signal processing topics in one video! Exciting to learn about a robust platform with so much room for a lot of creative micro modulations.
I’m a ham operator. I setup a LoRa base station using the lora ham shield that runs on top of an arduino. With that arduino plugged into my raspberry pi at home, and another arduino with lora hsm shield running in my car. I was able to TX/RX short text messages first try back/forth about 9 miles apart. This was at only 1 watt or less power output, on 440 mhz. I was dumbfounded. It took some pass band filters, and good antennas, but still… Able to communicate well beyond any voice, digital voice, or digital modes on UHF from a very tough location to another, separated by multiple freeways, high rise buildings, trees, cars, etc, etc…
@paddler-sn7ub I don't sorry. It was an old project based on the LoRaChat program, and lora hamshield. The youtube channel was run by username inductive twig or something, and the arduino code for LoRaChat is on his github page. The key to making these cheap single board transceivers communicate much further than what is possible, is by using band pass filters to block out all the other RF noise. So I used very tight, 435 to 450 mhz band pass filters when experimenting. Also very good coax and antennas. My base station during that test had 1/2" hardline running up to a good folded dipole 15' above my roof. So just reducing the losses. Especially at the receive side.
@ I don't think LoRa is possible on HF due to it's spread spectrum nature. The FCC only allows a single transmitting station to use and occupy so much of a frequency span simultaneously. Even on the upper bands, the power has to be kept low to avoid breaking the spectrum bandwidth restrictions.
This wasn't really emphasized but usually more bits per symbol means worse performance for a given SNR, but in LoRas case, a higher SF also greatly increases the symbol's duration (as well as the bits per symbol), increasing SF by 1 means 1 more bit per symbol but it also doubles the symbol length, so that gives you more effective spreading, and lets you go to lower SNRs.
This is an extremely important point that confused me at first. Since the symbol duration doubles with each increase in the spreading factor by one, the symbol duration increases exponentially with the SF. However, the number of bits per symbol increases linearly with the SF. Consequently, the overall data rate decreases with an increased SF. There's no magic there; a lower data rate improves the permissible signal-to-noise ratio.
This is what I call well-balanced video making and editing: normal transitions, clear presentation, voice level fairly constant, background tune merely present and allows or even helps one to get immersed in the topic without being disturbed either by its loudness or a crappy tune choice. Your explanation is pretty good and shows you have a good understanding of the principles, but math is my weak side so I mostly skip over calculus and differential equations.
Great video! Just one comment: The LoRa demodulator is basically a correlator plus a bank of filters, the latter being implemented using FFT. And, the LoRa symbols are basically time shifted versions of each other. Conceptually it is very similar to an FMCW radar that also uses a similar demodulator. Instead of the symbols, the radar receives time delayed versions of the chirp waveform depending on the location of the target. The correlator output is a sine wave (for a single point target) whose frequency is proportional to the time delay (i.e. the range). Bank of filters (i.e. FFT) can thus be used to discriminate targets.
@@eswnl1 The FFT IS the bank of matched filters. Each FFT bin is computing how well the input signal matches the frequency for that bin. For CSS, the highest bin number is the symbol. For FMCW radar, the highest bin number is the range.
I've been very impressed with the performance I've been getting with LoRa, and this was a wonderful addition to the documentation from Semtec. They make it easy enough to use, but this understanding is invaluable.
This the very original way in which knowledge should be conveyed. Structured, well articulated language and definitely accurate. Thank you for your time and effort. New subscriber.
Man, your explanation is awesome. I really liked the way you added the paper information and brought a nice explanation. Please, keep going with these kind of videos. Regards, Pedro.
I'm new to radio staff. But I have basic knowledge of signal processing from my university studied 30 years ago. That is best described LoRa that I really understood. Keep up with a great job spreading knowledge and understanding!!! 🙏🙏🙏
Many thanks for posting this video. I had no idea how LoRa worked beforehand but your video clearly explained it. It took a while to figure out how convert your Matlab code into Octave code and correct my typos. But the final result worked exactly like your demo showed.
Thanks for such a well presented and clear description of the modulation scheme used. In response to your question, the LoRa modulation scheme is still subject to the Shannon limit, the maximum information rate is a function of channel SNR and bandwidth. If you increase the spreading factor in a channel where the SNR is constant, you will need more bandwidth to maintain the received symbol error rate. As bandwidth is usually fixed for a given channel, the SF can be varied to optimise information throughput for a given channel SNR. This can be done adaptively as the SNR varies over time, due to radio fading and interference sources.
As a visual learner - THANK YOU! I don't think I could have ever wrapped my head around this without your visual representation of time. All of it makes sense and, when you see how it works, it is one of those things that makes you go - yeah, why did it take so long for this to be figured out?! THANK YOU!!!
Awesome explanation and really amazing that higher s gives better performance on low snr. Should definitely be watched by many hams here on YT since it seems they still mess up all the terms and don't really understand LoRa
Thanks for explaining this what I always considered RF wizardry. Even though I don't have the mathematical fundament to stand on to understand it thoroughly, I have the feeling that I'm a lot smarter than before the video
Thanks for the video and very clear explanation. As a graduated in electronic engineering at the Padua university ( the same of Lorenzo Evangelista) I studied spread spectrum in the nineties but at the time I didn't catched the concept: too much theory and few concrete examples. At the time spread spectrum modulation was probably used only by military and hardware was not able to support the computation needed. After this video I want to go deeper on how Lora works, I think I will take the mathlab simulation you have developed to play a bit by myself.
Wow beautiful! From a new modulation concept with a complex maths expressions to a smart way of computational representation, that’s incredible! Cannot imagine how people invented this smart are!
