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LoRaPHY.m
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LoRaPHY.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \file LoRaPHY.m
%
% \brief Physical Layer LoRa Modulator/Demodulator/Encoder/Decoder
%
% \version 0.2.1
%
% \repo https://github.com/jkadbear/LoRaPHY
%
% \copyright MIT License, 2020-2022
%
% \author jkadbear
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
classdef LoRaPHY < handle & matlab.mixin.Copyable
%LORAPHY LoRa physical layer implementation
%%% Example %%%
% rf_freq = 470e6;
% sf = 12;
% bw = 125e3;
% fs = 1e6;
% phy = LoRaPHY(rf_freq, sf, bw, fs);
% phy.has_header = 1; % explicit header mode
% symbols = [2541,1153,673,2397,1189,3509,41,3089,3237,3917,2729,2765,1417,2833,1389,801,3197,345,961,745,3101,297,1893,469]';
% [data, checksum] = phy.decode(symbols);
% disp(data); % CODE: 09 90 40 01 02 03 04 05 06 07 08 09 BA 2E
% disp(checksum);
properties
rf_freq % carrier frequency
sf % spreading factor (7,8,9,10,11,12)
bw % bandwidth (125kHz 250kHz 500kHz)
fs % sampling frequency
cr % code rate: (1:4/5 2:4/6 3:4/7 4:4/8)
payload_len % payload length
has_header % explicit header: 1, implicit header: 0
crc % crc = 1 if CRC Check is enabled else 0
ldr % ldr = 1 if Low Data Rate Optimization is enabled else 0
whitening_seq % whitening sequence
crc_generator % CRC generator with polynomial x^16+x^12+x^5+1
header_checksum_matrix % we use a 12 x 5 matrix to calculate header checksum
preamble_len % preamble length
sig % input baseband signal
downchirp % ideal chirp with decreasing frequency from B/2 to -B/2
upchirp % ideal chirp with increasing frequency from -B/2 to B/2
sample_num % number of sample points per symbol
bin_num % number of bins after FFT (with zero padding)
zero_padding_ratio % FFT zero padding ratio
fft_len % FFT size
preamble_bin % reference bin in current decoding window, used to eliminate CFO
cfo % carrier frequency offset
fast_mode % set `true` for fast execution (ignore low-pass filter)
is_debug % set `true` for debug information
hamming_decoding_en % enable hamming decoding
end
methods
function self = LoRaPHY(rf_freq, sf, bw, fs)
%LORAPHY Construct an instance of this class
% Hexadecimal or binary values representation require at least
% MATLAB R2019b
% https://www.mathworks.com/help/matlab/matlab_prog/specify-hexadecimal-and-binary-numbers.html
if verLessThan('matlab', '9.7')
error('Error. Newer version of MATLAB is required ( >=R2019b ).');
end
self.rf_freq = rf_freq;
self.sf = sf;
self.bw = bw;
self.fs = fs;
self.has_header = 1;
self.crc = 1;
self.fast_mode = false;
self.is_debug = false;
self.hamming_decoding_en = true;
self.zero_padding_ratio = 10;
self.cfo = 0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The whitening sequence is generated by an LFSR
% x^8+x^6+x^5+x^4+1
% Use the code below to generate such sequence
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% reg = 0xFF;
% for i = 1:255
% fprintf("0x%x, ", reg);
% reg = bitxor(bitshift(reg,1), bitxor(bitget(reg,8), bitxor(bitget(reg,6), bitxor(bitget(reg,5), bitget(reg,4)))));
% end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
