Standard LoRa demodulator initiates demodulation by looking for a preamble sequence in the received buffer. LoRa packets have typically 8 base upchirps at the start followed by 2 SYNC words with distinct starting frequencies and then followed by 2.25 downchirps. Repeated base upchirps along with sync word and downchirps serve as a LoRa preamble. Std. LoRa maintains a window of length equal to a symbol length and jumps it across the received buffer such that there is no overlap of I/Q samples in between two jumps of the window. At each jump, it dechirps the buffer with a downchirp and takes FFT. If a LoRa symbol were present in the buffer, it would result in a peak at a distinct frequency in the resulting FFT. While jumping the window across the received buffer, std. LoRa looks for peaks appearing at same frequency across 8 consecutive dechirping windows. If such consecutive windows having symbols with same frequency are detected, it signals the presence of 8 base upchirps and therefore presence of a packet. The presence of the packet is further confirmed by looking for 2 SYNC words and 2.25 Downchirps. Once a preamble is detected, std. LoRa then aligns itself to data symbol boundaries and then jumps its demodulation window over each data symbol. At each jump, it performs dechirping with a downchirp followed by an FFT which yields a peak. The index of the peak therefore tells the starting frequency of the original (pre-dechirping) LoRa symbol and marks the completion of std. LoRa demodulation.
FTrack is one such demodulator which tries to separate out the collided packets and extract the frequency contents of each symbol.
FTrack relies on Short Time Fourier Transform (STFT) to obtain time and frequency features. Applying STFT to the LoRa symbols results in frequency tracks that increases linearly with time. An appropriate STFT window size that offers good frequency resolution to identify the frequency and good time resolution to follow the progression of a chirp is challenging to determine.
FTrack proposes to apply STFT on the dechirped LoRa symbol to leverage the spread spectrum gain as well as to remove the linear change in frequency with time. Dechirping the received buffer results in a sinusoid whose frequency remains constant throughout the symbol duration. This allows FTrack to choose a window size of a symbol length that yields a good frequency resolution (of upto 1 bin) if perfectly aligned with the symbol boundaries. Dechirping allows STFT to have the least possible frequency variation with time (single frequency over a symbol duration) and therefore yields the best possible frequency resolution. It yields a constant frequency track over a symbol duration, rendering it simpler to track the frequency of a packet of interest.
FTrack, thus, employs dechirping followed by STFT to extract the longest frequency tracks to detect preamble as well as data symbols. FTrack extracts symbol edges from preambles and uses this time information to detect the symbol boundaries of payload. FTrack builds on the observation that all the interfering packets are misaligned in time and hence their symbol boundaries are misaligned in time. FTrack detects the preambles of all colliding packets and leverages the time offset between colliding packets to differentiate transmitters. The receiver aligns itself with the boundaries of a packet of interest : once aligned, it observes the frequency tracks of current packet as well as that of the interfering tracks. The frequency track of the packet of interest will be continuous in the given window whereas all the interfering tracks will change abruptly. Therefore, after detecting all the LoRa packets in a received buffer, FTrack iteratively demodulates each packet. While demodulating a specific packet, FTrack cancels out interfering symbols by tracking the frequency continuity. FTrack’s performance suffers in low-SNR conditions. At SNRs below 5 dB, energy of the frequency tracks corresponding to preamble and data symbols are not high enough and hence are buried in the noise floor and is not decoded.
CoLoRa, another collision resolution technique, proposes a novel algorithm to translate time offsets to frequency features, using that to resolve packet collisions at low-SNR regimes. CoLoRa starts with a misaligned window size of one symbol length. It determines the presence of interference based on the number of peaks appearing in the FFT obtained after dechirping; since multiple peaks imply packet collisions. Once collisions are confirmed, CoLoRa proposes an interleaved window selection strategy. It chooses a misaligned window such that no chirp is covered fully by the window i.e., each chirp is segmented and thus falls into two consecutive windows such that the normalized FFT peak is bounded within [1/3, 3] in each window. It then jumps the window over received buffer and performs dechirping followed by FFT at each point. The resulting spectrum contains peaks whose height is proportional to the segment of chirp appearing in the current window. CoLoRa observes that when a chirp is split into 2 windows, the frequency at which the peaks appear in the FFT remains the same across the 2 windows. However, the energy and hence the height of the FFT peak at the corresponding frequency in each window is proportional to the duration of the chirp segment within that window.
