Journal of Signal Processing, Vol.27, No.4, pp.

111-114, July 2023

SELECTED PAPER AT NCSP'23

Stochastic Resonance Assisted Successive Interference Cancellation Receiver

for Signal Detection Performance Improvement

Yuta Tomida, Hiroyuki Hatano, Kosuke Sanada and Kazuo Mori

Graduate School of Engineering, Mie University

1577 Kurimamachiya-cho, Tsu, Mie 514-8504, Japan
E-mail: { yuta.tomida@com., hatano@, k.sanada@, kmori@ } elec.mie-u.ac.jp

Abstract scheme for future 5G [2]. NOMA is an intra-cell multiuser

In the 5th-generation mobile communication system (5G), a multiplexing scheme that intentionally utilizes nonorthogo-
multiuser multiplexing scheme, nonorthogonal multiple ac- nality in either the time, frequency, or code domain. The im-
cess (NOMA), has been proposed to accommodate the mas- portant difference between NOMA schemes and conventional
sive connectivity in wireless communication systems. By orthogonal multiple access (OMA) schemes is that multiple
nonorthogonality, NOMA allows the use of a new domain users are not divided by orthogonal resources. OMA schemes
that is ineffectively utilized in conventional orthogonal mul- remove the effect of interference between user signals by allo-
tiple access (OMA) schemes. In power-domain NOMA (PD- cating orthogonal resources to multiple users. Time division
NOMA), user signals are allocated different power levels and multiple access (TDMA), frequency division multiple access
multiplexed by superposition coding at a transmitter. NOMA (FDMA) and code division multiple access (CDMA) are ex-
employs interference cancellation schemes such as succes- amples of OMA schemes that allocate orthogonal resources,
sive interference cancellation (SIC) at receivers to avoid in- i.e., time, frequency and code, to multiple users, but they do
terference between the signals. The use of nonlinear systems not have the spectral efficiency to achieve the 5G require-
such as low-resolution analog-to-digital converters (ADCs) ments.
is favorable in terms of energy consumption since the load On the other hand, multiple users could be served with
of SIC processes increases proportionally to the number of a single orthogonal resource in NOMA schemes. By
users. However, on the other hand, the use of nonlinear sys- nonorthogonality, NOMA allows the use of a new domain
tems leads to the degradation of signal detection performance. that is ineffectively utilized in OMA schemes. There are
Stochastic resonance (SR) is a nonlinear phenomenon that two types of NOMA scheme; power-domain NOMA (PD-
improves the response of nonlinear systems to weak power NOMA) and code-domain NOMA (CD-NOMA)[3]. In this
signals. In this paper, we propose the application of SR to the paper, we focus on PD-NOMA, which serves multiple users
nonlinear system in SIC. Through computer simulations, we at the same time, frequency, or code by using the power do-
show that the proposed method can improve the signal detec- main, i.e., different power levels. In PD-NOMA, the user
tion performance without losing the advantage of low energy signals are allocated different power levels and multiplexed
consumption. by superposition coding at the transmitter. Compared with
OMA schemes, PD-NOMA provides much higher connectiv-
1. Introduction ity because it can serve multiple users simultaneously with a
The rapid development of wireless mobile communication single orthogonal resource.
and internet services necessitates new mobile and wireless In contrast to OMA schemes, NOMA schemes require
communication systems that will be able to support 10 to 100 countermeasures against interference between the user sig-
times more connected devices [1]. As a new global wireless nals because of the nonorthogonality due to sharing the same
standard, there is the 5th generation mobile communication orthogonal resources. Users are not able to obtain their de-
system (5G) whose research and operation has already be- sired user signals buried in the interference comprising other
gun. There are the three following requirements in 5G: (1) en- user signals having higher power. Dealing with the prob-
hanced mobile broadband (eMBB), (2) ultrareliable and low- lem caused by the occurrence of interference, NOMA sys-
latency communication (URLLC) and (3) massive machine- tems employ multiuser detection schemes such as successive
type communication (mMTC). interference cancellation (SIC) at the receivers. The basic
To accommodate the continuous growth in data traffic and concept of SIC is to successively decode the superposed sig-
the number of wireless users, nonorthogonal multiple access nals in order of signal power levels. SIC removes the signals
(NOMA) has been proposed as an effective multiple access having higher power regarded as interference and obtains the