self.whitening_seq = uint8([0xff, 0xfe, 0xfc, 0xf8, 0xf0, 0xe1, 0xc2, 0x85, 0xb, 0x17, 0x2f, 0x5e, 0xbc, 0x78, 0xf1, 0xe3, 0xc6, 0x8d, 0x1a, 0x34, 0x68, 0xd0, 0xa0, 0x40, 0x80, 0x1, 0x2, 0x4, 0x8, 0x11, 0x23, 0x47, 0x8e, 0x1c, 0x38, 0x71, 0xe2, 0xc4, 0x89, 0x12, 0x25, 0x4b, 0x97, 0x2e, 0x5c, 0xb8, 0x70, 0xe0, 0xc0, 0x81, 0x3, 0x6, 0xc, 0x19, 0x32, 0x64, 0xc9, 0x92, 0x24, 0x49, 0x93, 0x26, 0x4d, 0x9b, 0x37, 0x6e, 0xdc, 0xb9, 0x72, 0xe4, 0xc8, 0x90, 0x20, 0x41, 0x82, 0x5, 0xa, 0x15, 0x2b, 0x56, 0xad, 0x5b, 0xb6, 0x6d, 0xda, 0xb5, 0x6b, 0xd6, 0xac, 0x59, 0xb2, 0x65, 0xcb, 0x96, 0x2c, 0x58, 0xb0, 0x61, 0xc3, 0x87, 0xf, 0x1f, 0x3e, 0x7d, 0xfb, 0xf6, 0xed, 0xdb, 0xb7, 0x6f, 0xde, 0xbd, 0x7a, 0xf5, 0xeb, 0xd7, 0xae, 0x5d, 0xba, 0x74, 0xe8, 0xd1, 0xa2, 0x44, 0x88, 0x10, 0x21, 0x43, 0x86, 0xd, 0x1b, 0x36, 0x6c, 0xd8, 0xb1, 0x63, 0xc7, 0x8f, 0x1e, 0x3c, 0x79, 0xf3, 0xe7, 0xce, 0x9c, 0x39, 0x73, 0xe6, 0xcc, 0x98, 0x31, 0x62, 0xc5, 0x8b, 0x16, 0x2d, 0x5a, 0xb4, 0x69, 0xd2, 0xa4, 0x48, 0x91, 0x22, 0x45, 0x8a, 0x14, 0x29, 0x52, 0xa5, 0x4a, 0x95, 0x2a, 0x54, 0xa9, 0x53, 0xa7, 0x4e, 0x9d, 0x3b, 0x77, 0xee, 0xdd, 0xbb, 0x76, 0xec, 0xd9, 0xb3, 0x67, 0xcf, 0x9e, 0x3d, 0x7b, 0xf7, 0xef, 0xdf, 0xbf, 0x7e, 0xfd, 0xfa, 0xf4, 0xe9, 0xd3, 0xa6, 0x4c, 0x99, 0x33, 0x66, 0xcd, 0x9a, 0x35, 0x6a, 0xd4, 0xa8, 0x51, 0xa3, 0x46, 0x8c, 0x18, 0x30, 0x60, 0xc1, 0x83, 0x7, 0xe, 0x1d, 0x3a, 0x75, 0xea, 0xd5, 0xaa, 0x55, 0xab, 0x57, 0xaf, 0x5f, 0xbe, 0x7c, 0xf9, 0xf2, 0xe5, 0xca, 0x94, 0x28, 0x50, 0xa1, 0x42, 0x84, 0x9, 0x13, 0x27, 0x4f, 0x9f, 0x3f, 0x7f]');
self.header_checksum_matrix = gf([
1 1 1 1 0 0 0 0 0 0 0 0
1 0 0 0 1 1 1 0 0 0 0 1
0 1 0 0 1 0 0 1 1 0 1 0
0 0 1 0 0 1 0 1 0 1 1 1
0 0 0 1 0 0 1 0 1 1 1 1
]);
self.crc_generator = comm.CRCGenerator('Polynomial','X^16 + X^12 + X^5 + 1');
self.preamble_len = 6;
self.init();
end
function init(self)
% init Initialize some parameters
self.bin_num = 2^self.sf*self.zero_padding_ratio;
self.sample_num = 2*2^self.sf;
self.fft_len = self.sample_num*self.zero_padding_ratio;
self.downchirp = LoRaPHY.chirp(false, self.sf, self.bw, 2*self.bw, 0, self.cfo, 0);
self.upchirp = LoRaPHY.chirp(true, self.sf, self.bw, 2*self.bw, 0, self.cfo, 0);
% Low Data Rate Optimization (LDRO) mode in LoRa
% If the chirp peird is larger than 16ms, the least significant
% two bits are considered unreliable and are neglected.
if 2^(self.sf)/self.bw > 16e-3
self.ldr = 1;
else
self.ldr = 0;
end
end
function pk = dechirp(self, x, is_up)
% dechirp Apply dechirping on the symbol starts from index x
%
% input:
% x: Start index of a symbol
% is_up: `true` if applying up-chirp dechirping
% `false` if applying down-chirp dechirping
% output:
% pk: Peak in FFT results of dechirping
% pk = (height, index)
if nargin == 3 && ~is_up
c = self.upchirp;
else
c = self.downchirp;
end
ft = fft(self.sig(x:x+self.sample_num-1).*c, self.fft_len);
ft_ = abs(ft(1:self.bin_num)) + abs(ft(self.fft_len-self.bin_num+1:self.fft_len));
pk = LoRaPHY.topn([ft_ (1:self.bin_num).'], 1);
end
function x = detect(self, start_idx)
% detect Detect preamble
%
% input:
% start_idx: Start index for detection
% output:
% x: Before index x, a preamble is detected.
