Error Performance of Wireless Powered
Cognitive Relay Networks with Interference

arXiv:1712.04744v1 [] 13 Dec 2017

Alignment

Sultangali Arzykulov∗ , Galymzhan Nauryzbayev, Theodoros A. Tsiftsis∗
and Mohamed Abdallah‡
∗
‡

School of Engineering, Nazarbayev University, Astana, Kazakhstan

Division of Information and Computing Technology, College of Science and Engineering,
Hamad Bin Khalifa University, Qatar Foundation, Doha, Qatar
Email: {sultangali.arzykulov, theodoros.tsiftsis}@nu.edu.kz,
nauryzbayevg@gmail.com, moabdallah@hbku.edu.qa
Abstract
This paper studies a two-hop decode-and-forward underlay cognitive radio system with interference
alignment technique. An energy-constrained relay node harvests the energy from the interference signals
through a power-splitting (PS) relaying protocol. Firstly, the beamforming matrices design for the
primary and secondary networks is demonstrated. Then, a bit error rate (BER) performance of the system
under perfect and imperfect channel state information (CSI) scenarios for PS protocol is calculated.
Finally, the impact of the CSI mismatch parameters on the BER performance is simulated.
Keywords
Decode-and-forward (DF) relaying, energy harvesting (EH), cognitive radio (CR), interference
alignment (IA), wireless power transfer, bit error rate (BER).

I.

I NTRODUCTION

C

OGNITIVE RADIO (CR) has attracted a significant attention by being an intelligent
technology that can utilize radio spectrum and increase the spectral efficiency in wireless

networks [1]. The main idea of CR is to provide secondary users (SUs), which are unlicensed
nodes, with possibility to communicate in a licensed spectrum on the condition that primary
users (PUs) should not receive harmful interference [1], [2]. There are three types of spectrum
sharing CR paradigms, namely, interweave, underlay and overlay [1]. The interference mitigation
at receivers can be managed by a promising technique named interference alignment (IA). IA
provides free signaling dimensions by aligning the interference into one subspace [3], [4]. IA can
be also applied in CR to cancel interference at primary and secondary receivers. A mitigation of
the severe effect of interference at primary receivers allows secondary transmitters to increase
their transmit power which consequently leads to an improvement of the performance of the
secondary network (SN) [5]. In [6], degrees of freedom (DoFs) of the network were increased
by implementing an IA technique in a multiple-input multiple-output (MIMO) relay CR.
Another promising technique, known as energy harvesting (EH), which harvests energy from
ambient signals through time-switching (TS) and power-splitting (PS), was introduced in [7], [8].
IA and simultaneous wireless information and power transfer (SWIPT) in MIMO networks were
jointly studied in [9], where an improvement of the performance of the network was analyzed
through a dynamical selection of users as EH or information decoding (ID) terminals. The EHbased CR network was studied in [10], where authors developed a spectrum sensing policy in TS
mode to guarantee EH possibility for SUs from primary signals. An identical system was studied
in [11], where an optimal information and energy cooperation methods between primary and
secondary networks was investigated. Finally, the work in [12] represented a resource allocation
method in EH-based CR network with imperfect channel state information (CSI) cases.
In this paper, we study an underlay IA-based CR with an energy-restricted relay operating
in PS mode. The performance of both the primary network (PN) and SN after interference
mitigation is analyzed. In particular, a bit error rate (BER) performance of the proposed system
model is calculated for PS relaying protocol under different imperfect CSI cases.

II.

S YSTEM M ODEL

The proposed system model is composed of a PN with two pairs of PUs and a SN with three
SUs. Each primary transmitter (Ti ) transmits to its corresponding receiver by interfering with
another primary receiver (Rj ) and relay as shown in Fig. 1. The SN is composed of a source
(S), a relay (R) and a destination (D) nodes. An energy constrained R operates in decode-andforward (DF) half-duplex mode by relaying the signal from S to D in two time periods. R
uses harvested energy from interference signals as its transmit power, while S and D supplied
with stationary power sources. Also, it is assumed that D is located far from PN and does
not receive any interference. All nodes of the network are assumed to have MIMO antennas.
We also assume that all interference at Rj are canceled by IA technique, thus, S and R are
not restricted by the level of transmit power. Another assumption is that the channels remain
constant during a transmission block time T , but vary independently from one block to another.
The definition of channel links between nodes can be denoted by the next. For channels of PN
[k]