Journal of Signal Processing, Vol. 27, No. 4, July 2023 111

desired user signal with the signals having lower power be- 𝐔𝐔𝐄𝐄𝟏𝟏
Power 𝒚𝒚𝟏𝟏 (𝒕𝒕) 𝐔𝐔𝐄𝐄𝟐𝟐
ing regarded as noise. Because of the operation principle of 𝒚𝒚𝟐𝟐 (𝒕𝒕)
𝒑𝒑𝟏𝟏
SIC, the number of SIC processes increases proportionally to 𝐔𝐔𝐄𝐄𝒋𝒋
the increase in the number of user signals. That is, when the 𝒚𝒚𝒋𝒋 (𝒕𝒕)
𝒑𝒑𝒋𝒋
desired user signal is allocated the weakest power, the user
must decode all signals superposed in the multiplexed signal. 𝒚𝒚𝑱𝑱 (𝒕𝒕)
𝒑𝒑𝑱𝑱 𝐔𝐔𝐄𝐄𝑱𝑱
Therefore, depending on the internal system configuration of Time, Frequency, Code BS
SIC, explosive increases in processing load and energy con-
sumption might occur. Figure 1: Wireless downlink PD-NOMA network model
An analog-to-digital converter (ADC) is a device that con-
cussed in Sect. 2. The conditions of the simulations are dis-
verts an analog signal, which is continuously variable, into
cussed in Sect. 3. Through computer simulations, the im-
a multilevel digital signal, which is discrete. The ADC
provement of the signal detection performance of the SIC
power consumption increases exponentially with the number
with the nonlinear system by the proposed method is con-
of ADC resolution bits [4], i.e, using a high-resolution ADC
firmed. In comparison with the linear system, the proposed
might lead to an explosive increase in the energy consumption
method shows the same performance. In comparison to the
of the SIC system. Therefore, using low-resolution ADCs is
conventional scheme of weak signal detection, the proposed
favorable to save the energy consumption of the SIC system.
method shows higher performance. These results indicate
On the other hand, the use of low-resolution ADCs might that it is possible to improve the signal detection performance
lead to degradation in signal detection performance, since of the proposed method without losing the advantage in en-
low-resolution ADCs are unable to detect signals weaker than ergy consumption.
the resolution. Consequently, multiplexing more user sig-
nals in PD-NOMA, i.e., allocating more power level varia- 2. System Model
tions, using high-resolution ADCs is desirable. At the same
A wireless downlink PD-NOMA network model is shown
time, supposing that the signal detection performance of low-
in Fig. 1, in which a base station (BS) is transmitting a multi-
resolution ADCs could be improved, there is a possibility of
plexed signal modulated by BPSK towards J user equipments
saving the energy consumption of the SIC system. In this
(UEs). UE1 is the farthest and UEJ is the nearest to the BS.
paper, the linear system, which behaves continuously, is as-
Each user signal is allocated a different power level on the ba-
sumed for the high-resolution ADC and the nonlinear system,
sis of its distance from the BS. Additive white Gaussian noise
which behaves discretely, is assumed for the low-resolution
assuming is added to the multiplexed signal as the channel
ADC.
noise.
Stochastic resonance (SR) is a nonlinear phenomenon that The received signal yj (t) (j = 1, 2, ..., j, ..., J) at UEj can
improves the response of nonlinear systems to weak input sig- be given as
nals [5]. The effects and principles of SR have been studied
J
∑
and confirmed in various fields, from biology to physics and
engineering. SR enables nonlinear systems to detect weak yj (t) = hj sj (t) + nj (1)
j=1
subthreshold signals by intentionally adding a noise signal √
√
that raises the weak signals to above-threshold signals ran- sj (t) = pj xj (t) = P αj xj (t) (2)
domly. However, SR has a limitation in its implementation,
where hj is the channel coefficient, sj (t) is the transmitted
as the tuning of the added noise intensity is required for it to
signal, nj is the channel noise with mean 0 and variance σ 2 ,
be effective. To overcome this limitation, ways to adjust the
pj is the signal power, xj (t) is the transmitted data, P is the
noise intensity, e.g., adaptive SR [6] and parallel SR [7], have
total of transmit power and αj is the allocated power factor
been developed.
for UEj .
In this paper, we propose the application of SR to the non- The transmitted signal sj (t) is modulated using BPSK as
linear system in SIC. To reveal the possibility of saving the
energy consumption of SIC systems, we evaluate the perfor- sj (t) = Aj cos(2πfc t + ϕj ) (3)
{
mance of the SIC with the nonlinear system incorporating Aj cos(2πfc t + 0)
SR. The performance of four-user PD-NOMA is evaluated =
Aj cos(2πfc t + π)
in terms of bit error rate versus signal-to-noise ratio (SNR) {
for the baseband binary phase shift keying (BPSK) modula- Aj (xj = 0)
tion scheme. We aim to reveal the possibility of saving the =
−Aj (xj = 1)
energy consumption of the SIC system by using the nonlin-
√
ear systems as low-resolution ADCs and SR. BER curves are where Aj = pj is the signal amplitude, fc is the carrier
computed through simulations with the system model, as dis- frequency and ϕj is the phase.