% x = -1 if no preamble detected
ii = start_idx;
pk_bin_list = []; % preamble peak bin list
while ii < length(self.sig)-self.sample_num*self.preamble_len
% search preamble_len-1 basic upchirps
if length(pk_bin_list) == self.preamble_len - 1
% preamble detected
% coarse alignment: first shift the up peak to position 0
% current sampling frequency = 2 * bandwidth
x = ii - round((pk_bin_list(end)-1)/self.zero_padding_ratio*2);
return;
end
pk0 = self.dechirp(ii);
if ~isempty(pk_bin_list)
bin_diff = mod(pk_bin_list(end)-pk0(2), self.bin_num);
if bin_diff > self.bin_num/2
bin_diff = self.bin_num - bin_diff;
end
if bin_diff <= self.zero_padding_ratio
pk_bin_list = [pk_bin_list; pk0(2)];
else
pk_bin_list = pk0(2);
end
else
pk_bin_list = pk0(2);
end
ii = ii + self.sample_num;
end
x = -1;
end
function [symbols_m, cfo_m, netid_m] = demodulate(self, sig)
% demodulate LoRa packet demodulation
%
% input:
% sig: Baseband signal in complex
% output:
% symbols_m: A matrix containing the demodulated results.
% Each column vector represents the symbols of
% a successfully demodulated packet.
% cfo_m: A vector containing the carrier frequency offset
% results. Each element represents the CFO of the
% packet in symbols_m.
self.cfo = 0;
self.init();
if ~self.fast_mode
sig = lowpass(sig, self.bw/2, self.fs);
end
% resample signal with 2*bandwidth
self.sig = resample(sig, 2*self.bw, self.fs);
symbols_m = [];
cfo_m = [];
netid_m = [];
x = 1;
while x < length(self.sig)
x = self.detect(x);
if x < 0
break;
end
% align symbols with SFD
x = self.sync(x);
% NetID
pk_netid1 = self.dechirp(round(x-4.25*self.sample_num));
pk_netid2 = self.dechirp(round(x-3.25*self.sample_num));
netid_m = [netid_m;
[mod((pk_netid1(2)+self.bin_num-self.preamble_bin)/self.zero_padding_ratio, 2^self.sf), ...
mod((pk_netid2(2)+self.bin_num-self.preamble_bin)/self.zero_padding_ratio, 2^self.sf)]
];
% the goal is to extract payload_len from PHY header
% header is in the first 8 symbols
symbols = [];
pk_list = [];
if x > length(self.sig) - 8*self.sample_num + 1
return;
end
for ii = 0:7
pk = self.dechirp(x+ii*self.sample_num);
pk_list = [pk_list; pk];
symbols = [symbols; mod((pk(2)+self.bin_num-self.preamble_bin)/self.zero_padding_ratio, 2^self.sf)];
end
if self.has_header
is_valid = self.parse_header(symbols);
if ~is_valid
x = x + 7*self.sample_num;
continue;
end
end
% number of symbols in the packet
sym_num = self.calc_sym_num(self.payload_len);
% demodulate the rest LoRa data symbols
if x > length(self.sig) - sym_num*self.sample_num + 1
return;
end
for ii = 8:sym_num-1
pk = self.dechirp(x+ii*self.sample_num);
pk_list = [pk_list; pk];
symbols = [symbols; mod((pk(2)+self.bin_num-self.preamble_bin)/self.zero_padding_ratio, 2^self.sf)];
end
x = x + sym_num*self.sample_num;
% compensate CFO drift
symbols = self.dynamic_compensation(symbols);
symbols_m = [symbols_m mod(round(symbols),2^self.sf)];
cfo_m = [cfo_m self.cfo];
end
if isempty(symbols_m)
warning('No preamble detected!');
end
end
function is_valid = parse_header(self, data)
% parse_header Parse LoRa PHY header and set parameters
%
% input:
% data: An eight elements vector containing header symbols
% output:
% is_valid: `true` if the header is valid
% `false` if the header is invalid
% compensate CFO drift
symbols = self.dynamic_compensation(data);
% gray coding
symbols_g = self.gray_coding(symbols);
% deinterleave
codewords = self.diag_deinterleave(symbols_g(1:8), self.sf-2);
% parse header
