Energy-Efficient Internet of Things Monitoring with
Content-Based Wake-Up Radio
Anay Ajit Deshpande, Federico Chiariotti, Andrea Zanella

arXiv:2312.04294v1 [cs.NI] 7 Dec 2023

Department of Information Engineering, University of Padova
Via G. Gradenigo 6/B, Padova, Italy
Email: {anayajit.deshpande,federico.chiariotti,andrea.zanella}@unipd.it

Abstract—The
use
of
Wake-Up Radio (WUR)
in
Internet of Things (IoT) networks can significantly improve
their energy efficiency: battery-powered sensors can remain in
a low-power (sleep) mode while listening for wake-up messages
using their WUR and reactivate only when polled. However,
polling-based WUR may still lead to wasted energy if values
sensed by the polled sensors provide no new information to the
receiver, or in general have a low Value of Information (VoI).
In this paper, we design a content-based WUR that tracks
the process observed by the sensors and only wakes up the
sensor if its estimated update’s VoI is higher than a threshold
communicated through the poll. If the sensor does not reply to
the polling request, the Gateway (GW) can make a Bayesian
update, knowing that either the sensor value substantially
confirms its current estimate or the transmission failed due
to the wireless channel. We analyze the trade-off between the
tracking error and the battery lifetime of the sensors, showing
that content-based WUR can provide fine-grained control of
this trade-off and significantly increase the battery lifetime of
the node with a minimal Mean Squared Error (MSE) increase.
Index Terms—Wake-Up Radio, Scheduling, Remote monitoring, Energy efficiency

I. I NTRODUCTION
The explosion of the Internet of Things (IoT) has led to
new developments in remote monitoring applications [1], [2],
which use distributed sensors to keep track of remote environments and wide areas, as well as manufacturing plants and
cities. Since the inception of the IoT, however, energy has been
a major issue for system design [3]: battery-powered nodes
face significant constraints in terms of computational and
communication capabilities, and often resort to uncoordinated
random access schemes like ALOHA to avoid the signaling
overhead.
However, the limits of random access schemes are wellknown: unless the traffic is extremely light, these schemes
suffer from packet collisions and congestion [4], and do not
allow the Gateway (GW) to request new data from a specific
sensor [5]. The challenge is then to avoid the significant energy
consumption incurred by nodes constantly listening for request
messages, without tying the schedule to a fixed duty cycle.
One possible solution to this problem is provided by
Wake-Up Radio (WUR) technology, standardized as part
This work was supported by the European Union as part of the Italian
National Recovery and Resilience Plan of NextGenerationEU, under the
partnership on “Telecommunications of the Future” (PE0000001 - program
“RESTART”) and the “Young Researchers” grant REDIAL (SoE0000009).

of IEEE802.11ba [6]: the system includes an extremely
low-power radio only capable of receiving simple signals and making some basic calculations, which is kept
in listening mode, while the sensor’s main processor and
Primary Communication Radio (PCR) are only turned on
when needed. Typically, the WUR is used to reduce the
downlink response time of a node whose PCR is in sleep mode
to save energy [7], achieving both a relatively low latency
and a limited energy consumption. The standard defines the
physical and Medium Access Control (MAC) parameters for
communication with the WUR, as well as the wake-up procedure for the PCR when a WUR signal is received from the GW
along with the power management scheme to be implemented
and associated Duty Cycle (DC) specifications and synchronization schemes. Crucially, it defines the channelization of
wake-up frames to be sent to WUR. The standard explains
the usage of ID-based wake-up messages to be sent to each
node, waking up their PCRs.
However, the basic WUR design defined in IEEE802.11ba,
hereforth referred to as ID-based WUR, does not take into
account the Value of Information (VoI) from the polled sensors. Hence, the concept of content-based WUR was proposed
in [8]. In content-based WUR, the polling packet carries not
only the ID of the target node, but also a condition on the
VoI of the data to be collected (generally, in the form of
a range of interesting values). The target node then wakes
the PCR and replies to the poll on if its data satisfies the
VoI requirement. Hence, in this work, we design a scheme
for joint ID- and content-based WUR, defining the optimal
estimate response and proposing a scheduling policy that can
take into account the VoI of the update using Kalman filter
estimates to increase the network lifetime while trading off
some Mean Squared Error (MSE) performance. The proposed
solution can improve the former by about 40% in some cases,
while only increasing the MSE by 10%.
The rest of this paper is organized as follows: first, in Sec. II,
we present the basic system model for kalman filter estimation
and energy consumption. We then present the censored update
computation and the scheduling policy in Sec. III. Results in a
realistic setting are provided and discussed in Sec. IV. Sec. V
concludes the paper and presents some possible avenues of
future work on the subject.

