How LoRa Modulation really works - long range communication using chirps 

Which modulation scheme should I cover next? 🤔

This is possibly the best explanation of Lora modulation I’ve seen ever…

“You can always detect a sine wave in noise….if you are willing to “wait” long enough” - E.J. Swanson

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…

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.

It absolutely blew my mind how clearly you have explained the LoRa modulation despite the complex maths behind it.

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.

Dont know what amazed me more - the LoRa protocol or your explaination. Thanks for the video.

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.

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.

Perfect material for our LoRa APRS group!

thank you so much, kind person! Without you it would have taken ages for to learn all of that

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.

at 4:09 you put up both down chirps. Thanks for the lecture

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!!!

Great tutorial! RU-vid at it's finest. Thank you.

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.

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!!! 🙏🙏🙏

Truly wonderful and comprehensive explanation. Thanks a lot!

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.

Wonderful video. Amazing. I'm working with LoRA modeling on my thesis. Great job and great explanation.

What a great video and details explanation! That helps me a lot with my project in LoRa IoT! Thank you very much!

Truly amazing work . Thanks for your efforts. Inspiring ❤

This is a super valuable video! Simple and to the point. Thanks!

This video really explains not only LoRa protocol. But Modulation/Demodulation process in general. Nice!

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.

Life, the Universe and Everything. Excellent Teaching.

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.

Excellent ! Really helped me to grasp the intution about LoRa !

This video is simply unbelievable, very clever explanation!

Excellent explanation. Excellent content. Excellent topic. Keep up the good work.

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.

Incredible explanation! Thanks!

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!

Great video. I love learning the theory behind stuff like LoRa. Keep it up.

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.

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.

Really good explanation! Again this shows the power of FFT. OFDM uses a similar mathimatical trick with the FFT btw.

Signed up! Love so deep math analysis.

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!

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!!

impressive explaination, perfectly explained

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

Thank you for this excellent explanation !

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.

Perfect video. It's like a missed Digital Communications lecture that I finally found. Thank you.

Brilliant explanation. Thank you

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?

Great Vid! Although I mostly forgot university maths, I got to understand the principle of spreading factor and symbols on LORA.

Super explanation, many thanks!

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

Well produced! I'll investigate more with MatLab; very inspiring!

May I ask which tool or video method do you use to simulate the explanations, like 3.05, 4.07, 6.20 and similar ones ? Thanks, regards

Explanation is great. Subscribed

Fantastic explanation!

Thank you for this good explanation!

This protocol is being used in Ukraine by both sides now, due to its resistance to jamming, range, and lack of the need for constant back-and-forth handshakes. I couldn't understand how jamming wouldn't work, but this explains it

Thank you, that's really interesting

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

Amazing video. Thank you!

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)

Really good explanation

Awesome explanation, thanks!

@ 7:44 Does the emitted signal amplitude have to present a discontinuity or can it be phase-continuous ?