This is a really good video you did explaining LoRa "mathematics', i.e. the magic of decoding a symbol where signal is less than noise i.e. SNR negative 8-) and the Matlab code is really useful. Thank you!
Well done. It would be interesting to add information about the bandwidth of the signal vs SF. This relates directly to the received noise and hence the S/N ratio. This will perhaps also shed a light on your question how far one can go by increasing the SF.
Wow - great explanation - usually there are 3 features but youre only allowed 2 of them - here you can choose 3 simultanously :) Low Bitrate, Low Power and Long Range :) - great idea :)))
Well technically the desirable traits are High Bitrate, Low Power and Long Range. Power and bitrate are low to begin with. Each time you increment the spreading factor, symbol duration has to double, but so does the number of bits per symbol. I think the trade-off there is in the processing power needed by the larger FFT in the receiver.
There is an error starting at about 13:40 about complex conjugate, and goes on further at 16 etc. The actual demodulation chirp is of the same slope as the modulated signal. With multiplication you get sum and difference of the frequencies, and that does the dechirping.
Great explanation. Here is the code if you want to play with it. clear all SF = 7; %Spreading Factor BW = 1000;% Bandwidth Fs = 1000;%Sampling Frequency s = 127; %send symbol '10' SNR = -10;%Signal to Noise Ratio %Generate a data symbol num_samples =(2^SF)*Fs/BW; k = s; %add s to k to start (defines the data symbol) lora_symbol = zeros(1,num_samples); for n=1:num_samples if k>= (2^SF) k = k-2^SF; end k = k+1; lora_symbol(n) = (1/(sqrt(2^SF)))*exp(1i*2*pi*(k)*(k/(2^SF*2))); end loop = 100; ind2 = zeros(1,loop); for j=1:loop %Add noise lora_symbol_noisy = awgn(lora_symbol,SNR,'measured'); %Transmit %Receiver below % Generate the Base Down Chirp base_down_chirp = zeros(1,num_samples); k=0; for n=1:num_samples if k>= (2^SF) k = k-2^SF; end k = k + 1; base_down_chirp(n) = (1/(sqrt(2^SF)))*(exp(-1i*2*pi*(k)*(k/(2^SF*2)))); end dechirped = lora_symbol_noisy.*(base_down_chirp); corrs = (abs(fft(dechirped)).^2); figure(1); plot(corrs) [~, ind] = max(corrs); ind2(j) = ind; pause(0.01) end figure(2); histogram(ind2,2^SF) symbol_error_rate = sum(ind2~=s+1)/j figure(3); spectrogram(lora_symbol)
Thanks for the video-i’m an Amateur radio operator with an interest in digital modes and LORA. I’m not sophisticated enough to follow along with the calculations in the video, but I understood the scene behind interpreting the symbols based on your description.
Very well presented! In thinking about the limits to the number of symbols, as the symbol duration increases distortions in propagation will modulate the baseband coordinates and increase the error rate. This is not ‘noise’ and will not show up in simulation. A noise driven delay modulation term would cover this.
Years ago with a friend i did a equivalent experiment using GNU-Radio. Not related to LoRa but the target was using width bandwidth spreadspectrum to get a signal over a long distance 100 - 200 km (60-100Mi) I also added a noise generator to see what happened.... it's long ago, but you retriggered my interest.
Man, how have I not come across your channel before and how are your subscriber numbers not 10x?! Instant subscribe, super clear explanation thank you!!
Minus 20 dB means that the noise magnitude is 10 times greater than the signal magnitude when we talk about amplitudes, but 100 times greater when talking about power.
Well, done! I was having a discussion in a math class where I introduced "i" and Complex Numbers to my 9 & 10.5 year old grandsons! (Yes, great joy in doing that!). I was immediately asked words to the effect of, "Well, that's all nice and consistent, and even beautiful if you wish, but it is all based on something that doesn't exist - the square root of negative one. How how can that have any practical value?" My answer then was (based on old analog oscillators I had studied early in EE in college) that when the complex roots of a quadratic equation have an imaginary component, the oscillator is unstable.) Neither a practical nor a very fascinating example for a 10-year old. But this! You've given me the most practical use of complex numbers - even more than the FFT itself - to be the basis of communication with a signal well below the noise level. As a long time amateur radio operator, liking CW (Morse code), we really appreciate digging a usable signal out of the noise. It can save lives. Some ham communications (lower frequency bands) bounce up and down off the ionosphere to make global communication with just milliwatts. Just subscribed. Will properly thank soon!
Overall great video. Good job extracting the bottom line information from the sinusoidal equations. Small correction needed: 20 db implies a magnitude of 100, not 10. Meaning the at -20db, the Noise is 100x the Signal magnitude, further driving the point of just how effective the signaling scheme is at handling noise, especially when you show the -10dB signal... just imagine 10x that. I do wish that you explained the Y axis of the Err Rate vs SNR a little bit, because the way its graphed in the video (right to left) almost implies that the higher value on the Y axis is good, but for anyone viewing, having an error rate of 1 is of course unusable. Maybe a horizontal line on the graph that shows an acceptable error rate wouldve helped. Oh, and thank you VERY much for providing a Matlab example
what if instead of one sweep of frequency you have a "chord" of a few frequencies; If the spread between the chord was constant/known by both parties could that be used to further reduce the SER/dB by trying to pick out which one is the signal (i.e. its more improbable that subsequent signals would share that pattern)... Only thing I could think of (non expert) could be that harmonics might produce similar correlated patterns, but if you had some other sort of shared pseudo-noise to pick the subsequent chord spacings ... or would having multiple signals being sent not be using the same SER/dB calculation?