II. S YSTEM M ODEL

Start

We consider a system with N distributed sensors, monitoring a physical process over a wide area. The sensors are
equipped with uplink radios with wake-up functionality, and
can be polled at will by the GW. In the following, we will
denote vectors using bold letters, e.g., x, and matrices using
bold capital letters, e.g., A. Individual elements of vectors
and matrices will be denoted using the same letter, with the
element index as a subscript, e.g., xn or Am,n .

We model the physical process monitored by the N sensors
as a linear dynamic process running in discrete time. The state
of the process at step k is the P × 1 column vector x(k) =
[x1 , . . . , xP ]T . The dynamic system update is defined by
(1)

where A ∈ RP ×P is the update matrix for the system and
v(t) ∼ N (0, Q) is the Gaussian perturbation noise of the
system, determined by the covariance matrix is Q ∈ RP ×P .
Each sensor n then measures value yn (k), and we collect the
measurements at timestep k in the N × 1 column vector y(k):
y(k) = Hx(k) + w(k),

(2)

where H ∈ RN ×P is the observation matrix and w(t) ∼
N (0, R) is the measurement noise vector, with covariance
matrix R ∈ RN ×N . As the GW knows the process statistics,
it can know or estimate A, H, Q, and R. It also has an initial
estimate of the process at step 0, x̂(0), and an initial estimation
covariance matrix P(0), defined as:
P(0) = E[(x(0) − x̂(0))T (x(0) − x̂(0))].

(3)

In the following, we will use the symbol z(k) to denote the
estimation error x(k)− x̂(k). We can then use a Kalman filter,
the Minimum MSE (MMSE) estimator for linear processes, to
obtain the a priori estimate after each step:
(
x̂(k|k − 1) = Ax̂(k − 1);
(4)
P(k|k − 1) = AP(k − 1)AT + Q.
If sensor n is polled, it can then report its measured value. Due
to the wireless channel conditions, this update might be lost,
in which case the a priori estimate remains the best possible
estimate of the state. Conversely, if the update is successfully
received, the Kalman filter observation is simply yn (k). In
the following, we will use symbol 1n to denote a one-hot row
vector of length N , whose values are all 0 except for the n-th,
which is equal to 1. We also define the innovation covariance
matrix S(k|n):
S(k) = HP(k|k − 1)HT + R.

(5)

The Kalman gain is then:
g(k|n) =

P(k|k − 1)HT 1Tn
.
Sn,n (k)

(6)

SLEEP PCR

WAKE UP
MESSAGE

TX PACKET

ID SCAN
WAKE PCR
NO

A. Process Model and Kalman Filter Estimation

x(k) = Ax(k − 1) + v(k),

WUR
LISTEN

Matches ID?

YES

POLLED

Fig. 1: ID-based WUR sensor operation.
The a posteriori estimate is then:
(
x̂(k|n) = x̂(k|k − 1) + g(k|n) (yn (k) − x̂n (k|k − 1)) ;
P(k|n) = (IP − g(k|n)1n H) P(k|k − 1),

