Performance Analysis and Energy Optimization of Wake-Up Receiver Schemes for Wireless Low

Performance Analysis and Energy Optimization of Wake-Up Receiver Schemes for Wireless Low
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Performance analysis and energy optimization of
wake-up receiver schemes for wireless low-power
Nafiseh Seyed Mazloum and Ove Edfors
Department of Electrical and Information Technology, Lund University, Lund, Sweden
Email: {nafiseh.seyed mazloum, ove.edfors}
Abstract—The use of duty-cycled ultra-low power wake-up
receivers (WRxs) can significantly extend a node life time in
low-power sensor network applications. In the WRx design, both
low-power operation of the WRx and wake-up beacon (WB)
detection performance are of importance. We present a systemlevel analysis of a duty-cycled WRx design, including analog
front-end, digital base-band, WB structure, and the resulting WB
detection and false alarm probabilities. We select a low-power
WRx design, with about two orders of magnitude lower power
consumption than the main receiver. The associated cost is an
increase in raw bit-error rate (BER), as compared to the main
receiver, at the same received power level. To compensate, we
use a WB structure that employs spreading. The WB structure
leads us to an architecture for the digital base-band with a high
address-space scalability. We calculate closed form expressions
for detection and false alarm probabilities. Using these we analyze
the impact of design parameters. The analytical framework
is exemplified by minimization of WB transmit energy. For
this particular optimization, we also show that the obtained
results are valid for all transmission schemes with an exponential
relationship between signal-to-noise ratio and bit-error rate, e.g.,
the binary orthogonal schemes with non-coherent detection used
in many low-power applications.
Index Terms—Medium access, wake-up receiver, sensor network, energy optimization, low-power.
A long life-time network where the nodes can operate over
an extended time period is a main requirement in many sensor
network applications. With limited source of energy, both due
to node sizes and/or difficult battery replacements, it can be
very challenging to fulfill demanding life-time requirements.
To optimize the network life-time it is crucial to design an ultra
low power communication system [1]–[7]. The use of ultralow power wake-up receivers (WRxs) can significantly reduce
the overall power consumption of the system. Previous studies
on WRx schemes mainly address scenarios where delay is
the main design requirement and therefore the WRxs monitor
the channel continuously [8]–[11]. The energy consumption
of the WRx due to continuous channel monitoring, however,
becomes dominant in scenarios with rare data packets. Thus,
to further lower the system power consumption, we combine
the ultra-low power WRxs and duty-cycled channel listening
[12], [13]. For this class of WRx schemes, periodic wakeup beacons (WBs) are transmitted ahead of data packets
for synchronization of the communicating nodes. The WRx
is switched on periodically for a certain time interval to
Operating frequency
Sensitivity [dBm]
@ BER 10−3
Data rate [kbps]
Noise figure [dB]
Power consumption
Technology [nm]
Supply voltage
observe the channel, listening for the WB. The WB consists
of a preamble and an address part. The main receiver is
only powered up when the WRx detects a WB with the
correct address. We have shown in [12] that by optimizing
the sleep time of a duty-cycled WRx we can minimize energy
consumption while meeting delay requirements. It is therefore
of interests to further pursue this type of WRx schemes.
Previous studies on low-power WRxs focus mainly on the
design of the analogue front-end for always-on WRx schemes,
but these front-ends can of course be used in duty-cycled
schemes as well. We list the design parameters of some
of these published works in Table I. The largest difference
between always-on and duty-cycled schemes is in the digital
base-band processing performed to detect WBs. In the always
on case the processing is continuous while for the duty cycled
case it is done in a block wise (periodic) fashion. In this paper
we focus on the latter case and the performance expressions
are therefore not directly applicable to always-on schemes.
A WRx is designed for low power operation, typically two
orders of magnitude lower than the power consumption of a
main transceiver, e.g. in the order of 10µW under realistic
assumptions [11]. To meet strict power consumption requirements, early attempts avoided power-hungry components such
as mixers and synthesizers and simple modulation schemes
were often selected. One early such design is given in [20],
where a competitive power consumption of 65 µW is achieved,
at the cost of a -50 dBm WRx sensitivity. Later designs [14]–
[19]1 have refined the design concepts to improve sensitivity
and, in several cases, different low-power mixing strategies
have been introduced [15]–[17]. Today we see power consumption levels at around 50 µW and corresponding sensitivity
levels at about -70 dBm, in the 2.4GHz frequency range used
in this paper. These sensitivity levels are typically related to
raw bit-error rates (BERs) in the order of 10−3 , cf. Table
I. While the improvements are impressive, the sensitivity
levels reached are significantly worse than the ones for main
receiver designs, where we allow orders of magnitude higher
power consumption. This also means that orders of magnitude
higher transmit power is needed when waking up a node,
as compared to normal data transmission. Using a single
transmitter structure, such large variations in transmit power
will make the design more complicated and also less power
efficient [21]. We therefore aim for a simple and power
efficient solution with a single transmitter, using the same
transmit power both for data and wake-up. With a low-power
WRx front-end, and the corresponding loss in sensitivity, the
raw BER will be higher than the 10−3 level normally used
for receiver benchmarking. We show that, by applying proper
WB structures and digital base-band processing, the processing
gain can compensate for the high raw BER, even for very
aggressive power savings in the WRx analog front-end. The
costs to pay are longer WBs and longer wake-up delays, which
may cause congestion in situations with high enough data
traffic. However, in extreme low-power networks with rare
data transmission and low demands on delay, these costs can
be quite tolerable.