112 Journal of Signal Processing, Vol. 27, No. 4, July 2023

 SR 𝒚𝒚𝒋𝒋𝑺𝑺𝑺𝑺 Nonlinear system resenting a portion of the interference that remained uncan-
𝒚𝒚𝒋𝒋 Demodulator ෞ𝟏𝟏
𝒙𝒙
system Input
Detecting 𝒔𝒔𝟏𝟏
−𝜼𝜼 celled.
+𝜼𝜼
+ x�j is estimated by the demodulator as
－ Regenerating 𝒔𝒔𝟏𝟏 𝝃𝝃𝟏𝟏 𝟏𝟏
・
(𝒋𝒋−𝟏𝟏) (𝒋𝒋−𝟏𝟏)
𝒚𝒚𝒋𝒋 𝒚𝒚𝒋𝒋𝑺𝑺𝑺𝑺 ( )
・
𝒚𝒚𝒋𝒋
(𝟏𝟏) Output
・・・

𝑲𝑲
・
(j−1)
𝒋𝒋−𝟏𝟏 −𝜼𝜼 Scaled x�j = sgn yjSR (9)
(𝒋𝒋−𝟏𝟏) SR 𝒚𝒚𝒋𝒋𝑺𝑺𝑺𝑺 +𝜼𝜼  ( )
𝒚𝒚𝒋𝒋 Demodulator 𝒙𝒙ෝ𝒋𝒋
system  (j−1)
Detecting 𝒔𝒔𝒋𝒋 ( ) +1.0 yjSR > 0
Intentional noise 𝝃𝝃𝑲𝑲 (j−1)
sgn yjSR = ( ) (10)
(a) Multiuser SIC system (b) SR system 
−1.0 (j−1)
yjSR ≤ 0
Figure 2: Receiver model of proposed method at UEj
(j−1) (j−1)
where yjSR is the signal yj detected by the SR system.
Idealizing Eq. (1) with hj = 1 at the baseband, Eq. (1) can
also be given as 2.2 SR system
J
∑ In the SR system shown in Fig. 2(b), we employ parallel
yj = Aj cos(ϕj ) + nj (4) SR, which is proposed to optimize the response of nonlin-
j=1 ear systems without noise tuning [7]. As a low-resolution
ADC, we assume that the nonlinear system has the threshold
Therefore, the SNR of the received signal can be given as η. First, the SR system parallelizes the received signal into
( )2 K units. Before passing through the nonlinear system, the
∑J
intentional noise ξk with mean 0 and variance σSR 2
= 1 is
Aj cos(ϕj )
j=1 added to the received signal. ξk must be independent of the
SN R = (5) other units. The output of the SR system is the average of K
σ2
parallelized units.
The received signal is detected and demodulated at each
receiver of UEj using the SIC. The receiver model of the pro- (The input 窶登 ) utput characteristic of the nonlinear system
(j−1)
posed method at UEj is shown in Fig. 2. Figures 2(a) and h yj + ξk can be given as
2(b) show the multiuser SIC and SR systems, respectively. In  ( )
(j−1)
the proposed method, by applying SR before each demodula- 
 +1.0 yj + ξk > +η
( ) 