(7)
where IP is the P × P identity matrix. We consider a scenario
in which the process dynamics are significantly slower than
the time it takes to poll a sensor, i.e., the process is much
slower than polls. Hence, to avoid draining the battery of all
the sensors in every single timestep, the GW can choose to poll
M ≤ N sensors sequentially. The updated estimate from (7)
after each poll then becomes the a priori estimate to determine
the next polled sensor.
B. Communication and Energy Model
We consider a system in which one GW communicates
with N wake-up capable receivers. The communication model
is then a simple Packet-Erasure Channel (PEC) with erasure
probability εn , which includes three possible failure events:
1) The wake-up message might be lost due to wireless
channel conditions or interference from outside the
sensor network, and the sensor might not wake up and
transmit its update;
2) The wake-up message might be misunderstood by another sensor, who then wakes up along with the intended
node and causes a packet collision by transmitting out
of turn;
3) The wireless channel conditions or interference from
outside the network might not allow the GW to correctly
decode the packet transmitted by the sensors even if no
other sensors transmit.
As sensors are geographically spread out over the environment,
their failure probabilities will be different. We assume that
these probabilities are known to the receiver, or can be
estimated beforehand.
III. E NERGY-AWARE VO I-BASED P OLLING
Using the communication and energy model defined, we
consider the three sensor operations that consume energy:
the reception of a wake-up message Ew , the measurement
of a new observation of the physical process monitored by
the sensor Es , and the transmission of an update Et . WUR

Start
WUR

SLEEP PCR

LISTEN
WAKE UP

TX PACKET

ID SCAN

NO

Matches ID?

YES

POLLED

SILENCE

ACTIVE
First

CHANNEL

Next message?

Threshold
Second

In Range?

Threshold

WAKE PCR

YES

NO

Fig. 2: Content-based WUR sensor operation.
systems are designed to reduce the energy necessary for the
wake-up radio, Ew , as much as possible [9]. The power
consumption of the WUR can be as low as 2 µW [10],
much lower than the power required to keep the main sensor
computing unit and radio in sleep mode, which may be close
to 1 mW even for low-energy LoRa devices [11]. Moreover,
Es is usually much lower than Et , which may require up to
100 mJ in LoRa devices, depending on the packet length and
spreading factor [11].
Hence, we can consider the energy expenditure of the
sensor: in a standard wake-up model, shown in Fig. 1, the
sensor needs only a limited amount of energy Ew to receive a
wake-up radio message and check if its ID matches the target
one, while it consumes a much larger Et to wake up the PCR
and transmit a message. We can then envision a content-based
scheme, depicted in Fig. 2, which adds two more messages to
the wake-up procedure. The two messages correspond to two
thresholds, a and b which are compared to the measured value.
If b ≤ a, the sensor will wake up its PCR and transmit any
value outside the range [b, a], while if b > a, it will transmit
values only inside the interval [a, b]. If no further message is
received after the ID message, the sensor falls back to a simple
ID-based wake-up and transmits the sensed values directly.
The total cost of the scheme is then 3Ew + Es , rather than
Ew + Es as in standard WUR.
The scheme relies on sensors being able to obtain measurements using relatively low energy, and the PCR being the
most significant factor when measuring energy consumption.
However, this assumption is realistic and shared by other wellknown content-based WUR schemes [8], [12], [13].
A. Censored Kalman Update
As the energy consumption of the WUR is designed to be
orders of magnitude lower than the PCR’s, we can then use
the content-based wake-up to improve the battery lifetime of

the sensors by avoiding the transmission of updates with a
lower VoI. In the following, we consider the simpler case in
which N = P and H = IP , i.e., the case in which each
sensor observes a component of the system state, with no
influence from others, leaving the general case for future work.
In particular, we consider information that confirms the GW’s
estimate to be less relevant than surprising updates that may
significantly change it, i.e., we set the thresholds a = x̂n (k)−θ
and b = x̂n (k) + θ. If the measured value yn (k) is outside the
specified silent range, i.e., yn (k) ∈
/ [x̂n (k) − θ, x̂n (k) + θ],
the sensor transmits it, and the update occurs as described
above for a normal Kalman filter. If the GW does not receive
an update, this can either be due to a channel error or to the
sensor remaining silent. The probability of sensor n remaining
silent, an event we denote as ξ, is then:






−1
−1
−1
pn (ξ) =Φ −θRn,n2 − Φ θRn,n2 = 1 − 2Φ θRn,n2 ,
(8)
where Φ(x) is the Cumulative Density Function (CDF) of the
standard Gaussian distribution. We can then easily compute
the probability that an update is missing because the sensor
was silent, and not because the packet was lost, as:
pn (ξ)
pn (ξ|χ) =
,
(9)
pn (ξ) + (1 − pn (ξ))εn
where χ indicates that there was no successful update from
the sensor. The probability of having no update is then:
pn (χ) = εn + (1 − εn )pn (ξ).