If our goal is to optimize an entire wake-up scheme, to
achieve as low power consumption as possible, we need to
look beyond sensitivity levels and in a more elaborate way take
into account mechanisms that influence power consumption. A
missed WB leads to additional WB transmissions by the source
node and a falsely detected WB leads to an unnecessary powerup of the main transceiver by the WRx. Hence, we should
focus our attention on the WB detection performance, and its
connection to WB transmit power consumption. A few studies
[22], [23] address WB detection performance and digital baseband processing, and there are also studies addressing the
entire WRx chain, e.g. [24]. However, none of these attempts
to make a complete analysis where system parameters can be
Our approach is to analyze the complete system-level design
of a duty-cycled WRx, including the analog front-end and
digital base-band architectures, the WB packet structure, and
the resulting WB detection and false alarm probabilities. First
we express the characteristics of the analog front-end for the
resulting BER in terms of signal to noise ratio. We then select
a WB packet structure that allows for high flexibility in the
size of the address-space and makes the design an attractive
candidate both for small networks as well as massive ones.
The choice of the WB structure leads us to an architecture
for the digital base-band, where we improve the design as
compared to [25]. We show that by adjusting the WB packet
1 The design presented in [16] is intended for a duty-cycled WRx scheme,
but this is not explicitly analyzed.
parameters we can compensate for increased raw BERs from
the analog front-end and achieve adequate levels of WB
detection performance, at the same received power levels
as the main receiver sensitivity. Finally, given the raw BER
characteristics of the analog front-end, the WB structure,
and the digital base-band architecture, we perform analytical
calculations of WB detection and false alarm probabilities.
These probabilities are defined per listening interval which,
without loss of generality, simplifies calculations and make
them independent of the length of the sleep interval. Having
this analytical framework, we have the prerequisites for a
complete analysis of energy/power consumption of the entire
system, along the lines of what is introduced in [12], where
the influence of the length of the sleep interval is included in
the energy models rather than in the detection and false-alarm
probabilities. Performing such a complete energy analysis is
however beyond the scope of this paper and, as an example, we
perform a simplified analysis where we focus on the energy
required to transmit the WBs. Using this simplified energy
model we illustrate how to optimize WB design parameters
for different address-space sizes.
This paper is organized as follows. In Section II we give a
description of the overall operation of the addressed system.
We present a design choice for the WRx analog front-end
and propose a basic structure for the WB packet in Section
III. In Section IV we further detail a structure for the digital
base-band of the WRx and then present analytical expressions
for the detection performance of the proposed design configuration. In Section V simulations are performed to validate
the analytical expressions and to evaluate the performance of
the proposed structure. These expressions are further used in
Section VI to determine the optimal design parameters of WRx
schemes. Conclusions and final remarks are given in Section
When targeting wireless sensor network applications with
low traffic intensity, idle channel listening becomes a dominant
source of power consumption. One of the solutions to this
problem is duty-cycled channel listening, where the receiver
only periodically wakes-up. This can be done using the
main receiver [1]–[7], which is also used for data communication, but we can reduce power consumption even more
if a dedicated low-power WRx is employed. This concept,
Duty-Cycled Wake-up receiver based Medium ACcess (DCWMAC), was outlined and partly analyzed in [12]. As the
medium access is the center of the analysis in this study, we
describe the DCW-MAC scheme in some more detail below.
In the DCW-MAC scheme, as shown in Fig. 1(a), a node
consists of a transmitter, a high performance main receiver,
and a low-power/high-BER WRx. All these components are
switched off when they are not in use, and thereby we can save
energy at the receiver side. The transmitter is used both for
data and WB transmissions. In data-transmission mode it may
(a) Simplified node architecture block diagram, with control
signaling shown. The wake-up receiver is broken down in
slightly finer structure.
WB acknowledgment (WACK). Between the transmitted WBs
the SN is listening to the channel with its main receiver and,
when a WACK is received, data transmission is initiated.
One thing that we need to guarantee is that the listening
interval of the WRx can cover a complete WB, despite lack
of synchronization. In other words, the WRx needs to listen
to the channel long enough so that if it barely misses one WB
it still has a chance to capture the next one in the same listen
interval. This means that the listening interval has to be longer
than twice the time-extent of the WB plus the time between
the WBs. The time between the WBs is assumed to be long
enough to contain a WACK packet. Ideally no error is involved
in the detection of the WB, but in reality the transmitted WB
is corrupted by noise and possibly interference. This leads
to imperfections in terms of detection errors and associated
energy costs. While we include the above effects in our
analysis, we assume that the data packets are rare and far
between, so that effects of collisions can be ignored.
B. Event probabilities and energy costs
(b) Timing diagram of the DCW-MAC scheme for one packet arrival
and a network of N nodes, with one source node (SN), one destination
node (DN), and N − 2 non-destination nodes (NDNs).
Fig. 1. Sensor node architecture and timing diagram used for the DCW-MAC
use any suitable modulation technique, while in WB transmission mode it resorts to OOK to allow simple low-power
detection at the destination node. All nodes in a network share
the same radio resource and transmissions are time duplexed.
Figure 1(b) shows the timing diagram of the DCW-MAC
for one packet arrival and a network of N nodes. The node
that has data available for transmission is called the source
node (SN), while the intended receiving node is called the
destination node (DN). The remaining N − 2 nodes are what
we call non-destination nodes (NDNs), which are the ones that
suffer from the false alarms mentioned in the introduction.
Periodic WBs are transmitted by the SN ahead of the data
packet to synchronize communication between the SN and
the DN. The WRxs of all nodes are switched on periodically,
in an asynchronous way, and listen to the channel for WBs.