nibbles = self.hamming_decode(codewords, 8);
self.payload_len = double(nibbles(1)*16 + nibbles(2));
self.crc = double(bitand(nibbles(3), 1));
self.cr = double(bitshift(nibbles(3), -1));
% we only calculate header checksum on the first three nibbles
% the valid header checksum is considered to be 5 bits
% other 3 bits require further reverse engineering
header_checksum = [bitand(nibbles(4), 1); de2bi(nibbles(5), 4, 'left-msb')'];
header_checksum_calc = self.header_checksum_matrix * gf(reshape(de2bi(nibbles(1:3), 4, 'left-msb')', [], 1));
if any(header_checksum ~= header_checksum_calc)
warning('Invalid header checksum!');
is_valid = 0;
else
is_valid = 1;
end
end
function s = modulate(self, symbols)
% modulate Modulate a baseband signal
%
% input:
% symbols: A vector of chirp symbols to be modulated
% valid symbol range: 0 to 2^sf-1
% output:
% s: A valid LoRa baseband signal
uc = LoRaPHY.chirp(true, self.sf, self.bw, self.fs, 0, self.cfo, 0);
dc = LoRaPHY.chirp(false, self.sf, self.bw, self.fs, 0, self.cfo, 0);
preamble = repmat(uc, self.preamble_len, 1);
netid = [LoRaPHY.chirp(true, self.sf, self.bw, self.fs, 24, self.cfo, 0); LoRaPHY.chirp(true, self.sf, self.bw, self.fs, 32, self.cfo, 0)];
chirp_len = length(uc);
sfd = [dc; dc; dc(1:round(chirp_len/4))];
data = zeros(length(symbols)*chirp_len, 1);
for i = 1:length(symbols)
data((i-1)*chirp_len+1:i*chirp_len) = LoRaPHY.chirp(true, self.sf, self.bw, self.fs, symbols(i), self.cfo, 0);
end
s = [preamble; netid; sfd; data];
end
function symbols = encode(self, payload)
% encode Encode bytes to symbols
%
% input:
% payload: Payload of LoRa packet
% output:
% symbols: A vector representing the symbols of the packet
if self.crc
data = uint8([payload; self.calc_crc(payload)]);
else
data = uint8(payload);
end
plen = length(payload);
sym_num = self.calc_sym_num(plen);
% filling all symbols needs nibble_num nibbles
nibble_num = self.sf - 2 + (sym_num-8)/(self.cr+4)*(self.sf-2*self.ldr);
data_w = uint8([data; 255*ones(ceil((nibble_num-2*length(data))/2), 1)]);
data_w(1:plen) = self.whiten(data_w(1:plen));
data_nibbles = uint8(zeros(nibble_num, 1));
for i = 1:nibble_num
idx = ceil(i/2);
if mod(i, 2) == 1
data_nibbles(i) = bitand(data_w(idx), 0xf);
else
data_nibbles(i) = bitshift(data_w(idx), -4);
end
end
if self.has_header
header_nibbles = self.gen_header(plen);
else
header_nibbles = [];
end
codewords = self.hamming_encode([header_nibbles; data_nibbles]);
% interleave
% first 8 symbols use CR=4/8
symbols_i = self.diag_interleave(codewords(1:self.sf-2), 8);
ppm = self.sf - 2*self.ldr;
rdd = self.cr + 4;
for i = self.sf-1:ppm:length(codewords)-ppm+1
symbols_i = [symbols_i; self.diag_interleave(codewords(i:i+ppm-1), rdd)];
end
symbols = self.gray_decoding(symbols_i);
end
function header_nibbles = gen_header(self, plen)
% gen_header Generate a valid LoRa header
%
% input:
% plen: Payload length
% output:
% header_nibbles: Header in nibbles
header_nibbles = zeros(5, 1);
header_nibbles(1) = bitshift(plen, -4);
header_nibbles(2) = bitand(plen, 15);
header_nibbles(3) = bitor(2*self.cr, self.crc);
header_checksum = self.header_checksum_matrix * gf(reshape(de2bi(header_nibbles(1:3), 4, 'left-msb')', [], 1));
x = header_checksum.x;
header_nibbles(4) = x(1);
for i = 1:4
header_nibbles(5) = bitor(header_nibbles(5), x(i+1)*2^(4-i));
end
end
function checksum = calc_crc(self, data)
% calc_crc Calculate payload CRC
%
% input:
% data: Data in bytes
% output:
% checksum: CRC result
switch length(data)
case 0