Everything about Lora is counterintuitive. Increasing the spreading factor which means increasing the possible symbols IMPROVES performance? Incredible how the maths proves the fact. Does make you think about what more advanced tech the military has hidden away
Let me see, as stated in some comments, if the SF increases by 1, the symbol length (and window) doubles. That effectively lowers the bitrate, which makes total sense. Then, why the chirp at all? You could do exactly the same with nFSK, just have more possible values per symbol, over a longer time with a lower bitrate. For this to work so well, the chirp has to provide some important benefit. Perhaps less reliance in the oscillator stability? I'd love to see a comparison between LoRa and an equivalent nFSK in Matlab. BTW awesome video!
I guess the nFSK system would fail much sooner due to frequency selective multipath or constant carrier interference. That interference won't match the chirp rate. The difference wouldn't show in a simulation using AGWN like in this video. Just a guess, this video is the only real research I've done into LoRa.
@realsolarcars I guess, but you could address those problems in nFSK in an upper level of spreading and FEC, no one said the FSK should be simple and straight, after all LoRa isn't. I think what I try to say is that there is no real need for the continuous shifting in frequency, you could instead do discrete jumping between the n subcarriers. The reason could very well be making it patentable. Anyway I am just guessing. Regards!
The benefit is each symbol is spread across the entire bandwidth, so no symbol can be lost in a multipath null, unlike what could happen with nFSK. When you DONT use forward error correction this has big advantage!
Although I wasn't able to follow most of the parts related to the mathematical bases, but I got the concept behind and I've learned something new and interesting. I am sure I will never use it... but thanks :)
Thanks for the clear explanation! I do wonder what happens if there are 2 LoRa transmitters in an area though, how would the receiver distinguish between them?
I have only a high-school education. a total of 13 years of formal education, and no math beyond a semester of intro to algebra, but my fascination with RF led me to do a bit of research, and I ended up building a LowFER antenna and transmitter (175 kHz) transmitting BPSK ASCII using a computer program called Coherent, and with my transmitting beacon sending a short, repetitive text message, using crystal ovens at the beacon and in a homebrew receiver in my car, and averaging out the noise I was able to receive my beacon's text message, ( except for a couple of minutes in De Moines, Iowa, every foot of the way as I drove over a distance of 800 miles. It would have worked further, but I had not included sufficient front-end gain for copying the signal at great distances. I realized this because instead of my CRT screen printing out random characters, as it would with my transmitter turned off, in a low noise location it stopped displaying anything at all. Not enough gain. So, based on my simple experiments there is no SNR that a good modulation technique is incapable of receiving a signal through if the effective bandwidth is narrow enough, (i.e. a synchronized message repeated enough times to average out the noise.) The only limitation is how long you're willing to wait for the data to appear correctly. BTW, I estimated the EIRP of my transmit antenna to be 7 mW, which is very good for a LowFER antenna and 1 W transmitter. A friend took a receiver with him on his vacations each summer and received the beacon all over the western USA, day and night. So if chirp modulation can reduce the amount of time necessary to receive a given symbol and act in a manner similar to what we were doing with crystal ovens, BPSK, and Coherent, I'd say they have a winner.
Excellent explanation of a highly technical subject. I guess I'm going to have to experiment more with Lora, if I can find a worthy use. Thanks for investing the time to show this.
Is there anything superior here compared to a classic MFSK, that can also be optionally spread with DSSS or something? All the low power perf just seems like a natural outcome of the super long correlation times, which would boost perf of any scheme. What am I missing?
Somehow, I just knew the clever math trick would involve fourier transforms. Invariably in signals, compression, or other similar domains, converting between time and frequency domains opens up all sorts of interesting options for improving the efficiency of the process. Great video, very enlightening! LoRa is no longer magic to me. I'd love to see you cover CDMA, especially the way code-based modulations are combined with other methods to provide efficient band sharing and tolerance for multipath interference.
Is this insensivity to nosie make it possible to hide in the same band with other traditonal transmission like DVB-T is possible teorethicaly in analog TV channel ?
That was a very nice description - thank you. As a retired signal processing engineer it's nice to hear a good explanation! You suggest that the performance might keep on increasing with spreading factor without limit - it would be interesting (necessary, even) to include the initial detecton and synchronisation process, in noise, in your simulation, and then perhaps the effects of multipath, fading and Doppler. The decoder could be quite sensitive to symbol timing variation thoughout the packet - how long would a packet be? Terrestrial DAB modulation is based on frequencies rather than chirps, but the receive process is not disimilar - do you have any idea of the relative performance? I'm not familiar with the papers or the intended applications, but I would expect there to be further gains from hard or soft error detection/correction coding at the data level.
It is traditional to modulate a signal with a carrier that is many times the frequency of the signal. If you were interested in doing the reverse and wanted to swap the carrier to be (for example 30MHz) and the signal to have a frequency of many times the carrier (for example 30GHz), how would you go about doing that and what modulation scheme would you propose?
Carrier would be lost (attenuated) when the distance is higher much more than signal having the base frequency? (I mean that the carrier would be lost much sooner with the distance increased than the base range)
@@vencdee That is the behaviour we would expect for a higher frequency signal but what if that higher frequency signal is modulated or embedded in a lower frequency carrier, wouldn't that allow the signal to cover much longer distances?