The WBs carry both the SN and DN addresses/identities and
this way we can avoid overhearing [1] by the NDNs in the
network. If the WRx listening interval coincides with a WB
transmission with the correct address and the WB is detected,
the receiving node switches on its transmitter to reply with a
As a preparation for the coming analysis of detection errors,
let us discuss them in general terms and introduce some of the
notation we will use. When we have noise and interference,
there is a certain probability that the transmitted WB is missed
by the WRx or the WRx accidentally detects a WB that is
not there. The latter can happen both when only noise is
received or, more likely, when a WB addressed to another
node is present on the channel. We will call these events
a miss (M) and a false alarm (FA), respectively. The miss
and generates extra
event occurs with some probability PM
energy consumption in the SN, since additional WBs need
to be transmitted before the DN WRx listening time and the
SN WB transmission coincide again. The false alarm event
and generates additional
happens with a probability PFA
energy consumption on the receiver side, since the main
transceiver is switched on by the WRx without receiving any
The choice of the WB structure as well as the design of the
WRx, and the resulting raw BER, highly influence the miss
and false alarm probabilities, and consequently the total power
consumption of the entire network. For instance, transmission
of a long WB may, on the one hand, reduce the miss and
false alarm probabilities, and consequently lowers the total
energy cost due to WB re-transmissions. A long WB, on the
other hand, may also increase the consumed power at both
SN and WRx DN. The SN needs to transmit longer WBs and
the WRx has to both listen for longer periods and be able to
process longer sequences. While this type of mechanisms lead
to a complex energy analysis, it also allows us to optimize the
total energy consumption in a structured way. Our focus in this
paper is on deriving the performance of our wake-up scheme,
in terms of PM
and PFA
, while we illustrate the principle
of energy optimization using a simplified energy model.
To be able to analyze the performance of the wake-up
scheme we need to find characterizations of the different parts
of the WRx, as shown in Fig. 1(a), and provide a more detailed
description of the chosen WB structure.
Fig. 2. Simplified block diagram of the low-power/low-complexity WRx
analog front-end (AFE) and On-Off Keying (OOK) detector.
As we saw in Table I, different structures are available for
design of the analog front-end (AFE) with different characteristics in terms of operating frequency and receiver sensitivity.
In these works, different modulation techniques such as OOK,
Pulse Position Modulation (PPM), and Frequency Shift Keying
(FSK) are used to keep the power consumption of the WRx
at a low level. For the analysis in this paper, details like the
source of the noise or the choice of the modulation technique
is not of prime interest. From a conceptual point of view, as
long as the relationship between BER and SNR is known for
a certain configuration, the analysis framework of this paper
can be applied. Nevertheless, we will use a WRx reference
design and characterize its BER vs. S/N performance using
We have chosen a simple non-coherent OOK modulation
for the WB transmission and thereby avoid the use of powerhungry components such as frequency-synthesizer and mixer
at the AFE. Figure 2 presents a simplified block diagram of the
AFE and OOK detector of the WRx. The RF signal is downconverted to the base-band by an envelope detector. A direct
current (DC) blocker and a low-pass filter follow the envelope
detector to filter out the DC component and components at
the multiples of carrier frequency, generated by the nonlinear
characteristics of the envelope detector. The OOK detector
measures the energy content of the incoming signal during
one symbol interval and converts the base-band signals to a
bit-sequence. As mentioned, the drawback of such a design is
a generally poor receiver sensitivity. However, our entire WRx
design is based on relaxing the requirements on raw BER and
thereby allowing it to operate at the same received power level
as the main receiver, in our case -90 dBm [13], thus allowing
the same transmit power for WB transmission and data. In the
following we analyze, by simulation, the performance of the
OOK detector and adopt a fitted exponential expression for
the BER that later allows us to analytically optimize energy
A. OOK detector performance simulation
Figure 3 shows the simulated BER performance for an AFE
and OOK detector consisting of the above components and
in an Additive White Gaussian Noise (AWGN) channel. The
design is tailored to the 80MHz wide 2.4GHz ISM band
Fig. 3. BER performance of the WRx analog front-end and OOK detector
shown in Fig. 2, for an Additive White Gaussian Noise (AWGN) channel.
The S/N is measured directly after the 80 MHz wide band-pass filter, at the
input of the envelope detector. As reference, we show the BER performance
of an optimal OOK detector, operating on the same signal. This shows that
our low-power design has about 11 dB implementation loss.
[13] and, to allow for on-chip integration and ultra-low power
consumption, the bandwidth of the first filter (bandpass filter)
is chosen as the full 80MHz. We further model the envelope
detector by a component that outputs the squared input signal.
The bandwidth of the low-pass filter is 250kHz to fit the
250kbps data rate [13]. With the binary transmission, the
number of information bits per symbol is one where each
bit is sampled once. After simulation we find an analytical
expression for the raw BER pb , by curve fitting,
pb = 0.5 e−12 S/N ,
where S/N is the SNR at the input of the envelope detector.
At this point it is worth noting that the BER resulting from
our AFE and OOK detector follows that of other non-coherent
detection schemes in that it is an exponential function of the
S/N, while the low SNRs are a result of the 80 MHz wide
band-pass filter on the input. Comparing to an optimal OOK
detector, operating on the same signal, the implementation loss
is about 11 dB. This is the price we pay to reduce the power
consumption of the WRx in the range of 20 dB compared to
the main receiver [11]. Further, the exponential relationship
between BER and S/N in (1) will carry through to our energy
analysis and optimization in Section VI, making the results
more general and valid for all non-coherent detection schemes
with the same type of BER relationship.
Since we have deliberately chosen to operate our WRx at
the same received power level as the main receiver sensitivity,
we will have to operate at very low SNRs on the input. In our
numerical examples we use a nominal raw BER of pb = 0.15,
operating at S/N = −10 dB. To compensate for these high
raw BERs, it is essential to find a WB structure that allows for
low-complex/low-power compensation in a digital base-band
(DBB) processing.
Fig. 5. Block diagram of a detector consisting of a matched filter (MF) and
a threshold unit.