checksum = [0; 0];
case 1
checksum = [data(end); 0];
case 2
checksum = [data(end); data(end-1)];
otherwise
input = data(1:end-2);
seq = self.crc_generator(reshape(logical(de2bi(input, 8, 'left-msb'))', [], 1));
checksum_b1 = bitxor(bi2de(seq(end-7:end)', 'left-msb'), data(end));
checksum_b2 = bitxor(bi2de(seq(end-15:end-8)', 'left-msb'), data(end-1));
checksum = [checksum_b1; checksum_b2];
end
end
function data_w = whiten(self, data)
% whiten Whitening process in LoRa
%
% input:
% data: Data in bytes
% output:
% data_w: Data after whitening
len = length(data);
data_w = bitxor(data(1:len), self.whitening_seq(1:len));
self.print_bin("Whiten", data_w);
end
function codewords = hamming_encode(self, nibbles)
% hamming_encode Hamming encoding process in LoRa
%
% input:
% nibbles: Data in nibbles
% output:
% codewords: Data after hamming encoding
nibble_num = length(nibbles);
codewords = uint8(zeros(nibble_num, 1));
for i = 1:nibble_num
nibble = nibbles(i);
p1 = LoRaPHY.bit_reduce(@bitxor, nibble, [1 3 4]);
p2 = LoRaPHY.bit_reduce(@bitxor, nibble, [1 2 4]);
p3 = LoRaPHY.bit_reduce(@bitxor, nibble, [1 2 3]);
p4 = LoRaPHY.bit_reduce(@bitxor, nibble, [1 2 3 4]);
p5 = LoRaPHY.bit_reduce(@bitxor, nibble, [2 3 4]);
if i <= self.sf - 2
% the first SF-2 nibbles use CR=4/8
cr_now = 4;
else
cr_now = self.cr;
end
switch cr_now
case 1
codewords(i) = bitor(uint8(p4)*16, nibble);
case 2
codewords(i) = LoRaPHY.word_reduce(@bitor, [uint8(p5)*32 uint8(p3)*16 nibble]);
case 3
codewords(i) = LoRaPHY.word_reduce(@bitor, [uint8(p2)*64 uint8(p5)*32 uint8(p3)*16 nibble]);
case 4
codewords(i) = LoRaPHY.word_reduce(@bitor, [uint8(p1)*128 uint8(p2)*64 uint8(p5)*32 uint8(p3)*16 nibble]);
otherwise
% THIS CASE SHOULD NOT HAPPEN
error('Invalid Code Rate!');
end
end
end
function symbols_i = diag_interleave(self, codewords, rdd)
% diag_interleave Diagonal interleaving
%
% input:
% codewords: Data in nibbles
% rdd: Bits with redundancy
% For example, code rate 4/5 means rdd = 5
% output:
% symbols_i: Symbols after diagonal interleaving
tmp = de2bi(codewords, rdd, 'right-msb');
symbols_i = uint16(bi2de(cell2mat(arrayfun(@(x) circshift(tmp(:,x), 1-x), 1:rdd, 'un', 0))'));
self.print_bin("Interleave", symbols_i);
end
function symbols = gray_decoding(self, symbols_i)
% gray_decoding Gray decoding
% `gray_decoding` is used in the ENCODING process
%
% input:
% symbols_i: Interleaved symbols
% output:
% symbols: Final symbols to be modulated in a packet
symbols = zeros(length(symbols_i), 1);
for i = 1:length(symbols_i)
num = uint16(symbols_i(i));
mask = bitshift(num, -1);
while mask ~= 0
num = bitxor(num, mask);
mask = bitshift(mask, -1);
end
if i <= 8 || self.ldr
symbols(i) = mod(num * 4 + 1, 2^self.sf);
else
symbols(i) = mod(num + 1, 2^self.sf);
end
end
end
function sym_num = calc_sym_num(self, plen)
% calc_sym_num Calculate number of symbols
%
% input:
% plen: Payload length
% output:
% sym_num: Number of symbols
sym_num = double(8 + max((4+self.cr)*ceil(double((2*plen-self.sf+7+4*self.crc-5*(1-self.has_header)))/double(self.sf-2*self.ldr)), 0));
end
function plen = calc_payload_len(self, slen, no_redundant_bytes)
% calc_payload_len Calculate payload length
%
% input:
% slen: Number of symbols
% no_redundant_bytes: `true` to fill the 0.5 redundant bytes
% output:
% plen: Payload length
if nargin < 3
no_redundant_bytes = false;
end
% plen_float possibly has fractional part 0.5, which means
% there would be 0.5 uncontrollable redundant byte in a packet.