(10)

Pm,n (k) = E[zn (k)zm (k)|P(k|k − 1)],

(11)

If the sensor is silent, the prior estimate x̂(k|k − 1) is simply
maintained. On the other hand, we need to consider the
effect of the new information on the estimate covariance. We
then consider each element Pm,n (k) in the covariance matrix
P(k|k − 1):
and then compute Pm,n (k|ξ), i.e., each individual element
of the covariance matrix in case the sensor was silent. In
the following, we omit the timestep index for readability’s
sake. In order to compute the expected value from (11), we
need to apply Bayes’ theorem to compute the a posteriori
Probability Density Function (PDF) of zn :
 




−θ−zn
Φ √θ−zn − Φ √
φ √zn
Pn,n
Rn,n
Rn,n
,
p(zn |ξ) =
pn (ξ)
(12)
where φ(x) is the PDF of the standard Gaussian distribution.
By the definition of the covariance matrix, the conditional
expected value of zm is simply:
Pm,n (k|k − 1)zn
.
(13)
E[zm |zn ] =
Pn,n (k|k − 1)
The value of Pm,n (k|ξ) is then:
Z ∞
p(zn |ξ)zn E[zm |zn ] dzn ,
Pm,n (k|ξ) =
−∞
Z
Pm,n ∞
p(zn |ξ)zn2 dzn .
=
Pn,n −∞

(14)

TABLE I: Simulation Parameters
Parameter

Symbol

Value

Number of episodes
Timesteps per episode
Number of nodes
Number of polls per step
Value threshold
Transmission energy
Sensing energy
Wake-up energy
Sleep energy
Battery size

L
K
N
M
θ
Et
Es
Ew
E0
Emax

100
1000
50
{1,2,5,10,20,50}
{0.5, 1, 1.5, 2, 2.5, 3} × σ
50 mJ
10 mJ
10 mJ
1 mJ
9000 mAh, 5 V (162 kJ)

This integral does not have an analytical solution, as it involves
the Gaussian CDF, but it can be computed numerically. The
calculation can then be repeated for each element of the n-th
column of P(k), so as to obtain P(k|ξ), but the integral only
needs to be solved once, as the only element that changes is
Pm,n (k|k − 1). The overall update if no packet is received is:
(
x̂(k|χ) = x̂(k|k − 1);
P(k|χ) = pn (ξ|χ)P(k|ξ) + (1 − pn (ξ|χ))P(k|k − 1).
(15)
B. Poll Scheduling
Using the system model definition, we need to define the
next polling sensor that would minimize the MSE while
also maximizing the network lifetime. Hence, the scheduling
strategy using the previous estimates {x̂(k − 1), P(k − 1)} can
be defined as
a(k) = arg max tr(P(k|k − 1)) − pn (χ) tr(P(k|χ)
n∈{1,...,N }

(16)

− (1 − pn (χ)) tr(P(k|n)).
This strategy selects the sensor which offers the highest
expected reduction in the overall MSE, considering the possibility of a failed or censored update. After each sensor is
polled, the scheduling should be computed again with the new
estimate covariance matrix, and the value of already polled
sensors is set to 0.
This polling strategy is, hence, a one-step optimal heuristic [14], as it greedily computes the next sensor to be polled
without considering correlations. More advanced scheduling
schemes that take correlations and longer-term trends into
account are left for future developments.
IV. S IMULATION S ETTINGS AND R ESULTS
In this section, we verify the performance of the scheduling
scheme by setting up a Monte Carlo simulation. We generate
a stable synthetic linear process, i.e., a process whose system
matrix eigenvalues are lower than 1, and apply the scheduling
approach for a relatively long time.
A. Simulation Settings
We consider two different linear systems, which we allow
to freely evolve over 100 episodes of 1000 timesteps each.
The Monte carlo simulation is run for both classical IDbased WUR and the content-based scheme proposed in this

paper, considering different values of the censoring threshold
θ, which is expressed as a function of the
p estimated a priori
uncertainty on the sensor reading, i.e., Pn,n (k) for sensor
n. In all cases, we consider the special case in which N = P
and H = IP . We consider two systems with N = 50 sensors
for which elements of the update matrix A are known. In the
first system, A(1) is:

3

if i = j;
4,
(1)
1
Ai,j = − 8 , if i 6= j, mod(i − 2j, 4) = 0;
(17)


0,
otherwise;

where mod(m, n) is the integer modulo function. In the second
system, A(2) is:

4

if i = j;
5,
(2)
1
(18)
Ai,j = − 9 , if i 6= j, mod(⌈i − 2.3j, 4⌉) = 0;


0,
otherwise.

The other parameters remain the same for both systems. The
measurement noise covariance matrix is set to R = I and the
perturbation noise covariance matrix Q is defined as:
 11+mod(i,5)

, if i = j;

5
(i,j)
Q
= 1,
if i 6= j, mod(i − j, 6) = 0; (19)


0,
otherwise.

Note that, in both systems, the sensors with higher indices have
a slightly higher variance. Additionally,
 the transmission error

and the Kalman filter
probabilities are set to εn = 0.02 n−1
25
is initialized at step 0 with x̂(0) = x(0) = 0 and P(0) = I.
Overall, we particularly choose these values so as to consider
two systems with distinct correlated processes: system 1 is
highly interdependent, i.e., state components affect each other
strongly, leading to a higher correlation, while system 2 is
sparser, with a lower correlation between state components.
The full simulation parameters are listed in Table I.
As discussed above, the main trade-off in the system is
between tracking accuracy and energy efficiency. In order to
measure the former, we use the standard MSE over the state
estimate and average it over all episodes:
L

K

1 X X (ℓ)
(x (k)−x̂(ℓ) (k))T (x(ℓ) (k)−x̂(ℓ) (k)),
LKN
ℓ=1 k=0
(20)
where x(ℓ) (k) denotes the state of the system in step k of the
ℓ-th episode. On the other hand, we measure energy efficiency
through the sensor lifetime, i.e., the average duration of the
sensor batteries:

N 
1 X
Emax
L=
,
N n=1 ftx Et + fw (Es + 3Ew ) + (1 − fw )E0
(21)
where ft (n) is the fraction of the total timesteps in which
sensor n transmitted an update and fw is the fraction of the
total timesteps in which sensor n was polled (including the
ones in which the update was not transmitted). If we consider
MSE =

M =5

M =5
M =2

MSE

M = 10

M =1

M =2

M = 20

102

0

0.5

1
1.5
2
Lifetime L (years)

2.5

M = 20

102

Content-based WUR
ID-based WUR

M = 50

M =1

M = 10

MSE

10

103

3

Content-based WUR
ID-based WUR

M = 50

0

3

0.5

1
1.5
2
Lifetime L (years)

2.5

3

500

600

(b) System 2.

(a) System 1.

Fig. 3: Pareto curves for the lifetime and accuracy of the schemes in the two scenarios.
0.8
0.6
0.4
0.2
0

1

ID (L = 0.4 y)
θ = 0.5σ(L = 0.43 y)
θ = σ(L = 0.47 y)
θ = 1.5σ(L = 0.52 y)
θ = 2σ(L = 0.57 y)
θ = 2.5σ(L = 0.62 y)
θ = 3σ(L = 0.67 y)

0

100

200

300
MSE

Empirical CDF

Empirical CDF

1

400

500

600

(a) System 1.

ID (L = 0.4 y)
θ = 0.5σ(L = 0.43 y)
θ = σ(L = 0.47 y)
θ = 1.5σ(L = 0.52 y)
θ = 2σ(L = 0.57 y)
θ = 2.5σ(L = 0.63 y)
θ = 3σ(L = 0.69 y)

0.8
0.6
0.4
0.2
0

0

100

200

300
MSE

400

(b) System 2.