Fig. 4. Wake-up beacon structure consisting of a length M preamble, and
length L destination/source addresses. The address bits are, in turn, spread
by a K bit sequence.
propose a design, based on the WB structure given above, and
develop analytical expressions for the detection performance
in terms of the WB detection and false alarm probabilities per
listen interval.3 The analytical expressions are later used to
analyze the WRx operating characteristic for different design
B. Wake-up beacon structure
A basic WB, as depicted in Fig. 4, should consist of a
preamble, a destination address, and a source address. The
M -bit preamble sequence, used to detect the presence of a
WB and for time synchronization, is selected to be the same
for all WBs. The preamble is followed by the L-bit destination
and source node addresses. The destination address is needed
to prevent power-up of other nodes, while the source address
is used in the destination address field of the WACK message.
A. Digital base-band design
During the listen interval, the front-end of the WRx delivers
its received signal in the form of a bit sequence, with a high
raw BER since we operate at lower received power than the
sensitivity level. The task of the digital base-band (DBB) is
to detect the presence of a WB in this bit sequence. We
We use matched filters (MFs) as the main building blocks
in our DBB, a very common approach to detect known
deterministic sequences in noise. The overall operation of a
detector unit is illustrated in Fig. 5. The incoming signal is
correlated with the known sequence and whenever the output
of the MF exceeds a certain threshold, the sequence is declared
to be present by the threshold device.
Figure 6(a) illustrates the proposed DBB design consisting
of two detector units and an address decoder. The detector
units contain a preamble matched filter (PMF) of length M
and an address-spreading matched filter (AMF) of length
K, respectively. This particular DBB structure with binaryinput matched filters can be implemented with very high
energy efficiency, similar to [25]. Initially the DBB can power
up only the PMF and search for the preamble to obtain
synchronization, since detecting address bits only makes sense
after synchronization is obtained. A WB/preamble may arrive
at any random time in the listening interval, which is twice
the time-extent of the WB M + 2 KL plus the time-extent of
the WACK message δ. The PMF can catch a complete WB
only if the WB arrives at a position i ∈ [0 M + 2 KL + δ],
as shown in Fig. 6(b). Note that, since the WACK is received
by the main receiver of the SN, no spreading needs to be
applied and therefore the WACK window is short compared
to the WB length. To simplify the analysis, we therefore set
δ = 0 in the remainder of this paper. With the unknown
arrival time i of the WB, the PMF may need to correlate the
incoming bit-sequence with all the possible arrival times of the
preamble, i ∈ [0 M + 2 KL]. The MF stops the correlation
whenever the PMF output exceeds the decision threshold and
announces that a preamble is detected. After the preamble
detection, the AMF and the address decoder are activated and
the remainder of the input sequence is fed to the AMF, where
the individual address bits are detected by correlating the bitsequence with the address-spreading. Knowing the position of
the preamble, the positions of the address bits in the sequence
are also known. Therefore, the AMF correlation only needs
to be performed once per address bit. Finally, the detected
bits are collected by an address decoder and compared against
2 Even if the choice of spreading code is less critical for the address bits,
some sort of pseudo-random code would be used in a real system to avoid a
DC level. In our simulations we use m-sequences.
3 Here we change from using the probability of miss, P WB , to using the
WB = 1 − P WB , since it will simplify the coming
probability of detection, PD
mathematical expressions.
As we mentioned previously, the WB is received by a high
BER front-end and nodes are not synchronized. Therefore,
to find an accurate starting-point of the WB and to achieve
low probabilities of miss and false alarm, the preamble needs
to provide both a processing gain and should be selected
from sequences with good auto-correlation properties. We have
chosen to generate the preamble using maximum-length shiftregister sequences (m-sequences). An important characteristic
of an m-sequence is the high peak auto-correlation function
while the off-peak values of the auto-correlation function
relative to the peak value are small [26]–[28]. For the address
bits we do not need good auto-correlation properties, but still
need a processing gain to compensate for the high BER. Each
bit in both the source and destination address fields is therefore
spread by an arbitrary K-bit code2 . The total number of bits
of both source and destination addresses, when spreading is
applied, is KL. In this work we select the same spreading,
K, for both the destination and source addresses. In principle,
however, the spreading can be different.
Additional fields can be attached to the WB to carry
information such as maximum number of WBs or the next
listen interval of the SN WRx [23], [29]. To keep the analysis
tractable, we disregard any such fields and focus on how WRx
performance is related to the WB parameters M , K, and L.
sions to derive closed form expressions for the WB detection
and false alarm probabilities.
Let us assume a binary symmetric channel, where the bit
errors at the OOK detector occur independently and with
probability pb , for instance given by (1). When the known
sequence is present on the channel, the probability P (n, W )
that n bits in the sequence of length W are detected correctly,
P (n, W ) =
(1 − pb )n pW
(a) Digital base-band (DBB) block-diagram with a detector for the
preamble, a detector for the address bits, and an address decoder.
Assuming that the arrival time of the sequence at the MF
is known, an MF detects the known sequence correctly with
ρ (γ) =
P (n, W ) =
(1 − pb )n pW
, (3)
if the number of correct bits n in the length W sequence
is above the threshold γ ∈ [0, W − 1]. When only noise is
present on the channel, the OOK detector generates random
bits with equal probability. Using (3), the probability that
the MF erroneously detects a non-existing sequence therefore
W 1 W X W
ν (γ) = ( )
(b) Illustration of a wake-up beacon (WB) arriving at time instant i
during a WRx listen interval.
Fig. 6. Block diagram of the proposed WRx digital base-band and an
illustration of the arrival of a wake-up beacon during a WRx listening interval.
the node address. If the detected address bits match the node
address, the main transceiver is powered up.
With the proposed architecture, the PMF and AMF are
identical in all nodes in the network. Only the address decoders
need to be programmed with the respective node addresses.
This leads to a very flexible WRx design, where the node
address-space is easily scaled without any major change of
the DBB. For instance, to change a network of 256 nodes to
a network of 8192 nodes, only the size of the address decoder
needs to be increased by 5 bits, while the PMF and AMF can
remain unchanged.