% The 0.5 byte results in unexpected symbols when called by
% function `symbols_to_bytes`. To make all specified symbols
% controllable, we use `ceil` instead of `floor` when
% no_redundant_bytes is true.
plen_float = (self.sf-2)/2 - 2.5*self.has_header + (self.sf-self.ldr*2)/2 * ceil((slen-8)/(self.cr+4));
if no_redundant_bytes
plen = ceil( plen_float );
else
plen = floor( plen_float );
end
end
function x_sync = sync(self, x)
% sync Packet synchronization
%
% input:
% x: Start index for synchronization
% output:
% x_sync: Index after up-down alignment
% find downchirp
found = false;
while x < length(self.sig) - self.sample_num
up_peak = self.dechirp(x);
down_peak = self.dechirp(x, false);
if abs(down_peak(1)) > abs(up_peak(1))
% downchirp detected
found = true;
end
x = x + self.sample_num;
if found
break;
end
end
if ~found
return;
end
% Up-Down Alignment
% NOTE preamble_len >= 6
% NOTE there are two NETID chirps between preamble and SFD
% NOTE `detect` has already shifted the up peak to position 0
pkd = self.dechirp(x, false);
if pkd(2) > self.bin_num / 2
to = round((pkd(2)-1-self.bin_num)/self.zero_padding_ratio);
else
to = round((pkd(2)-1)/self.zero_padding_ratio);
end
x = x + to;
% set preamble reference bin for CFO elimination
pku = self.dechirp(x - 4*self.sample_num);
self.preamble_bin = pku(2);
if self.preamble_bin > self.bin_num / 2
self.cfo = (self.preamble_bin-self.bin_num-1)*self.bw/self.bin_num;
else
self.cfo = (self.preamble_bin-1)*self.bw/self.bin_num;
end
% set x to the start of data symbols
pku = self.dechirp(x-self.sample_num);
pkd = self.dechirp(x-self.sample_num, false);
if abs(pku(1)) > abs(pkd(1))
% current symbol is the first downchirp
x_sync = x + round(2.25*self.sample_num);
else
% current symbol is the second downchirp
x_sync = x + round(1.25*self.sample_num);
end
end
function [data_m, checksum_m] = decode(self, symbols_m)
% decode Decode data from symbols
%
% input:
% symbols_m: A matrix of symbols to be decoded. Each column
% vector represents demodulated symbols from a
% LoRa packet.
% output:
% data_m: A matrix of bytes representing the decoding
% result of `symbols_m`. The last two bytes are the
% decoded CRC checksum if CRC is enabled.
% checksum_m: A vector of checksum based on the decoded
% payload.Checksum is empty if CRC is disabled.
data_m = [];
checksum_m = [];
for pkt_num = 1:size(symbols_m, 2)
% gray coding
symbols_g = self.gray_coding(symbols_m(:, pkt_num));
% deinterleave
codewords = self.diag_deinterleave(symbols_g(1:8), self.sf-2);
if ~self.has_header
nibbles = self.hamming_decode(codewords, 8);
else
% parse header
nibbles = self.hamming_decode(codewords, 8);
self.payload_len = double(nibbles(1)*16 + nibbles(2));
self.crc = double(bitand(nibbles(3), 1));
self.cr = double(bitshift(nibbles(3), -1));
% we only calculate header checksum on the first three nibbles
% the valid header checksum is considered to be 5 bits
% other 3 bits require further reverse engineering
header_checksum = [bitand(nibbles(4), 1); de2bi(nibbles(5), 4, 'left-msb')'];
header_checksum_calc = self.header_checksum_matrix * gf(reshape(de2bi(nibbles(1:3), 4, 'left-msb')', [], 1));
if any(header_checksum ~= header_checksum_calc)
error('Invalid header checksum!');
end
nibbles = nibbles(6:end);
end
rdd = self.cr + 4;
for ii = 9:rdd:length(symbols_g)-rdd+1
codewords = self.diag_deinterleave(symbols_g(ii:ii+rdd-1), self.sf-2*self.ldr);
% hamming decode
nibbles = [nibbles; self.hamming_decode(codewords, rdd)];
end
% combine nibbles to bytes