This video shows the mathematical basis for a trick used in the LoRa implementation to reduce the complexity and power requirements of LoRa receivers. How LoRa works is quite simple, it sends a fixed duration linear chirp between fixed low and high frequencies, for each symbol to be transmitted, which symbol is determined by when the abrupt transiton from the highest back to the lowest frequency of the chirp occurs. There is also an abrupt transition between symbol boundaries. en.wikipedia.org/wiki/LoRa#LoRa_PHY The core equation for the trick is a thick read if you're not an RF design engineer. At 6:40 into the video, it shows Equation 2 from the original paper: c(n*Ts+k*T) = 1/sqrt(2**SF)*e**(j*2*pi*((s(n*Ts)+k)mod(2**SF))*(k*T*B/(2**SF)) c(): The complex number result from the equation, to be evaluated at each moment in time n*Ts+k*T: The time in seconds from time 0, when the k'th sample of the n'th symbol is sent SF: The "Spreading Factor", which is the number of bits in each symbol. k: An integer that increments up from 0 to (2**SF)-1 for each sample within a symbol Ts: The time it takes to send each symbol, there are 2**SF samples in each symbol n: An integer that increments up (starting from 0) with each symbol to be transmitted s(n*Ts): The integer value of the n'th symbol to be transmitted, a value between 0 and (2**SF)-1 B: The bandwidth that the complete LoRa signal will occupy in Hz pi: 3.14159265... (Ratio of the circumference over the diameter of a circle) e: 2.71828... (Euler's constant) j: The square root of -1 (some sources use the letter i instead of j) This is the equation for a complex sine wave using Euler's formula e**(j*2*pi*f*t) = cos(j*2*pi*f*t) + j*sin(j*2*pi*f*t) Euler's formula converts what would be a trigonometric equation involving sines and cosines into an exponential in the complex plane that is much easier to manipulate mathematically. We are interested the real part cos(2*pi*f*t), equal to sin(2*pi*f*t) shifted 90 degrees. In sin(2*pi*f*t), the sin() operator expects a value in radians, not in degrees. There are 2*pi radians in a full cycle of 360 degrees, so 2*pi*f is the frequency expressed in radians per second. Multiplying that by the time t in seconds we get the number of radians that have passed since time zero, and can evaluate the sin() function to determine the value (perhaps in Volts) of the sine wave at that moment. As t increases to infinity, the result of sin(2*pi*f*t) repeatedly cycles through values between +1 and -1. The complex conjugate of Equation 2 is: e**(-j*2*pi*f*t) = cos(j*2*pi*f*t) - j*sin(j*2*pi*f*t) At 15:00 minutes into the video he multiplies Equation 2 by its complex conjugate while performing the convolution, the imaginary parts involving j cancel out leaving only a real result. The mathematical trick is that the complex conjugate can be broken down into two terms, we need only multiply each incoming symbol by a base down-chirp (the complex conjugate of a base up-chirp), and this will result in a different constant tone for each possible symbol. The receiver must first be synchronized to the symbol boundaries by inspecting the preamble sequence. But forget complex conjugates, let's evaluate the real part of Equation 2: v(n*Ts + k*T) = 1/sqrt(2**SF) * sin(2*pi*((s(n*Ts)+k) mod(2**SF))*(k*T*B/(2**SF))) The v(n*Ts + k*T) means that the formula gives a value (perhaps in Volts) for the k'th sample of the n'th symbol to be transmitted. The 1/sqrt(2**SF) is a constant for the amplitude in Volts of the sine wave, which scales with the power of the transmitter. This is arbitrary, and we can ignore this factor. The remainder of the equation is: sin(2*pi*((s(n*Ts)+k) mod(2**SF))*(k*T*B/(2**SF))) and we expect this to be of the form: sin(2*pi*f*t). Since k is the number of steps and T is the seconds per step, then (k*T) is the elapsed time since the start of the symbol, and thus equal to "t". With that resolved, the remaining terms must be the frequency f in Hz: f = ((s(n*Ts)+k) mod(2**SF))*(B/(2**SF)) Lets make this all a bit more concrete by specifying that SF=7, so the symbols transmitted have 7 bits of information, and thus each symbol can take any of the 128 integer values between 0 and 127. We will further assume that the transmitter is continuously sending the same symbol of s(n*Ts) = 0. The text above Equation 2 in the paper says LoRa (arbitrarily?) sets the bandwidth B equal to the inverse of the sample time T, or B = 1/T. Let's assume a LoRa bandwidth of 10400 Hz, (one of the standard choices) so the sample time is 1/10400 = 0.000096 seconds When all the above substitutions are made, the equation for f in Hz simplifies to: f = ((0+k) mod(128))*(10400Hz/(128)) With the symbol value held at 0, the mod(128) no longer has any effect since it never sees an argument greater than 127: f = k * 10400Hz/128 And now it is clear that the frequency varies from 0 to 10400*127/128 = 10318.75 Hz with a step size of 10400/128 = 81.25 Hz as k increments from 0 to 127 during each symbol. This is a baseband signal. The signal must later be translated up to the target center frequency for transmission, in the US this would typically be in the 915 MHz ISM band. It seems likely that the discrete frequencies given by equation 2 would be the frequency at the center of each sample period, and that the frequency is varied continuously. Given that, the bandwidth will indeed be 10400 Hz. Each symbol in our example with SF=7 takes 128/10400 seconds to transmit, giving us a data rate of 7/(128/10400) = 568.75 bits/second. There will be overhead added to that for the preamble sequence used for synchronization, a header to identify the transmitter, and the proprietary LoRa Forward Error Correction. As others have noted in the comments, if we increase SF from 7 to 8 bits per symbol then the time it takes to send one symbol goes up from 128 sample periods to 256. Given the much longer time per bit spent transmitting, it is not surprising that noise immunity improves. Receiving signals below the noise floor has been done by radio amateurs for at least 50 years. Other services likely had similar schemes long before that. www.sigidwiki.com/images/a/a5/Coherent_CW_arrl.pdf

The clearest explanation in the history of explanations.

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!

LoRa is incredible in that it can work below the noise floor

Great Video! Thanks so much!

amazing video, thank you sir

Fantastic analysis and explanation of the signal. So does this breakdown such that many of the newer SDR equipment could utilize this as a new digital mode as well? This could be a new mode to explore for ham radio.

If you can bury signal in the noise can you scan for unexpected/secret trasmissions or does the attenuation of a signal mean its still obvious near the transmitter,

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

Thank you

Absolutely nailed it!!!!!!!

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.

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

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.

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!

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 :)

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.

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 :)))

Hi, would you please let me know how can I plot LoRa spreading Factor for RSSI and Distance?

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.

Armsman Pham Trinli at the On-Off star would be very happy with this encoding scheme for his nanopower localizers...

wow. I'm totally not a EE or hardware guy but I find this so interesting. I'm surprising that a higher SF results in lower error rare since it seems to me that a higher SF actually means more data is transmitted (unless I'm misunderstanding or somehow the length of transmission is longer for compensate) but with lower error. very cool video!!!

Great video, why the code in the exponential part divided by 2^SF*2? in the paper, it is devided by 2^SF, the same in dechirp part? Thanks a lot.^_^

Quick correction at 18:23: SNR ratio of -20 db means that the noise is 100 times greater than signal.

Did this come out of SETI research? Or could it be applied to SETI data like the SETI at Home recordings from the Arecebo dish back in the late 90s?

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.

you just earned a subscriber.

you deserve more subs and viewers

fascinating,thanks

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.

Amazing lecture indeed. Would you make more tutorials on LoRaWAN implementation, hacking, and defending?

Incredible!

Good explanation. Keep it up

"Spreading factor is between 7 and 12 in Lora" Fascinating, I'll be sure to let her know.