B. Detection Performance Analysis
After discussing the overall operation of the DBB, we move
on to characterization of the DBB in terms of WB detection
and false alarm probabilities. More precisely, the detection
probability PDWB is defined as the probability of successful
WB detection during one channel listening interval, when a
WB is indeed transmitted to the DN. The WB false alarm
probability PFA
is the probability of detecting either a WB
with an incorrect address or a non-existing WB, during a WRx
listening interval.
The outline of our analysis is as follows. Our DBB consists
of two MF-threshold units with slightly different parameters.
Therefore, we first express the detection performance of a
generic MF-threshold unit and then use these generic expres-
Now, lets continue with the detection performance of the
DBB, using the above generic expressions. A WB is declared
to be detected only if both the preamble and the node address
are correctly detected. The PMF and AMF outputs used
for detection are calculated using different parts of the bit
sequence and are therefore independent. Hence, the probability
PDWB of detecting a WB when it is present on the channel is
equal to the product of the respective detection probabilities
of the preamble and the address,
PDWB = PDpre PDaddr ,
where PDpre is the probability that the PMF detects the preamble correctly and PDaddr is the probability that the address
decoder correctly detects the node address. The DBB falsely
detects a WB if i) both the preamble and the address code are
falsely detected or ii) the preamble is correctly detected, but
the address decoder falsely detects an address which belongs
to another node. We define the WB interference level, α, as
the probability that a WB with an incorrect address is present
during the WRx listening. The probability PFA
that a WB is
falsely detected can therefore be calculated as
pre addr
PFA + α PDpre PeFA
where PFA
is the probability that the PMF falsely detects a
non-existing preamble, PFA
is the probability that a nonexisting address is erroneously detected as the correct one
by the address decoder, and PeFA
is the probability that the
address decoder falsely detects an address, which belongs to
another node, as its own.
Below we first detail how to calculate the preamble detecpre
tion performance PDpre and PFA
and then turn our attention
to the calculation of the node address detection performance
in terms of PDaddr , PFA
, and PeFA
When a WB is present on the channel during the WRx
listening interval, the preamble detection probability PDpre is
determined by three factors: i) the probability f (i) that the WB
arrives at time i, ii) the probability ρpre (γ1 ) of detecting the
preamble at the correct arrival time i, and iii) the probability
Ωpre (γ1 , i) of no erroneous detection of the preamble before
time i, where i ∈ [0 M + 2 KL] and γ1 ∈ [0 M − 1] is
the PMF threshold level. Considering all the possible arrival
times of the WB, we get
PDpre (γ1 ) =
M +2
[f (i) ρpre (γ1 ) Ωpre (γ1 , i)] .
Since the nodes are un-synchronized, the arrival time i of the
WB is unknown and it is reasonable to assume that all arrival
times are equally likely, i.e.,
0 ≤ i ≤ M + 2 KL.
M + 2K L
To calculate ρpre (γ1 ), we use (3) and substitute the preamble
length M and the threshold γ1 for W and γ. Assuming
ideal correlation properties and denoting the probability of a
preamble detection at an incorrect time instant by ν pre (γ1 ),
the probability Ωpre (γ1 , i) becomes
When there is no data available on the channel, the AMF
generates random address bits. Therefore the probability PFA
that the address decoder falsely announces that the correct
address is detected becomes
= ( )L .
Finally, it is likely that a WB which refers to another node
is falsely detected. To derive the expression for the probability
, we introduce q which refers to the number of bits that
the nodes own address differs from the address that belongs
to another node. Given q, the probability PeFA
is expressed
(γ2 )
To calculate ν pre (γ1 ), we assume that detecting a preamble at
incorrect timing is equivalent to detecting a preamble when no
data is available on the channel, since we assume ideal autocorrelation properties. Using (4), we substitute the preamble
length M and the threshold level γ1 for W and γ. Replacing
(8) and (9) back in (7) the preamble detection probability
PDpre (γ1 )
ρpre (γ1 )
M + 2K L
M +2
(1 − ν
(γ1 ))
The probability PFA
, that the PMF erroneously detects a
preamble when no data is available in the listening interval, is
equivalent to the probability that the number of random bits
that matches the preamble sequence goes above the threshold
γ1 at least once in the observation interval, i.e.,
(γ1 ) = 1 − (1 − ν pre (γ1 ))M +2 KL−1 .
As shown in (6), to calculate the detection performance
of the node address, we consider the operation of the AMF
together with the address decoder. The probability PDaddr of
detecting an address correctly in the address decoder is equal
to the probability that the AMF detects all individual address
bits correctly. Since the outputs of the AMF are uncorrelated,
being based on different parts of the bit sequence,
PDaddr (γ2 ) = (ρspcode (γ2 ))L ,
where ρ
denotes the detection probability of an address
bit and is calculated by substituting the spreading code length
K and the AMF threshold level γ2 ∈ [0 K − 1] for W and
γ in (3).
f (i) =
Ωpre (γ1 , i) = (1 − ν pre (γ1 ))i−1 .
/2L ρspcode (γ2 )
q i
1 − ρspcode (γ2 )
where Lq /2L is the probability that q bits are different in
randomly chosen L-bit addresses. The second factor is the
probability that the AMF detects the L − q matching address
bits correctly. The third factor represents the probability that
the q non-matching address bits are erroneously detected. We
approximate (14) using the fact that errors caused by a single
address bit error (q = 1) are the most likely,
1 − ρspcode (γ2 ) . (15)
(γ2 ) ≈ L ρspcode (γ2 )
The analysis below has been performed using both the exact
expressions (14) and the approximation (15), without noticeable differences in the results. For the sake of brevity, we only
present expressions based on the approximation.