bytes = uint8(zeros(min(255, floor(length(nibbles)/2)), 1));
for ii = 1:length(bytes)
bytes(ii) = bitor(uint8(nibbles(2*ii-1)), 16*uint8(nibbles(2*ii)));
end
% dewhitening
len = self.payload_len;
if self.crc
% The last 2 bytes are CRC16 checkcum
data = [self.dewhiten(bytes(1:len)); bytes(len+1:len+2)];
% Calculate CRC checksum
checksum = self.calc_crc(data(1:len));
else
data = self.dewhiten(bytes(1:len));
checksum = [];
end
data_m = [data_m data];
checksum_m = [checksum_m checksum];
end
end
function symbols = dynamic_compensation(self, data)
% dynamic_compensation Compensate bin drift
%
% input:
% data: Symbols with bin drift
% output:
% symbols: Symbols after bin calibration
% compensate the bin drift caused by Sampling Frequency Offset (SFO)
sfo_drift = (1 + (1:length(data))') * 2^self.sf * self.cfo / self.rf_freq;
symbols = mod(data - sfo_drift, 2^self.sf);
if self.ldr
bin_offset = 0;
v_last = 1;
for i = 1:length(symbols)
v = symbols(i);
bin_delta = mod(v-v_last, 4);
if bin_delta < 2
bin_offset = bin_offset - bin_delta;
else
bin_offset = bin_offset - bin_delta + 4;
end
v_last = v;
symbols(i) = mod(v+bin_offset, 2^self.sf);
end
end
end
function symbols = gray_coding(self, din)
% gray_coding Gray coding
% `gray_coding` is used in the DECODING process
%
% input:
% data: Symbols with bin drift
% output:
% symbols: Symbols after bin calibration
din(1:8) = floor(din(1:8)/4);
if self.ldr
din(9:end) = floor(din(9:end)/4);
else
din(9:end) = mod(din(9:end)-1, 2^self.sf);
end
s = uint16(din);
symbols = bitxor(s, bitshift(s, -1));
self.print_bin("Gray Coding", symbols, self.sf);
end
function codewords = diag_deinterleave(self, symbols, ppm)
% diag_deinterleave Diagonal deinterleaving
%
% input:
% symbols: Symbols after gray coding
% ppm: Size with parity bits
% output:
% codewords: Codewords after deinterleaving
b = de2bi(symbols, double(ppm), 'left-msb');
codewords = flipud(bi2de(cell2mat(arrayfun(@(x) ...
circshift(b(x,:), [1 1-x]), (1:length(symbols))', 'un', 0))'));
self.print_bin("Deinterleave", codewords);
end
function bytes_w = dewhiten(self, bytes)
% dewhiten Data Dewhitening
%
% input:
% bytes: Bytes after deinterleaving
% output:
% bytes_w: Bytes after dewhitening
len = length(bytes);
bytes_w = bitxor(uint8(bytes(1:len)), self.whitening_seq(1:len));
self.print_bin("Dewhiten", bytes_w);
end
function nibbles = hamming_decode(self, codewords, rdd)
% hamming_decode Hamming Decoding
%
% input:
% codewords: Codewords after deinterleaving
% rdd: Bits with redundancy
% output:
% nibbles: Nibbles after hamming decoding
p1 = LoRaPHY.bit_reduce(@bitxor, codewords, [8 4 3 1]);
p2 = LoRaPHY.bit_reduce(@bitxor, codewords, [7 4 2 1]);
p3 = LoRaPHY.bit_reduce(@bitxor, codewords, [5 3 2 1]);
p4 = LoRaPHY.bit_reduce(@bitxor, codewords, [5 4 3 2 1]);
p5 = LoRaPHY.bit_reduce(@bitxor, codewords, [6 4 3 2]);
function pf = parity_fix(p)
switch p
case 3 % 011 wrong b3
pf = 4;
case 5 % 101 wrong b4
pf = 8;
case 6 % 110 wrong b1
pf = 1;
case 7 % 111 wrong b2
pf = 2;
otherwise
pf = 0;
end
end
if self.hamming_decoding_en
switch rdd
% TODO report parity error
case {5, 6}
nibbles = mod(codewords, 16);
case {7, 8}
parity = p2*4+p3*2+p5;
pf = arrayfun(@parity_fix, parity);
codewords = bitxor(codewords, uint16(pf));
nibbles = mod(codewords, 16);
otherwise
% THIS CASE SHOULD NOT HAPPEN
error('Invalid Code Rate!');
end
else
nibbles = mod(codewords, 16);
end
self.print_bin("Hamming Decode", codewords);
end
function bytes = symbols_to_bytes(self, symbols)
