Dear Poonam:

At the first, The modulation scheme in a chirp spread spectrum (CSS) communication system uses linear frequency-modulated chirps to represent message symbols. Due to its robustness against narrow-band interference, constant envelope and resistance against multi-path fading and Doppler effect, CSS modulation has been adopted in various low-power wide-area (i.e., long-range) wireless applications. For example, the IEEE 801.15.4a standard has provisions for CSS modulation along with the burst-position modulation scheme. More recently, LoRa technology has been introduced for Internet-of-Things (IoT) applications, which is also based on frequency-shift chirp modulation and more commonly referred to as LoRa modulation. Historically, linear chirps have been used in continuouswave frequency-modulated radars due to their good autocorrelation properties. In digital communications, CSS was first introduced in a simple form of binary modulation, in which two linear-frequency modulated chirps with opposite sweep directions, i.e., up chirp and down chirp, are used to represent an information bit. Such a scheme is also known as slope-shift keying. Although the up and down chirps are nearly orthogonal to each other, they are not completely orthogonal. As a consequence, the lack of complete orthogonality affects the bit-error-rate (BER) performance of slope-shift keying. For non-binary transmission.

You can benefit from this valuable article about your topic:

"Nonlinear Quasi-Synchronous Multi User Chirp Spread Spectrum Signaling

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Nozhan Hosseini, Member, IEEE, David W. Matolak, Senior Member, IEEE"

@https://nhz.us/Content/QSChirpJournal_5oct2020csubmitted_tcom.docx.html

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Also this one

"How Orthogonal is LoRa Modulation"

@https://www.researchgate.net/publication/360107024_How_Orthogonal_is_LoRa_Modulation

I hope it will be helpful....

Best wishes.....

Hassan Nasser Thanks for sharing the information. I will go through the paper suggested by you. However, I didn't get mathematical proof for the quasi-orthogonality of the up-chirps and down-chirps. In the simulation, while demodulating the signal (overlap of up-chirp and down-chirp symbols), the simulator is always able to demodulate the up-chirp symbol when multiplying the signal with conjugate up-chirp and vice versa for down-chirp. I am unable to understand the logic behind it. The contradiction between the simulation results and theoretical results about the quasi orthogonality of up chirp and down chirp.

Read this article to know more about orthogonal combinations.

Hassan Nasser Thank you for recommending our article . I hope you find it useful Poonam Maurya

Simply put, they are, but to a certain degree. When you have concurrent chirps of various gradients, including negative gradients, your noise floor increases during demodulation. This results in reduced SNR.

Let me take a common scenario. An SF12 chirp is orthogonal to an SF7. But this does not mean we can pack as many as concurrent SF-7 transmissions and expect the SF-12 frame to be not impacted. During the demod process, the noise floor during the the SF-12 chirp will increase when you have an SF-7 (or any other orthogonal chirps) present.

Let me please refer you to https://wands.sg/publications/full_list/papers/TOSN_22_1.pdf for further information.

Amalinda Jg Thanks for information

Linear Chirp or Exponential Chirp. That is the first thing to know. After that the question of being orthogonal will come :)

Thanks. As far as I know, LoRa uses linear chirp.

In LoRa modulation, up-chirps and down-chirps are not perfectly orthogonal to each other, but they are approximately orthogonal.

LoRa modulation uses a technique called chirp spread spectrum (CSS), in which the carrier frequency of the signal varies linearly over time. In up-chirp modulation, the carrier frequency increases over time, while in down-chirp modulation, the carrier frequency decreases over time.

When up-chirp and down-chirp signals are transmitted simultaneously, they will overlap in time and frequency. While they are not perfectly orthogonal, the spectral overlap is minimized by the LoRa modulation scheme, which uses a spreading factor to increase the duration of each chirp and reduce the bandwidth of the signal. The longer the chirp duration, the less overlap there is between the up-chirp and down-chirp signals.

Overall, the up-chirp and down-chirp signals in LoRa modulation are designed to be as orthogonal as possible, but there will still be some level of correlation between them due to their overlapping spectral content.

For more on LoRa, you can read this recent survey here [1] and a dual mode CSS which preserves orthogonality here [2]

[1] Azim, Ali Waqar, et al. "A Survey on Chirp Spread Spectrum-based Waveform Design for IoT." arXiv preprint arXiv:2208.10274 (2022).

[2] Azim, Ali Waqar, et al. "Dual-Mode Chirp Spread Spectrum Modulation." IEEE Wireless Communications Letters 11.9 (2022): 1995-1999.

Ahmad Bazzi Thanks a lot for the information.