If I understand the modulation scheme correctly, then the spreading factor correlates with the symbol transmission time. This means that it falls entirely with the expected strategy for improving the probability of error, which is to either reduce the data rate (larger spreading factor) or to increase the transmission power. You could get even better error performance by (a priori) agreeing to only use a subset of the the symbols provided by a given spreading factor, since reducing the constellation size increases the distance between symbols and therefore reducing the probability of misinterpreting a symbol.
How does the receiver perform in the presence of two transmitters of equal received power? For other spread spectrum modulations, other transmitters would become noise. I don't think that would happen for this modulation scheme, it would be hard to separate them.
What an extremely well presented video on a very complex subject. What I was wondering is what kind of bit rate you expect from this modulation scheme. You could always add a Foreward Error Correction protocol (FEC) to the original signal to improve the SNR. We use that extensively on high speed optical transmission systems
Amazing video! If i'm not wrong LoRa technique was used in Express LRS open source system used for example in FPV drones. You can get amazing range even at super small TinyWhoop like Mobula 7 1S ELRS. There is super tiny ceramic antenna and this system rocks in terms of penetration even on small transmitter power.
So, a SF=17 means each symbol could be treated as a 16-bit value, plus a parity bit, enabling the receiver to actually detect when the wrong symbol was received.
This is the fourth time I've seen this video. It covers everything I knew about LoRa modulation. Only the MatLab code is very important to me for educational reasons.
Hello, I read the paper by Vangelista (3-4 pages). I think I understood most of it except the proof to the equation (7). He changes a sum on the indicie k to a sum of sums to the indicies h*2^SF +p. I simply don't get it...
On the ultra short waves the bottleneck for the range is line of sight. Why there is no possibility to establish lora on lower bands where ranges me be huge?
Are you certain about your treatment of # of symbols at 5:30 etc? Based on other documentation it would seem that spread factor has to do with how long each symbol takes to transmit, not the number of discreet frequencies steps that can be measured. Data rates go down with increasing spread factors, not up.
Spreading factor of 7 = 128 possible symbols (7 bits). Spreading factor = 8 = 256 possible symbols (8 bits). But the SF=8 symbol takes twice as long. So, increasing the spreading factor by 1 allows you to send 1 more bit per symbol but at half the previous symbol rate. The net effect is the datarate goes down with spreading factor even though there are a greater set of possible symbols transmitted within each chirp.
I would guess that the reduction in noise is related to the square root of the number of samples if the noise is uncorrelated. Just a basic signal averaging process after you account for the chirp?
Which modulation scheme should I cover next? 🤔
I thought FT8, JT65, JT9, etc, were the best low noise schemes because of the very narrow bandwidth, which means you can use very narrow filters and get rid of almost all the noise.
This one....but after reading what Shannon limit is and Eb/N0...
Then you will compare apple to apples....
GPS Signals also come below the noise floor. They also have a correlation receiver type.
The descriptions of it, that I found, did not brought me insight how it really works on the modulation level.
I only understood that upper layer, there it receives from the 4 or more satellites their precise realtime and precise in space position, albeit the last digits of these numbers are enciphered for intentionally reducing the precision on non-military receivers.
I agree with Zach..894, any of the digital modes created by Dr. Joe Taylor. Use FT8 as your search term.
Go for WCDMA so you can compare processing gain against LoRa.
This is possibly the best explanation of Lora modulation I’ve seen ever…
It's like all of signal processing topics in one video! Exciting to learn about a robust platform with so much room for a lot of creative micro modulations.
No it is not !!
@@negvorsacould you link to a better one? I’d love to see that one too.
Why?
This is possibly the best explanation of anything I've ever seen.
I’m a ham operator. I setup a LoRa base station using the lora ham shield that runs on top of an arduino. With that arduino plugged into my raspberry pi at home, and another arduino with lora hsm shield running in my car. I was able to TX/RX short text messages first try back/forth about 9 miles apart. This was at only 1 watt or less power output, on 440 mhz. I was dumbfounded. It took some pass band filters, and good antennas, but still… Able to communicate well beyond any voice, digital voice, or digital modes on UHF from a very tough location to another, separated by multiple freeways, high rise buildings, trees, cars, etc, etc…
That is impressive.
Have a tutorial? I would be interested in your project 👍🏽
@paddler-sn7ub I don't sorry. It was an old project based on the LoRaChat program, and lora hamshield. The youtube channel was run by username inductive twig or something, and the arduino code for LoRaChat is on his github page.
The key to making these cheap single board transceivers communicate much further than what is possible, is by using band pass filters to block out all the other RF noise. So I used very tight, 435 to 450 mhz band pass filters when experimenting. Also very good coax and antennas. My base station during that test had 1/2" hardline running up to a good folded dipole 15' above my roof. So just reducing the losses. Especially at the receive side.
@ I don't think LoRa is possible on HF due to it's spread spectrum nature. The FCC only allows a single transmitting station to use and occupy so much of a frequency span simultaneously. Even on the upper bands, the power has to be kept low to avoid breaking the spectrum bandwidth restrictions.
This wasn't really emphasized but usually more bits per symbol means worse performance for a given SNR, but in LoRas case, a higher SF also greatly increases the symbol's duration (as well as the bits per symbol), increasing SF by 1 means 1 more bit per symbol but it also doubles the symbol length, so that gives you more effective spreading, and lets you go to lower SNRs.
Yes, you explain it well.
I was confused by this at first because I'm so used to more bits per symbol meaning worse performance, but this makes it clear, thanks!
Thanks for adding this crucial comment. I'm not sure why longer symbols give more effective spreading?
This is an extremely important point that confused me at first. Since the symbol duration doubles with each increase in the spreading factor by one, the symbol duration increases exponentially with the SF. However, the number of bits per symbol increases linearly with the SF. Consequently, the overall data rate decreases with an increased SF. There's no magic there; a lower data rate improves the permissible signal-to-noise ratio.