% symbols_to_bytes Derive the payload for a given symbol series
%
% input:
% symbols: Symbols to appear in the demodulation level
% output:
% bytes: Payload bytes
symbols = reshape(symbols, [length(symbols), 1]);
self.init();
self.hamming_decoding_en = false;
payload_len_ = self.payload_len;
if length(symbols) <= 4
slen_tmp = 8 + self.has_header*(self.cr+4);
else
slen_tmp = 8 + ceil((length(symbols)-4*(1-self.has_header))/4) * (self.cr+4);
end
self.payload_len = self.calc_payload_len(slen_tmp, true);
symbols_ = zeros(self.calc_sym_num(self.payload_len), 1);
if self.has_header
jj = 9;
else
jj = 1;
end
for ii = 1:4:length(symbols)
if ii+3 <= length(symbols)
symbols_(jj:jj+3) = symbols(ii:ii+3);
else
symbols_(jj:jj+3) = [symbols(ii:end); zeros(ii-length(symbols)+3, 1)];
end
if jj == 1
jj = 9;
else
jj = jj + self.cr + 4;
end
end
if self.has_header
% construct header
symbols_tmp = self.encode(zeros(self.payload_len, 1));
symbols_(1:8) = symbols_tmp(1:8);
end
[bytes, ~] = self.decode(symbols_);
if self.crc
bytes = bytes(1:end-2);
end
self.hamming_decoding_en = true;
self.payload_len = payload_len_;
end
function time_ms = time_on_air(self, plen)
% time_on_air Calculate the flying time of a LoRa packet
%
% input:
% plen: Payload length
% output:
% time_ms: Flying time (in milliseconds)
sym_num = self.calc_sym_num(plen);
% milliseconds
time_ms = (sym_num + 4.25 + self.preamble_len) * (2^self.sf/self.bw) * 1000;
end
function print_bin(self, flag, vec, size)
if self.is_debug
if nargin == 3
size = 8;
end
len = length(vec);
fprintf("%s:\n", flag);
for i = 1:len
fprintf("%s\n", dec2bin(round(vec(i)), size));
end
fprintf("\n");
end
end
function print_hex(self, flag, vec)
if self.is_debug
len = length(vec);
fprintf("%s: ", flag);
for i = 1:len
fprintf("%s ", dec2hex(round(vec(i))));
end
fprintf("\n");
end
end
function log(self, flag, data)
if self.is_debug
fprintf("%s: ", flag);
len = length(data);
for i = 1:len
fprintf("%d ", data(i));
end
fprintf("\n");
end
end
function plot_peak(self, x)
figure;
c = [self.downchirp self.upchirp];
for jj = 1:9
for ii = 1:2
ft = fft(self.sig(x:x+self.sample_num-1).*c(:,ii), self.fft_len);
ft_ = abs(ft(1:self.bin_num)) + abs(ft(self.fft_len-self.bin_num+1:self.fft_len));
subplot(2, 9, (ii-1)*9+jj);
plot(ft_);
end
x = x + self.sample_num;
end
end
end
methods(Static)
function b = bit_reduce(fn, w, pos)
b = bitget(w, pos(1));
for i = 2:length(pos)
b = fn(b, bitget(w, pos(i)));
end
end
function w = word_reduce(fn, ws)
w = ws(1);
for i = 2:length(ws)
w = fn(w, ws(i));
end
end
function y = topn(pks, n, padding, th)
[y, p] = sort(abs(pks(:,1)), 'descend');
if nargin == 1
return;
end
nn = min(n, size(pks, 1));
if nargin >= 3 && padding
y = [pks(p(1:nn), :); zeros(n-nn, size(pks, 2))];
else
y = pks(p(1:nn), :);
end
if nargin == 4
ii = 1;
while ii <= size(y,1)
if abs(y(ii,1)) < th
break;
end
ii = ii + 1;
end
y = y(1:ii-1, :);
end
end
function y = chirp(is_up, sf, bw, fs, h, cfo, tdelta, tscale)
% chirp Generate a LoRa chirp symbol
%
% input:
% is_up: `true` if constructing an up-chirp
% `false` if constructing a down-chirp
% sf: Spreading Factor
% bw: Bandwidth
% fs: Sampling Frequency
% h: Start frequency offset (0 to 2^SF-1)
% cfo: Carrier Frequency Offset
% tdelta: Time offset (0 to 1/fs)
% tscale: Scaling the sampling frequency
% output:
% y: Generated LoRa symbol
if nargin < 8
tscale = 1;
end
if nargin < 7
tdelta = 0;
end
if nargin < 6
cfo = 0;
end
N = 2^sf;
T = N/bw;
samp_per_sym = round(fs/bw*N);
h_orig = h;
h = round(h);
cfo = cfo + (h_orig - h) / N * bw;