Substituting (7) and (12) in (5) and (11), (13), (7), and (15)
in (6) we can calculate the WB detection and false alarm
probabilities. The calculation is a relatively straightforward,
but tedious, operation that results in
PDpre PDaddr
M +2KL
ρpre (γ1 )
(1 − ν pre (γ1 ))i−1
M + 2KL
(γ2 )
n M −n
(1 − pb ) pb
M + 2 KL n=γ
M +2
1 − ( )M
n K−n
(1 − pb ) pb
pre addr
PFA + αPDpre PeFA
1 − (1 − ν pre (γ1 ))M +2KL−1 ( )L +
M +2KL
ρ (γ1 )
(1 − ν (γ1 ))
M + 2KL
L spcode
(γ2 )
(γ2 )
!M +2KL−1
 ( 1 )L +
= 1 − 1 − ( )M
(1 − pb )n pM
M + 2KL n=γ
Fig. 7. Simulated and calculated receiver operating characteristics, ROCs,
!i−1 
M +2KL
for a wake-up beacon (WB) with a preamble of length M = 63, L = 8
n M −n
bit addresses and address spreading K = 15, for two different levels of WB
(1 − pb ) pb
interference, α = 1 and α = 0.1.
symmetric, the address bit threshold level is set to the midpoint
(1 − pb )n pK−n
2L n=γ n
of the range of possible outcomes, γ2 = dK/2e. Figure 7
shows two example ROCs for a WB with a preamble length
M = 63, address spreading length K = 15, and a network
(1 − pb )n pK−n
of 256 nodes (L = 8). The ROCs are for two levels of WB
With the above derivations, we have closed form expressions
for the WB detection performance. The rest of the paper
will focus on verifying the expressions and illustrating how
they can be used to analyze and optimize wake-up receiver
The analytical expressions for WRx detection performance
were derived for ideal correlation properties, while realistic
WBs will have a certain amount of auto-correlation. By
performing Monte Carlo simulations in MATLAB, using msequences both for WB preamble and address spreading we
obtain realistic values on WRx performance. By comparing
simulated and calculated receiver operating characteristics
(ROCs), we both verify the correctness of the analytical derivations and the validity of the ideal-correlation assumptions
made. To enhance understanding of the analytical results, we
also discuss the overall influence from parameters such as raw
BER, preamble length, address spreading length, and network
We simulate the behavior of the entire WRx signal chain,
detecting WBs, as specified in sections III and IV, for an
Additive White Gaussian Noise (AWGN) channel. In the
simulation we set the nominal raw BER pb to 0.15, based on
a front-end operating at S/N = −10 dB, cf. Fig. 3. The length
of the preamble M determines the sharpness of the peak at the
PMF output and thereby the preamble detection performance,
while the address spreading K determines the performance of
the address decoding by the AMF. We change the threshold
level γ1 ∈ [0, M − 1] of the PMF, both in the simulations
and in the analytical expressions, to evaluate the behavior of
the WRx for different choices. As the outputs of the AMF are
interference, α = 1 and α = 0.1. The analytical ROCs match
the simulated ones well, but there is a small difference that
can be seen in the upper right part of the curve with full WB
interference α = 1. The analytical expressions over-estimate
the false alarm probability somewhat in this region of low to
medium threshold levels. The best detection probability PDWB
of 0.97 is achieved for both cases at a decision threshold γ1
in the
of 0.76 with a resulting false alarm probability PFA
order of 10 − 10 . For lower or higher thresholds γ1 , the
most significant effect on the ROC is the reduced detection
probability. For low thresholds we find the incorrect preamble
position and for high thresholds we miss the preamble entirely.
That the false alarm probability stays below a certain value,
less than 10−2 in this example, for all thresholds is a result
of using the destination address to decrease overhearing.
In Fig. 7 we can see clear asymptotic behavior of the
analytic ROC for small and large threshold levels. By quantifying these, we simplify the interpretation of how different
parameters influence the overall WRx detection performance.
For high thresholds γ1 , the relationship between PDWB and
can be approximated as
α L(1 − ρspcode )
The rationale behind the approximation is that at high thresholds γ1 , we may miss preambles on the channel, but if they
are detected it is most likely in the correct position. Further, at
high thresholds, it is also very unlikely that we make a falsealarm if there is no preamble on the channel. Therefore (10)
collapses to PDpre (γ1 ) ≈ ρpre (γ1 ) and (11) to PFA
(γ1 ) ≈ 0,
which through (5) and (6) leads to (18). The scaling factor
in (18) depends indirectly on the raw BER and the address
spreading length, through ρspcode , while the size of the node
address-space L and the WB interference level α have direct
For low thresholds γ1 , the false alarm probability is, as
we mentioned, upper limited by the use of a destination
address in the WB. At very low thresholds the probability
of erroneously detecting a preamble is close to one
and the probability of detecting a preamble at its correct
position is very low. This essentially leads to entirely random
detection of address bits and the probability that the obtained
address matches the node address depends only on the size
of the address-space – the more address bits, the smaller the
probability. In more detail, at low thresholds, (11) collapses
to PFA
(γ1 ) ≈ 1 and the WB false alarm probability PFA
(6) can be approximated
≈ ( )L .
In Fig. 8 we illustrate the principal detection behavior, using
the asymptotes (18) and (19), together with corresponding
theoretical ROCs. For performance reasons the primary region
of interest is where we have high detection probabilities, as
indicated in the figure. The nominal design, with full WB
interference α = 1, is shown as a solid blue line. If, on the
one hand, the WB interference level is decreased, α < 1,
the number of false alarms for high thresholds reduces and
the left asymptote is shifted accordingly. As a result, the
dotted red ROC curve is obtained and the region of interest
increases. If, on the other hand, the detection probability of
address bits ρspcode decreases, we can see in (18) that the false
alarm probability for high thresholds increases. As a result,
the left asymptote is shifted to the right and the region of
interest becomes smaller. Note that a lower ρspcode is obtained
through shorter address spreading K and/or higher raw BER
pb , according to (3) with W = K. Reducing the number
of bits L in the address-space results in higher number of
false alarms for both low thresholds and high thresholds and
therefore both asymptotes are shifted accordingly. The region
of interest, however, increases as compared to the nominal
design. If we reduce the preamble length M the asymptotes
stay in place, but the detection probability decreases in the
region of interest and the dashed green curve is obtained. The
detection probability in the region of interest is also decreased
if the raw BER increases4 .