So how does the performance versus the bit energy to noise density ratio (Eb/No) compare to other modulation schemes and how does it change with SF?
“You can always detect a sine wave in noise….if you are willing to “wait” long enough” - E.J. Swanson
It absolutely blew my mind how clearly you have explained the LoRa modulation despite the complex maths behind it.
Thanks!
Dont know what amazed me more - the LoRa protocol or your explaination. Thanks for the video.
This is what I call well-balanced video making and editing: normal transitions, clear presentation, voice level fairly constant, background tune merely present and allows or even helps one to get immersed in the topic without being disturbed either by its loudness or a crappy tune choice.
Your explanation is pretty good and shows you have a good understanding of the principles, but math is my weak side so I mostly skip over calculus and differential equations.
If he'd encoded the music using LoRa it could have been turned down to below the noise floor! /s
Great video!
Just one comment: The LoRa demodulator is basically a correlator plus a bank of filters, the latter being implemented using FFT. And, the LoRa symbols are basically time shifted versions of each other.
Conceptually it is very similar to an FMCW radar that also uses a similar demodulator. Instead of the symbols, the radar receives time delayed versions of the chirp waveform depending on the location of the target. The correlator output is a sine wave (for a single point target) whose frequency is proportional to the time delay (i.e. the range). Bank of filters (i.e. FFT) can thus be used to discriminate targets.
Are matched filters used to sense each frequency component?
The FFT by its nature is a matched filter to the fundamental sin/cos waves@@eswnl1
@@eswnl1 The FFT IS the bank of matched filters. Each FFT bin is computing how well the input signal matches the frequency for that bin. For CSS, the highest bin number is the symbol. For FMCW radar, the highest bin number is the range.
I've been very impressed with the performance I've been getting with LoRa, and this was a wonderful addition to the documentation from Semtec. They make it easy enough to use, but this understanding is invaluable.
Perfect material for our LoRa APRS group!
This the very original way in which knowledge should be conveyed. Structured, well articulated language and definitely accurate. Thank you for your time and effort. New subscriber.
Man, your explanation is awesome. I really liked the way you added the paper information and brought a nice explanation. Please, keep going with these kind of videos.
Regards,
Pedro.
Excellent video mate, cheers for that! Good to see matlab getting used as well, it is invaluable in so many ways.
I'm new to radio staff. But I have basic knowledge of signal processing from my university studied 30 years ago. That is best described LoRa that I really understood. Keep up with a great job spreading knowledge and understanding!!! 🙏🙏🙏
Many thanks for posting this video. I had no idea how LoRa worked beforehand but your video clearly explained it. It took a while to figure out how convert your Matlab code into Octave code and correct my typos. But the final result worked exactly like your demo showed.
Can you pls share your octave version?
I have been long time to browse such best explanation of Lora to understand, thanks for great lecture
Brilliant video, this has demystified how the modulation and below noise floor parts work for me far better than any other video I've watched.
Thanks for such a well presented and clear description of the modulation scheme used.
In response to your question, the LoRa modulation scheme is still subject to the Shannon limit, the maximum information rate is a function of channel SNR and bandwidth.
If you increase the spreading factor in a channel where the SNR is constant, you will need more bandwidth to maintain the received symbol error rate.
As bandwidth is usually fixed for a given channel, the SF can be varied to optimise information throughput for a given channel SNR. This can be done adaptively as the SNR varies over time, due to radio fading and interference sources.
As a visual learner - THANK YOU! I don't think I could have ever wrapped my head around this without your visual representation of time. All of it makes sense and, when you see how it works, it is one of those things that makes you go - yeah, why did it take so long for this to be figured out?! THANK YOU!!!
Awesome explanation and really amazing that higher s gives better performance on low snr. Should definitely be watched by many hams here on YT since it seems they still mess up all the terms and don't really understand LoRa
Thanks for explaining this what I always considered RF wizardry. Even though I don't have the mathematical fundament to stand on to understand it thoroughly, I have the feeling that I'm a lot smarter than before the video
🎯 Key points for quick navigation:
00:00:00 *Long-range IoT communication*
00:00:27 *Unique Lora modulation*
00:00:42 *Demodulating below noise*
00:01:12 *Chirp waveform basis*
00:04:12 *Up and down chirps*
00:05:10 *Frequency shift chirp*
00:06:18 *Symbol frequency continuity*
00:09:06 *Correlation similarity check*
00:11:00 *Frame synchronization issue*
00:13:07 *Efficient mathematical trick*
00:15:10 *Multiplication with downchirp*
00:17:08 *Detecting hidden signals*
00:18:20 *Excellent low SNR performance*
00:21:30 *MATLAB symbol error rate*
00:25:50 *Flexibility in spreading factor*
00:27:36 *Efficient chirp spectrum usage*
Made with HARPA AI
Thanks for the video and very clear explanation.
As a graduated in electronic engineering at the Padua university ( the same of Lorenzo Evangelista) I studied spread spectrum in the nineties but at the time I didn't catched the concept: too much theory and few concrete examples. At the time spread spectrum modulation was probably used only by military and hardware was not able to support the computation needed.
After this video I want to go deeper on how Lora works, I think I will take the mathlab simulation you have developed to play a bit by myself.
This video is simply unbelievable, very clever explanation!
Thanks!
This video is simply incredible. Thank you _so_ much for explaining this. Help me tons!
Wonderful video. Amazing. I'm working with LoRA modeling on my thesis. Great job and great explanation.
