Instrumentation & Measurement Magazine 23-9 - 31

side, again inside the LoRa wireless channel, is measured with
the only AWGN interference activated. The measured value of
useful LoRa signal power Ps, and AWGN interference power
level, PI, are finally used to calculate the SNR at receiver side
for the considered configuration according to:
	

SNR 

PS
	(1)
PI

Finally, the PLR is estimated on 10,000 transmitted packets. In particular, the LoRa Tx transmits the 10,000 LoRa
packets in succession to the LoRa Rx, which receives the noisy
signal. The packets sent are enumerated with an incremental
identification number from 0 to 9,999 at the higher application layer. This information is included in the payload. The
LoRa Rx demodulates the received packets and extracts the
identification number from the payload. An automatic measurement station in LabVIEW, capable of making a control on
the received value, calculates the number of packets lost during the communication. The packet loss ratio is expressed as
a percentage relative to the total number of packets sent. To
perform an exhaustive characterization of the LoRa receiver,
this measurement procedure must be repeated step-by-step
for each possible configuration of LoRa signal and several
value of AWGN power level. A full factorial experiment is required. However, this characterization activity would require
a notable effort and is very long. It could adversely affect the
production costs of the IoT devices. To overcome the considered limitation, the authors propose to adopt a Central
Composite Design (CCD) analysis, which allows to reduce
the number of necessary experiments without loss of significant information.

Design of Experiments
A central composite design (CCD) is an experimental design
typically used in response surface methodology. CCD allows
building a second-order quadratic polynomial model, able to
relate one or more process variables (factors) with one or more
response variables, without needing to perform a full factorial experiment [14]. In CCD, involved factors are tested at five
levels to obtain the " rotatability " of the design and the values
of the input quantities are encoded in an arbitrary unit interval: [-α, -1, 0, 1, α], where 0 corresponds to the mean value of
the considered factor XM ; ±α = ±2k/4 stands for the extrema of
the interval (+α = XMAX, −α = XMIN) , k being the number of the
factors. A straightforward relationship allows determining the
actual values corresponding to encoded ±1. The " rotatability "
ensures constant variance at points that are equidistant from
the center point, and therefore provides equal precision of response estimation in any direction of the design. The limited
number of experiments is the union of three distinct design
points (i.e. parameters configuration in each experiment):
(i) center points; (ii) axial points (2k experiments); (iii) factorial points (2k experiments). Center points involve the mean
values of each factors and are a set of repeated experiments exploited to estimate both repeatability and reproducibility of
the experiment. The set of axial points emulates a one-factorat-time analysis. The quantities of the axial point experiments
are the same as the center points (the mean values of the factors), except for one of them which assumes either maximum
or minimum value. Axial points are also used to estimate the
coefficients of quadratic terms. The last points to investigate
are the factorial points, used to estimate the coefficients of linear terms and interactions between factors on the response

 

Fig. 3. CCD design graphic representation of two factors, X1 and X2, on five-levels. (a) Center Points (indicated by yellow star markers); (b) Axial Points (indicated
by blue markers); (c) Factorial Points (indicated red square markers).
December 2020	

IEEE Instrumentation & Measurement Magazine	31



Instrumentation & Measurement Magazine 23-9

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