Above we provided a qualitative and quantitative understanding of how different parameters influence the detection
performance of the proposed WRx. We have done it by
discussing both the full ROC as well as the locations of highand low-threshold asymptotes.
By combining our detailed understanding of how detection
performance of the proposed WRx depends on different system
parameters with a cost function we can make optimal system
designs. Such a cost function will, for sensor networks, typically reflect energy consumption of individual nodes or of the
4 Note: A change in BER also affects the location of the left asymptote, as
described above.
Fig. 8. Illustration of the general properties of the receiver operating characteristic, ROC, for different design parameters, together with the asymptotes
in (18) and (19).
entire network. Assuming that the cost function J(θ) depends
on a number of parameters collected in θ and the permissible
range of parameters is D, the optimal system design is given
θ opt = argminJ(θ).
Most relevant cost functions related to energy will indirectly
depend on the ROC of the WRx, as derived above, since
detection performance has a fundamental impact on energy
consumption. Some of these mechanisms were briefly discussed in Section II.
A comprehensive optimization for an entire network is
a very complex task and therefore a topic that needs to
be covered separately. Therefore, to illustrate how the ROC
expressions can be used for WRx system optimization, we
have chosen a simplified case where we are only interested
in minimizing the energy used by the source node, SN, to
wake up the destination node, DN. When doing this, we
also assume that the total energy required at the SN to
transmit a WB is proportional to the received WB energy
at the DN. The proportionality factor includes transmitter
efficiency, propagation losses, etc. These assumptions result
in a tractable optimization where we find the optimal WB
parameters, preamble length M and address spreading K, for
different number of address bits L and raw BERs pb .
Our cost function can be expressed in terms of the energy
required to transmit a single WB, EWB , and the average
number of WBs, η̄, needed to activate the DN, according to
J(θ) = EWB (θ) η̄(θ),
where θ contains WB parameters we optimize, M and K. In
the sequel we will suppress θ in our expressions.
With the front-end characteristic from (1) the transmitted/received energy per bit is proportional to − ln(2 pb ). As
we already indicated in Section III, this expression will be the
same for all non-coherent schemes where the raw BER is an
exponential function of the S/N at the receiver input and the
following optimization is therefore valid for all schemes in
that class. With this proportionality, the total energy needed
to transmit a single WB with a length M preamble and two
L bit addresses spread by a factor K is
EWB ∝ − ln(2 pb ) (M + 2 KL).
We will not optimize the sleep time of the WRx, as was
done in [12], and simply assume a constant activity factor
where the listen period is a constant fraction of the entire
sleep-listen cycle. Through this, there will always be a fixed
number of WBs per sleep-listen cycle, independent of WB
length. Therefore, the average number of WBs transmitted
before a successful wake-up, η̄, is proportional to the average
number of sleep-listen cycles, i.e.
η̄ ∝ 0.5 + PDWB
k (1 − PDWB )k
Fig. 9. Optimal wake-up beacon (WB) length vs. OOK raw BER, for addressspaces of size 4, 8 and 16 bits.
− 0.5,
which is a result of random starting times, due to asynchronous
communication, and a probability PDWB of detecting the WB
during the listen interval. The proportionality factor is the, in
our case fixed, number of WBs per sleep-listen cycle.
Replacing (22) and (23) back in (21), the total energy cost
J ∝ − ln(2 pb ) (M + 2 KL)
The optimization parameters M and K influence the total
energy through two contradicting mechanisms. Increasing M
and K will increase the energy required per transmitted WB,
while, at the same time, it decreases the number of WBs
required to activate the DN. The balance between these two
mechanisms is what our analytical framework provides, in this
case, through (16).
Let us move on to numerical optimization of the preamble
length M and address spreading K to minimize the energy
cost (24) for different raw BERs pb , for three different sizes
of the address-space, namely 4, 8 and 16 address bits. To cover
both the reported BERs of the WRx designs in Table I and
our choice to use low-power/low-performance front-ends, we
perform the optimization for BERs from 0.001 to 0.3. For
these parameter ranges, with discrete parameter values, we
resort to a quite tractable exhaustive search for 30 values on
BER between 0.001 and 0.3. Figure 9 shows the optimal WB
length, resulting from the optimal choices of M and K. At
low BERs, there is no address spreading (K = 1) and only
a short preamble is used to obtain synchronization. When the
BER increases beyond a certain point, the WB length increases
sharply, since additional WB transmissions due to misses are
more costly than increasing the WB length. Both preamble
length and address spreading are increasing rapidly, but the
influence from increases in address spreading changes are
more visible, since its influence on the WB length is magnified
by the number of address bits.
It is quite natural that increasing BERs lead to longer WBs,
in general terms, since detection of them becomes increasingly
difficult. However, the relationship between BER and optimal
WB length is more intricate than that. Perhaps somewhat
counter-intuitively, there are also examples of increasing BERs
leading to shorter optimal WB-length. Several examples of
this can be seen in Fig. 9, especially for the 4-bit address
case where the shorter WB lengths make them more visible.
In these cases, even if shorter WBs mean lower detection
probability and a higher average number of WBs need to be
transmitted, the total cost becomes smaller for a shorter WB
since it requires less transmission energy.
The cost function we are using in this paper measures
the required transmit energy and, as such, it only depends
on the detection probability part of the ROC. The detection
probabilities resulting from the optimization are shown in
Fig. 10(a). The detection probability has a tendency to decrease with increasing BERs, but adjustments of WB length
in the optimization brings it back up again when this is
favorable from a transmission energy point of view. The largest
variations can be seen in the transition regions of BERs where
the WB length starts to increase rapidly, as we observed in
Fig. 9. The generally shorter WBs for smaller address spaces
also lead to the fact that transmission of additional WB due
to a miss in the WRx is less costly. Hence, we see that lower
detection probabilities can be optimal, from a transmit energy
point of view, for smaller address spaces.