Wow beautiful! From a new modulation concept with a complex maths expressions to a smart way of computational representation, that’s incredible! Cannot imagine how people invented this smart are!
Thanks! Yes, it is a smart idea with a lot of applications.
For as little as I do know about wireless, and even wired signal communications, this honestly feels like it fills a lot of gaps in my brain
Since TH-cam has trouble with comments on Shorts, if there are any here that are unrelated, @ me so I can just delete them
Perfect video. It's like a missed Digital Communications lecture that I finally found. Thank you.
thank you so much, kind person! Without you it would have taken ages for to learn all of that
This video really explains not only LoRa protocol. But Modulation/Demodulation process in general. Nice!
This is a really good video you did explaining LoRa "mathematics', i.e. the magic of decoding a symbol where signal is less than noise i.e. SNR negative 8-) and the Matlab code is really useful. Thank you!
Well done. It would be interesting to add information about the bandwidth of the signal vs SF. This relates directly to the received noise and hence the S/N ratio. This will perhaps also shed a light on your question how far one can go by increasing the SF.
Wow - great explanation - usually there are 3 features but youre only allowed 2 of them - here you can choose 3 simultanously :) Low Bitrate, Low Power and Long Range :) - great idea :)))
Well technically the desirable traits are High Bitrate, Low Power and Long Range. Power and bitrate are low to begin with. Each time you increment the spreading factor, symbol duration has to double, but so does the number of bits per symbol. I think the trade-off there is in the processing power needed by the larger FFT in the receiver.
at 4:09 you put up both down chirps. Thanks for the lecture
There is an error starting at about 13:40 about complex conjugate, and goes on further at 16 etc. The actual demodulation chirp is of the same slope as the modulated signal. With multiplication you get sum and difference of the frequencies, and that does the dechirping.
Great video. I love learning the theory behind stuff like LoRa. Keep it up.
Great Vid! Although I mostly forgot university maths, I got to understand the principle of spreading factor and symbols on LORA.
Life, the Universe and Everything.
Excellent Teaching.
Great explanation. Here is the code if you want to play with it.
clear all
SF = 7; %Spreading Factor
BW = 1000;% Bandwidth
Fs = 1000;%Sampling Frequency
s = 127; %send symbol '10'
SNR = -10;%Signal to Noise Ratio
%Generate a data symbol
num_samples =(2^SF)*Fs/BW;
k = s; %add s to k to start (defines the data symbol)
lora_symbol = zeros(1,num_samples);
for n=1:num_samples
if k>= (2^SF)
k = k-2^SF;
end
k = k+1;
lora_symbol(n) = (1/(sqrt(2^SF)))*exp(1i*2*pi*(k)*(k/(2^SF*2)));
end
loop = 100;
ind2 = zeros(1,loop);
for j=1:loop
%Add noise
lora_symbol_noisy = awgn(lora_symbol,SNR,'measured');
%Transmit
%Receiver below
% Generate the Base Down Chirp
base_down_chirp = zeros(1,num_samples);
k=0;
for n=1:num_samples
if k>= (2^SF)
k = k-2^SF;
end
k = k + 1;
base_down_chirp(n) = (1/(sqrt(2^SF)))*(exp(-1i*2*pi*(k)*(k/(2^SF*2))));
end
dechirped = lora_symbol_noisy.*(base_down_chirp);
corrs = (abs(fft(dechirped)).^2);
figure(1); plot(corrs)
[~, ind] = max(corrs);
ind2(j) = ind;
pause(0.01)
end
figure(2); histogram(ind2,2^SF)
symbol_error_rate = sum(ind2~=s+1)/j
figure(3); spectrogram(lora_symbol)
Great tutorial! TH-cam at it's finest. Thank you.
Thanks for the video-i’m an Amateur radio operator with an interest in digital modes and LORA. I’m not sophisticated enough to follow along with the calculations in the video, but I understood the scene behind interpreting the symbols based on your description.
Glad it was helpful!
The clearest explanation in the history of explanations.
Very well presented! In thinking about the limits to the number of symbols, as the symbol duration increases distortions in propagation will modulate the baseband coordinates and increase the error rate. This is not ‘noise’ and will not show up in simulation. A noise driven delay modulation term would cover this.
What a great video and details explanation!
That helps me a lot with my project in LoRa IoT!
Thank you very much!
Really good explanation! Again this shows the power of FFT. OFDM uses a similar mathimatical trick with the FFT btw.
Years ago with a friend i did a equivalent experiment using GNU-Radio.
Not related to LoRa but the target was using width bandwidth spreadspectrum to get a signal over a long distance 100 - 200 km (60-100Mi)
I also added a noise generator to see what happened....
it's long ago, but you retriggered my interest.
Man, how have I not come across your channel before and how are your subscriber numbers not 10x?! Instant subscribe, super clear explanation thank you!!
Excellent explanation. Excellent content. Excellent topic. Keep up the good work.
This is a super valuable video! Simple and to the point. Thanks!
Super. Best explanation possible using difficult math.
Truly wonderful and comprehensive explanation. Thanks a lot!
Minus 20 dB means that the noise magnitude is 10 times greater than the signal magnitude when we talk about amplitudes, but 100 times greater when talking about power.
@ 7:44 Does the emitted signal amplitude have to present a discontinuity or can it be phase-continuous ?
Well, done! I was having a discussion in a math class where I introduced "i" and Complex Numbers to my 9 & 10.5 year old grandsons! (Yes, great joy in doing that!).