Fig. 4: Tracking MSE CDF with M = 10 for the two systems.
ID-based WUR, we have ft = fw , but the energy required to
receive the wake-up signal is Es + Ew instead of Es + 3Ew .
Finally, we consider a timestep of 1 s for system state
evaluation, in which the GW chooses to poll a set of M sensors
chosen by the scheduler over a single step. We assume that M
is fixed over each episode, and use it as a system parameter
to control the trade-off between accuracy and battery lifetime.
B. Results
The trade-off between tracking accuracy and battery lifetime
can be visualized using a Pareto curve, which shows the
boundary of the performance feasibility region. Any point
on the curve is Pareto efficient, i.e., improving one of the
performance metrics would require sacrificing the other. Fig. 3
shows the Pareto curves for the two schemes in the two
simulation scenarios. Each large step for ID-based WUR
represents the accuracy and lifetime obtained with M polled
sensors, and each small step in content-based WUR represents
the accuracy and lifetime achieved for a different value of θ,
with M polled sensors. So, in this case, optimal performance
would be on the lower right of the plot. We can easily notice
that the content-based scheme is significantly more flexible
and outperforms the ID-based scheme given a fixed M sensors
are polled: while the two Pareto curves share some points
(if we set θ = 0, the content-based scheme is the same as
the legacy one), the content-based scheme can control the
trade-off better, achieving intermediate performance points that
trade some accuracy for a higher network lifetime. This is
particularly evident in the second scenario, shown in Fig. 3b,

in which increasing θ leads to a significantly smaller accuracy
degradation. If we consider M = 50, content-based WUR can
increase the network lifetime by around 100% at the cost of an
MSE increase of around 50% in both scenarios. This relative
advantage diminishes for smaller values of M , but the absolute
change in the MSE due to higher thresholds also decreases,
while the battery lifetime increase is approximately the same.
Additionally, the content-based scheme can reach a lifetime
of over 2.5 years at the lowest accuracy setting, while the
ID-based scheme would need to reduce the polling frequency
below 1 poll per second to do so.
We can analyze the accuracy-lifetime trade-off more in
depth by considering the empirical CDF of the MSE for
different values of θ, shown in Fig. 4. In this analysis, we
set M = 10, considering the intermediate part of the graph.
Firstly, we can note that the network lifetime increases in
a predictable fashion, as expected from the settings of the
scheme: as θ is a function of the predicted sensor reading
standard deviation σ, the probability of a censored update
scales in a similar fashion to the Gaussian complementary
CDF function. However, there are some minor differences between the lifetimes in the two scenarios
that can be attributed
p
p
to the definition of σ: which is Pn,n (k) instead of Rn,n ,
which depends on the state of the Kalman filter. The figures
clearly show that the MSE is relatively stable across episodes
and steps for all settings, as well as the trend we discussed
in the two scenarios: the difference between settings is more
significant in scenario 1, as the average MSE increases by

0

10

20
30
Sensor index

40

Silent

50

(a) θ = σ, System 1.

0.6
0.4
0.2
0

Update

0

10

20
30
Sensor index

40

Silent

50

(c) θ = σ, System 2.

Polling Frequency

Update

Polling Frequency

Polling Frequency
Polling Frequency

0.6
0.4
0.2
0

0.6
0.4
0.2
0

Update

0

10

20
30
Sensor index

40

Silent

50

(b) θ = 2σ, System 1.

0.6
0.4
0.2
0

Update

0

10

20
30
Sensor index

40

Silent

50

(d) θ = 2σ, System 2.

Fig. 5: Polling frequency for each sensor with M = 10.
10% for each increase in the threshold with respect to the
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V. C ONCLUSION AND F UTURE W ORK
In this work, we presented a content-based WUR scheme
that is able to control the trade-off between accuracy and
network lifetime at a finer scale than standard ID-based WUR.
To do so, the GW transmits threshold values along with the
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significant. The implicit communication when the sensor is
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overall network lifetime, with limited MSE degradation.
The promising results shown in this paper can be extended
in several direction: firstly, a dynamic optimization of the
threshold values to better represent VoI may be considered.
Another interesting optimization is on the schedule, which may
be designed with long-term consequences in mind, considering
individual sensors’ batteries as well as the average lifetime.

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