tion, it is possible to detect weak signals below the threshold (j−1) ( )
(resolution) of the nonlinear systems. h yj + ξk = −1.0
(j−1)
yj + ξk < −η (11)




2.1 Multiuser SIC system 0 otherwise
In the multiuser SIC system shown in Fig. 2(a), the signals The output of the SR system is input to the demodulator.
having higher power than the desired user signal are regarded
as interference and the signals having lower power than the 3. Simulation Results
desired user signal are regarded as noise. As the UE1 signal
is demodulated, it is subtracted from the multiplexed signal We evaluate the performance of the proposed method
before the next UE2 signal is detected. In this way, UE de- through computer simulations. The simulation parameters
modulates the signals having higher power and regenerates were set as shown in Table 1. The power factors empirically
replica signals to cancel them successively. determined to be sufficient for the communication by other
(j−1) simulations were set as shown in Table 2. In the simulations,
The signal yj after j − 1 interference cancellation at
we assume four users (J = 4), idealize hn as 1, and do not
UEj can be given as
consider channel conditions, e.g., Rayleigh fading.
J
∑ j−1
∑ First, we evaluate the proposed method in comparison with
(j−1)
yj = hj s j + nj − s�j (6) SIC a the linear system having the threshold η = 0. In this
j=1 j=1 simulation, we assume a linear system as the high-resolution
= hj sj + nj (7) ADC. Figure 3 shows the BER performance of SIC with each
J j−1 j−1 type of system. In Fig. 3, the proposed method shows almost
∑ ∑ ∑
+ hj s j + hj sj − s�j the same BER performance as the linear system. This result
j+1 j=1 j=1 is due to the enhancement of signal detection. By applying
= hj sj + nj + Ij + γj , (8) SR, the nonlinear system is able to detect weak signals with
the help of the intentionally added noise.
where Ij is the signal having lower power than sj and re- Second, we evaluate the proposed method in comparison
garded as interference noise, and γj is the residual noise rep- with the conventional method. In this simulation, we assume

Journal of Signal Processing, Vol. 27, No. 4, July 2023 113

 Table 1: Simulation parameters
BPSK signal s ∈ {−1, +1}
Threshold of nonlinear system, η 1
Total number of transmitted data 1 × 106
Total transmit power P 10
Number of parallel SR units, K 1 × 103

Table 2: Allocated power factor αj for UEj

Number of users j αj
1 0.81225 Figure 3: BER performance of SIC (symbols : nonlinear system;
2 0.169 lines : linear system)
3 0.012638
4 0.002356

weak signal detection by using power amplifiers that amplify

the weak signals as the conventional method. The amplifica-
tion gain G was set to 50, which was determined to be suffi-
cient for detection by other simulations. Figure 4 shows the
BER performance of SIC with the nonlinear system on apply- (a) Strong signals (UE1 , UE2 ) (b) Weak signals (UE3 , UE4 )
ing each method. Figure 4(a) and 4(b) show the performance Figure 4: BER performance of SIC with nonlinear system
of the UEs that receive signals above the threshold (UE1 and
UE2 ) and below the threshold (UE3 and UE4 ), respectively. tection with a nonlinear system and contribute to saving the
In Fig. 4, the proposed method shows higher performance at energy consumption of SIC systems.
all UEs. This is a result of the enhancement of signal detec-
tion by applying SR, as discussed above. Furthermore, as a References
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4. Conclusion
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114 Journal of Signal Processing, Vol. 27, No. 4, July 2023