I was immediately asked words to the effect of, "Well, that's all nice and consistent, and even beautiful if you wish, but it is all based on something that doesn't exist - the square root of negative one. How how can that have any practical value?" My answer then was (based on old analog oscillators I had studied early in EE in college) that when the complex roots of a quadratic equation have an imaginary component, the oscillator is unstable.) Neither a practical nor a very fascinating example for a 10-year old. But this!
You've given me the most practical use of complex numbers - even more than the FFT itself - to be the basis of communication with a signal well below the noise level.
As a long time amateur radio operator, liking CW (Morse code), we really appreciate digging a usable signal out of the noise. It can save lives. Some ham communications (lower frequency bands) bounce up and down off the ionosphere to make global communication with just milliwatts. Just subscribed. Will properly thank soon!
Overall great video. Good job extracting the bottom line information from the sinusoidal equations. Small correction needed: 20 db implies a magnitude of 100, not 10. Meaning the at -20db, the Noise is 100x the Signal magnitude, further driving the point of just how effective the signaling scheme is at handling noise, especially when you show the -10dB signal... just imagine 10x that.
I do wish that you explained the Y axis of the Err Rate vs SNR a little bit, because the way its graphed in the video (right to left) almost implies that the higher value on the Y axis is good, but for anyone viewing, having an error rate of 1 is of course unusable. Maybe a horizontal line on the graph that shows an acceptable error rate wouldve helped.
Oh, and thank you VERY much for providing a Matlab example
Thanks
Many thanks for your support.
Signed up! Love so deep math analysis.
what are the situations where higher spreading factor is better and what are the situations where lower spreading factor is better?
what if instead of one sweep of frequency you have a "chord" of a few frequencies; If the spread between the chord was constant/known by both parties could that be used to further reduce the SER/dB by trying to pick out which one is the signal (i.e. its more improbable that subsequent signals would share that pattern)... Only thing I could think of (non expert) could be that harmonics might produce similar correlated patterns, but if you had some other sort of shared pseudo-noise to pick the subsequent chord spacings ...
or would having multiple signals being sent not be using the same SER/dB calculation?
Well produced! I'll investigate more with MatLab; very inspiring!
Everything about Lora is counterintuitive. Increasing the spreading factor which means increasing the possible symbols IMPROVES performance? Incredible how the maths proves the fact. Does make you think about what more advanced tech the military has hidden away
As noted in other comments, the data rate falls in relation to improvement in noise performance
Let me see, as stated in some comments, if the SF increases by 1, the symbol length (and window) doubles. That effectively lowers the bitrate, which makes total sense.
Then, why the chirp at all? You could do exactly the same with nFSK, just have more possible values per symbol, over a longer time with a lower bitrate.
For this to work so well, the chirp has to provide some important benefit. Perhaps less reliance in the oscillator stability?
I'd love to see a comparison between LoRa and an equivalent nFSK in Matlab.
BTW awesome video!
I guess the nFSK system would fail much sooner due to frequency selective multipath or constant carrier interference. That interference won't match the chirp rate. The difference wouldn't show in a simulation using AGWN like in this video. Just a guess, this video is the only real research I've done into LoRa.
@realsolarcars I guess, but you could address those problems in nFSK in an upper level of spreading and FEC, no one said the FSK should be simple and straight, after all LoRa isn't. I think what I try to say is that there is no real need for the continuous shifting in frequency, you could instead do discrete jumping between the n subcarriers. The reason could very well be making it patentable. Anyway I am just guessing. Regards!
The benefit is each symbol is spread across the entire bandwidth, so no symbol can be lost in a multipath null, unlike what could happen with nFSK. When you DONT use forward error correction this has big advantage!
Although I wasn't able to follow most of the parts related to the mathematical bases, but I got the concept behind and I've learned something new and interesting. I am sure I will never use it... but thanks :)
Thanks for the clear explanation! I do wonder what happens if there are 2 LoRa transmitters in an area though, how would the receiver distinguish between them?
Hi, would you please let me know how can I plot LoRa spreading Factor for RSSI and Distance?
I have only a high-school education. a total of 13 years of formal education, and no math beyond a semester of intro to algebra, but my fascination with RF led me to do a bit of research, and I ended up building a LowFER antenna and transmitter (175 kHz) transmitting BPSK ASCII using a computer program called Coherent, and with my transmitting beacon sending a short, repetitive text message, using crystal ovens at the beacon and in a homebrew receiver in my car, and averaging out the noise I was able to receive my beacon's text message, ( except for a couple of minutes in De Moines, Iowa, every foot of the way as I drove over a distance of 800 miles. It would have worked further, but I had not included sufficient front-end gain for copying the signal at great distances. I realized this because instead of my CRT screen printing out random characters, as it would with my transmitter turned off, in a low noise location it stopped displaying anything at all. Not enough gain. So, based on my simple experiments there is no SNR that a good modulation technique is incapable of receiving a signal through if the effective bandwidth is narrow enough, (i.e. a synchronized message repeated enough times to average out the noise.) The only limitation is how long you're willing to wait for the data to appear correctly. BTW, I estimated the EIRP of my transmit antenna to be 7 mW, which is very good for a LowFER antenna and 1 W transmitter. A friend took a receiver with him on his vacations each summer and received the beacon all over the western USA, day and night. So if chirp modulation can reduce the amount of time necessary to receive a given symbol and act in a manner similar to what we were doing with crystal ovens, BPSK, and Coherent, I'd say they have a winner.
Quick correction at 18:23: SNR ratio of -20 db means that the noise is 100 times greater than signal.
Excellent explanation of a highly technical subject. I guess I'm going to have to experiment more with Lora, if I can find a worthy use. Thanks for investing the time to show this.