CoLoRa proposes Peak Ratio, which is defined as the ratio of peak heights of a chirp appearing in two consecutive windows; it captures time misalignment through frequency features. It proves that the peak ratio is identical for all chirps of the same packet since the in-window distribution of chirps is identical for all the symbols of the same packet. Additionally, peak ratios differ across packets since the in-window distribution of chirps is different due to misalignment of interfering packets. Since CoLoRa relies on accurate estimation of Peak ratio, it proposes an iterative peak recovery algorithm to estimate the heights of strong peaks first and cancel their contribution while estimating the low-SNR peaks. Since the chirps are segmented, wide side lobes appear around peaks that may bury low SNR peaks. CoLoRa uses k-means clustering (where k is the number of packets detected) to classify the packets of different clients. Peaks with identical peak ratios are clustered together, following the observation that the symbols of the same packet have the same peak ratio. Each cluster represents a unique packet, thus decoding multiple packets from the collided signal.
While FTrack and CoLoRa focus on decoding multi-packet collisions, their performance improvements over standard LoRa demodulator is noticeable at high SNR. NScale focuses on decoding packet collisions at SNRs as low as -10dB where the relative performance improvement of FTrack and CoLoRa degrades.
Similar to CoLoRa, NScale translates the timing offsets to frequency features and further amplifies the time offsets by non-stationary signal scaling. NScale’s strength lies in its ability to decode and resolve collisions of LoRa packets below -10 dB SNR. Instead of sliding the window as FTrack does, NScale jumps the window of size that promises maximum frequency resolution i.e. duration of a symbol. To retain sub-noise decodability, NScale relies on dechirping to accumulate energy at the single frequency. While jumping the window across the received buffer, NScale observes that, for a specific LoRa packet, all the symbols of interest will have same in-window distribution in consecutive windows whereas in-window distribution for interfering symbols will be different. Simply put, the location of symbol edges where one symbol transitions to next is same across all the windows of a given packet but across different packets, these symbol edges are different. This essentially stems from the fact that collisions are misaligned in time. Similar to CoLoRa, NScale translates symbol edge offsets to the peak heights.
NScale introduces a novel non-stationary scaled window as opposed to conventional rectangular window of FTrack and CoLoRa. Non-stationary scaling across the windows amplifies the timing misalignment of symbols of interfering packets. The linear amplitude scaled window scales the amplitude of peaks with respect to their in-window distribution and therefore amplifies the misalignment of different packets. This amplification helps estimate the time offsets for very low SNR packets. Consequently, different packets get a unique fingerprint in terms of peak heights while symbols of a specific packet share the same fingerprint. NScale detects the number of packets and their corresponding start and end indices using correlation and then performs k-means clustering to classify symbols based on their fingerprint.
Concurrent Interference Cancellation (CIC), similar to FTrack, leverages time and frequency domain analysis to decode multi-packet collisions. CIC introduces the concept of sub-windows, which are a portion of the demodulation window. It observes that, for a given packet of interest, symbols from the packet appear in all the sub-windows; symbols from interfering packets appear only in a subset of the sub-windows. Therefore, the intersection of FFT of all the sub-windows would result in the symbol of interest. CIC proposes a sub-window selection algorithm that maximizes interference cancellation.
CIC looks for the best sub-window which promises an acceptable time resolution while compromising the least on frequency resolution. It uses packet detection to determine the start of all the colliding packets in order to select the best set of sub-windows. Unlike standard LoRa, CIC uses downchirp correlation to detect the start of a packet. With prior knowledge of symbol duration, CIC determines symbol boundaries within each of the colliding packet. The sub-windows are chosen such that it contains the most of each interfering symbol, using CIC’s knowledge of the symbol boundaries of interfering packets. Spectral intersection of the FFT of the demodulating window and the optimum set of sub-windows selected results in a single FFT peak that corresponds to the symbol of interest. It iteratively demodulates the rest of the packets in the collided signal.
CIC also proposes fractional frequency offset to filter out interfering peaks that were not cancelled in the spectral intersection. Additionally, it uses power-filtering to estimate received power of each packet from its preamble and discards symbols which do not qualify a certain power threshold. Finally Spectral Edge Difference, filters interfering peaks further and chooses one peak to be the final demodulated peak.
In addition to the works presented above, other papers have focused on LoRa demodulator design. The modular design of our proposed framework renders it simple to integrate them. Pyramid is one such work which tries to resolve LoRa collisions by tracking the change in FFT peak heights corresponding to different interfering symbols. AlignTrack tracks and translates time offsets to frequency features, i.e. peak heights, similar to CoLoRa. AlignTrack chooses a window which completely overlaps the packet of interest instead of a misaligned window used by CoLoRa. AlignTrack’s complete overlap gives highest peaks in FFT and therefore, has least SNR loss. NeLoRa is another work which tries to push the limit of LoRa’s range by using deep-neural-network. Their results show that its ability to decode packets with SNR as low as -30dB.
Pyramid DOI: 10.1109/INFOCOM42981.2021.9488695
AlignTrack DOI: 10.1109/ICNP52444.2021.9651985
NeLoRa DOI: 10.1145/3485730.3485928