False alarm probabilities do not influence our cost function,
but the ROC relation implicitly gives us certain false alarm
values. These are related to other energy costs in the network,
due to unnecessary wake-ups. It is therefore of interest to
study these probabilities as well. The false alarm probabilities
resulting from the optimization are shown in Fig. 10(b). We
can see that they are about 5-10 times lower than the upper
asymptote (19) we derived for the ROC (solid line above each
curve). For reasonably large address-spaces, the false alarm
rates are at very low levels and unnecessary wake-ups should
not have a large impact on the total energy consumption of the
network. A detailed analysis of these influences is both nontrivial and requires more detailed and complete information
about how energy consumption relates to the optimization
parameters. While important, this analysis is beyond the scope
WB ) vs. OOK raw BER.
(a) Probability of detection (PD
Fig. 11. Optimal wake-up beacon (WB) transmit energies, per wake-up, for
different raw BERs and address-spaces of size 4, 8 and 16 bits. Energies are
normalized to the minimal energy for the smallest 4-bit address space.
quite small.
Since we aim at using the same transmitter and the
same transmit power both for data and wake-up, our lowcomplexity/low-power WRx will operate at high raw BERs,
and in this context the most interesting part of the energy
curves is at high BERs. The nominal BER in our WRx design
is therefore set to 0.15 , as discussed in Section III, and the
additional Tx energy cost as shown in Fig. 11 is only around
2-3 dB. This relatively small additional cost in transmit energy
for the SN should be compared to the roughly two orders of
magnitude power savings estimated on the WRx side for all
nodes in the network.
WB ) vs. OOK raw BER. The solid line
(b) Probability of false alarm (PFA
above each curve is the corresponding upper asymptote (19).
Fig. 10. Optimal probability of detection and the corresponding probability of
false alarm, resulting from the optimization, vs. OOK raw BER, for addressspaces of size 4, 8 and 16 bits.
of this paper.
Finally, let us study the optimal transmission energy cost,
per wake-up, as a function of raw BER. Since we only know
the energy cost up to proportionality, as detailed in (24),
we present the normalized optimal WB transmit energies in
Fig. 11, for the three investigated address-space sizes. The
normalization is with respect to the minimal energy cost for the
smallest, 4-bit, address space. For all three address-spaces, we
can see that the 10−3 BER used as a reference level in previous
studies, cf. Table I, is not the optimal point of operation when
using the duty-cycled wake-up scheme studied in this paper.
The optimal BER is closer to 10−2 for all three addressspaces and larger address-spaces tend to have a slightly lower
optimal BER. When raw BER is lower than the optimal one,
the increased transmit power required to lower the BER is
larger than the corresponding shortening of the WB, resulting
in a higher total energy cost. The differences are, however,
The goal of this paper has been to provide an analysis
framework for duty-cycled low-complexity/low-power wakeup receiver schemes, which can be used for design optimization. We perform a complete system-level analysis based on
a proposed wake-up beacon structure and the corresponding
WRx architecture. The analysis first leads to closed form
expressions for detection and false alarm probabilities, as well
as qualitative and quantitative understanding of how detection
performance relates to changes in design parameters. This
understanding of detection performance is fundamental to
system-level analysis and optimization of energy consumption.
Such an optimization can be done in many different ways,
depending on what the ultimate goal is. For instance, it is quite
possible to minimize the total power consumption of an entire
network, given that we have access to detailed enough information about how energy consumption is related to different
design parameters. With limited space we chose to focus on
how the detection performance expressions can be used for an
optimization of wake-up beacon transmit energy. This means
that the presented optimizations are only related to the transmit
energy of the source node. While somewhat limited in its
scope, the optimization led to several important observations
regarding the transmit energy required to successfully activate
a destination node. The trade-off between increasing transmit
power and the use of longer beacons becomes evident and a
combination of both is required to minimize transmit energy
related to WBs at the SN. Based on a specific analog front-end
and OOK detection scheme, we also showed that the obtained
optimization results are more general and valid for all schemes
with an exponential relationship between signal-to-noise ratio
and bit-error rate.
In more detail, our analysis shows that it is quite possible to
use duty-cycled low-complexity/low-power wake-up receivers,
with roughly two orders of magnitude less power consumption
in the WRx of all nodes in the network, while allowing the
transmitter to use the same transmit power for both wake-up
beacons and data. To achieve this, at our chosen nominal raw
BER of 0.15, we need to transmit longer beacons than those
that give minimal transmit energy. The increase in transmit
energy per wake-up is, however, quite moderate at a level of
about 2-3 dB for the studied address-space sizes and only
applies to the source node.
While analysis and optimization of wake-up beacon transmit
energy is performed in detail in this paper, the true value of
the analysis framework is that it can be used as a basis for
detailed studies and optimization of the energy consumption
of entire networks, where other energy models are used. The
nature, level of detail, and the particular energy costs taken
into account in these depend on the intended application.
The analysis framework should also be used to extend the
optimization beyond parameters used in this paper. One such
example is finding the optimal sleep/listen cycle, along the
lines of [12].
Other interesting extensions of the analysis framework is
to include more realistic channel models and interference
scenarios. As long as we know the relation between SNR
and the raw BER on our channel, we can apply the analysis
performed in this paper. The only modification needed is
to replace (1) with the particular relationship applying to
the analyzed channel. While self-interference from the own
network is included in the presented analysis, more generic
interference types can be included by either adjusting the noise
level in the BER expressions or providing a more detailed
interference analysis where the properties of the interference
signals are more realistic.
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