A Propagation Study of LoRa P2P Links for IoT Applications: The Case of Near-Surface Measurements over Semitropical Rivers

. 2021 Oct 16;21(20):6872. doi: 10.3390/s21206872

Algorithm 1. Signal processing for obtaining the mean signal and RF power.

Input: Spread factor SF; bandwidth BW; sampling rate fs; the number of symbols in each frame Nsym; receiver impedance Z; number of frames FrameNumbers.

Output: histograms of the average chirp’s signal as a power signal.

Initialization: SF = 7, BW = 125

\times 10^{3}

[Hz], fs = 5

\times 10^{6}

[SPS], Nsym = 12.25 (C3), FrameNumbers = 100 and Z = 50 [Ω].

(1)
Compute the symbol duration (T_sym), time on air (T_A), and the number of samples (N_S) as follows:

T_{s y m} = \frac{2^{S F}}{B W},

(4)

where SF is the spread factor and BW is the bandwidth in Hertz.

T_{A} = N_{s y m} \times T_{s y m},

(5)

where N_sym is the number of symbols in each frame and T_sym is the symbol duration in seconds.

N_{S} = f_{s} \times T_{A} .

(6)

where f_s is the sample rate in samples per second and T_A is the time on air in seconds.

(2)
Convert the captured I, Q signal from binary to complex:
$I, Q \leftarrow b i n a r y (d a t a . d a t) .$

(3)
Detect the start of each frame. Convolution is applied to the I, Q signal using the number of samples from (6) as follows:
$W i n d o w S i z e \leftarrow \frac{1}{N_{s}} \times n p . o n e s ((1, N_{S})),$

$s i g n a l = |I, Q|,$

$(s i g n a l * W i n d o w S i z e) [n] \leftarrow \sum_{k = 0}^{N_{S} - 1} s i g n a l [k] W i n d o w S i z e [n - k] .$

(4)
Search the local maximum (peaks) to discard the frames with a considerable attenuation:
$[P e a k s V e c t o r] \leftarrow f i n d_p e a k s (s i g n a l * W i n d o w S i z e [n]) .$
(5)
Select an empirical threshold (on the peaks) to identify the start of each frame:
$[i n d e x e s] \leftarrow f i n d (P e a k s V e c t o r > t h r e s h o l d * \max (P e a k s V e c t o r)) .$

The threshold parameter for each distance and height was obtained empirically so that the noise did not significantly affect the analyzed signal. These values are shown in Table 3.

(6)
At the beginning of each frame, determine its corresponding left and right indexes. The aim of this procedure is to create a vector of frames and to avoid the guard interval between each pair of frames:
$L e f t I n d e x \leftarrow P e a k s V e c t o r [i n d e x e s] - N_{s},$

$R i g h t I n d e x \leftarrow L e f t I n d e x + N_{s}$
.
(7)
Obtain a mean frame from the vector of 100 frames:

for

i = 1 \to F r a m e N u m b e r s

F r a m e \leftarrow I, Q [L e f t I n d e x (i) : R i g h t I n d e x (i)]

F r a m e V e c t o r \leftarrow [F r a m e V e c t o r F r a m e]

end
FrameVectorMatrixN_S[FrameNumbers]←FrameVector.

M e a n F r a m e [N_{s}] [1] \leftarrow M e a n V a l u e F o r C o l u m n s (F r a m e V e c t o r M a t r i x) .

(8)
Determine the signal power histograms of the mean frame:
$P o w e r H i s t d B m = h i s t [10 \times l o g_{10} (\frac{{(r e a l (M e a n F r a m e [n]))}^{2} + {(i m a g (M e a n F r a m e [n]))}^{2}}{2 Z}) + 30] .$
(9)
Compute the RF power of the mean frame:
$R F P o w e r = m e a n (P o w e r H i s t d B m) .$