@1.40 The diagram seems to indicatr frequency shift keying not phase shift keying
LoRa is incredible in that it can work below the noise floor
Is there anything superior here compared to a classic MFSK, that can also be optionally spread with DSSS or something? All the low power perf just seems like a natural outcome of the super long correlation times, which would boost perf of any scheme. What am I missing?
Nothing! This is known as orthogonal modulation. The price you pay is low bot rate and wide bandwidth for performance a low SNR's.
Somehow, I just knew the clever math trick would involve fourier transforms. Invariably in signals, compression, or other similar domains, converting between time and frequency domains opens up all sorts of interesting options for improving the efficiency of the process.
Great video, very enlightening! LoRa is no longer magic to me. I'd love to see you cover CDMA, especially the way code-based modulations are combined with other methods to provide efficient band sharing and tolerance for multipath interference.
Truly amazing work . Thanks for your efforts. Inspiring ❤
Is this insensivity to nosie make it possible to hide in the same band with other traditonal transmission like DVB-T is possible teorethicaly in analog TV channel ?
Excellent ! Really helped me to grasp the intution about LoRa !
why did you multiply the received signal with the conjugate of the symbol instead of the symbol itself
That was a very nice description - thank you. As a retired signal processing engineer it's nice to hear a good explanation! You suggest that the performance might keep on increasing with spreading factor without limit - it would be interesting (necessary, even) to include the initial detecton and synchronisation process, in noise, in your simulation, and then perhaps the effects of multipath, fading and Doppler. The decoder could be quite sensitive to symbol timing variation thoughout the packet - how long would a packet be? Terrestrial DAB modulation is based on frequencies rather than chirps, but the receive process is not disimilar - do you have any idea of the relative performance?
I'm not familiar with the papers or the intended applications, but I would expect there to be further gains from hard or soft error detection/correction coding at the data level.
Very good points raised here 👍
It is traditional to modulate a signal with a carrier that is many times the frequency of the signal. If you were interested in doing the reverse and wanted to swap the carrier to be (for example 30MHz) and the signal to have a frequency of many times the carrier (for example 30GHz), how would you go about doing that and what modulation scheme would you propose?
Carrier would be lost (attenuated) when the distance is higher much more than signal having the base frequency? (I mean that the carrier would be lost much sooner with the distance increased than the base range)
@@vencdee That is the behaviour we would expect for a higher frequency signal but what if that higher frequency signal is modulated or embedded in a lower frequency carrier, wouldn't that allow the signal to cover much longer distances?
"Spreading factor is between 7 and 12 in Lora"
Fascinating, I'll be sure to let her know.
If I understand the modulation scheme correctly, then the spreading factor correlates with the symbol transmission time. This means that it falls entirely with the expected strategy for improving the probability of error, which is to either reduce the data rate (larger spreading factor) or to increase the transmission power. You could get even better error performance by (a priori) agreeing to only use a subset of the the symbols provided by a given spreading factor, since reducing the constellation size increases the distance between symbols and therefore reducing the probability of misinterpreting a symbol.
How does the receiver perform in the presence of two transmitters of equal received power? For other spread spectrum modulations, other transmitters would become noise. I don't think that would happen for this modulation scheme, it would be hard to separate them.
How the spreading factor is related to the bandwidth?
What an extremely well presented video on a very complex subject. What I was wondering is what kind of bit rate you expect from this modulation scheme. You could always add a Foreward Error Correction protocol (FEC) to the original signal to improve the SNR. We use that extensively on high speed optical transmission systems
Amazing video! If i'm not wrong LoRa technique was used in Express LRS open source system used for example in FPV drones. You can get amazing range even at super small TinyWhoop like Mobula 7 1S ELRS. There is super tiny ceramic antenna and this system rocks in terms of penetration even on small transmitter power.
So, a SF=17 means each symbol could be treated as a 16-bit value, plus a parity bit, enabling the receiver to actually detect when the wrong symbol was received.
How can a receiver distinguish between transmitters? Can LoRa be jammed?
This is the fourth time I've seen this video. It covers everything I knew about LoRa modulation. Only the MatLab code is very important to me for educational reasons.
Hello, I read the paper by Vangelista (3-4 pages). I think I understood most of it except the proof to the equation (7). He changes a sum on the indicie k to a sum of sums to the indicies h*2^SF +p. I simply don't get it...
sorry not the equation (7) but the the proof that the product is nil when i-q is even. On page 2
On the ultra short waves the bottleneck for the range is line of sight. Why there is no possibility to establish lora on lower bands where ranges me be huge?
Have we looked into radio SETI data potentially using this or a similar modulation?
Excellent presentation! Thank you!
you deserve more subs and viewers
Incredible explanation! Thanks!
Thank you for this excellent explanation !
Are you certain about your treatment of # of symbols at 5:30 etc?
Based on other documentation it would seem that spread factor has to do with how long each symbol takes to transmit, not the number of discreet frequencies steps that can be measured. Data rates go down with increasing spread factors, not up.
Spreading factor of 7 = 128 possible symbols (7 bits). Spreading factor = 8 = 256 possible symbols (8 bits). But the SF=8 symbol takes twice as long. So, increasing the spreading factor by 1 allows you to send 1 more bit per symbol but at half the previous symbol rate. The net effect is the datarate goes down with spreading factor even though there are a greater set of possible symbols transmitted within each chirp.
Amazing lecture indeed. Would you make more tutorials on LoRaWAN implementation, hacking, and defending?
Explanation is great. Subscribed
I would guess that the reduction in noise is related to the square root of the number of samples if the noise is uncorrelated. Just a basic signal averaging process after you account for the chirp?