nodes, Hj,i ∈ CNj ×Mi , ∀i, j ∈ {1, 2} denotes the channel between Rj and Ti , where superscript
k indicates a certain time period when the data transmission occurs. Nj and Mi are the numbers
of antennas at Rj and Ti , respectively. For channels of SN nodes, HR,S and HD,R denote the
channel links related to the S-R and R-D transmissions while the inter-network channels are
given by Hj,R ∈ CNj ×NR , Hj,S ∈ CNj ×NS and HR,i ∈ CNR ×Mi , where NS , NR and ND denote
the numbers of antennas at S, R and D, respectively. Each entry of any matrix H is assumed to
be independent and identically distributed (i.i.d.) random variables according to CN (0, 1), where
CN (0, 1) denotes the complex normal distribution with zero mean and unit variance. Also, note
that each channel link is characterized by the corresponding distance and path-loss exponent
denoted by dm,n and τm,n , ∀m ∈ {1, 2, R, D}, ∀n ∈ A = {1, 2, S, R}, respectively. We assume
that each node is deployed with N antennas (Mi = Nj = NS = NR = ND = N) and IA is
exploited at R and Rj , accordingly. Therefore, each transmit node l with the power Pl employs
a precoding matrix Vl ∈ C(Ml

or Nl )×fl

, with trace{Vl VlH } = 1, ∀l ∈ A, where fl is the number

of the transmitted data streams. Then, each receive node, except D, employs the interference
suppression matrix Ut ∈ CNt ×ft , ∀t ∈ {1, 2, R}, where ft is the number of data streams that
needs to be decoded at the corresponding receiver. Thus, the received signal at Rj , in two time

N1

1

1

...

...

M1

...

T2

1

...

T1

1

M2

N2
NR

1

1

R1
PN
R2

1

...

S

R

...

...
D

SN

ND

NS

Intra-network interference

direct links

Inter-network interference

Fig. 1. IA and EH-based CRN with two PUs and one SU sharing the spectrum simultaneously.

periods, can be written as
s
s
P
Pi [k]H [k] [k]
j
[k]
[k]H [k] [k]
[k]
+
A[k]
Hj,j Vj sj +
Hj,i Vi si +ñj , k ∈ {1, 2}, (1)
yj =
τj,j Uj
τ U
|{z}
dj,j
dj,ij,i j
{z
} interference from SN |
{z
}
|
interference from PN, i 6= j

desired signal

[k]

[k] H

where the effective noise term ñj = Uj
[k] [k]H

(AWGN) vector, with E{ñj ñj

[k]

nj is a zero-mean additive white Gaussian noise

} = σñ2 j I, where E{·} denotes an expectation operator. More-

over, we have E{sl sH
l } = I, with l ∈ A, since sl is assumed to be a vector consisting of symbols
generated as i.i.d. Gaussian inputs. Finally, interference from SN to Rj can be determined as
r

[k]H
PS


 dτj,S Uj Hj,S VS sS , if k = 1,
j,S
A[k] = r
(2)

[k]H
P

R

 dτj,R Uj Hj,RVR sR , if k = 2.
j,R

The received signal at R, within transmission period of S-R, can be written as
s
s
2
PS H
Pi X H
[1]
UR HR,i Vi si +ñR ,
yR =
τR,S UR HR,S VS sS +
τR,i
dR,S
dR,i i=1
{z
} |
{z
}
|
desired signal

(3)

interference from PN

where ñR = UH
R nR is the effective noise after interference suppression beamforming at the

relay.
Then, R decodes and forwards the desired signal sS to D within R − D transmission period.
Thus, D obtains the following signal
yD =

s

PR
τD,R HD,R VR sR + nD ,
dD,R

(4)

2
where nD is the AWGN vector, with E{nD nH
D } = σD I.

The interference in receive nodes can be assumed to be completely canceled if the following
conditions are satisfied for Rj as [13], [14]
[k]H

[k]

[k]

Hj,i Vi = 0, ∀i, j ∈ {1, 2}, ∀i 6= j,


Hj,S VS , if k = 1,
[k]H [k]
[k]
Uj J = 0, where J =

H V , if k = 2,
j,R R


[k]H [k] [k]
rank Uj Hj,j Vj = fj , ∀j ∈ {1, 2},

Uj

(5a)
(5b)

(5c)

and for R as
[1]

UH
R HR,i Vi = 0, ∀i ∈ {1, 2},

rank UH
R HR,S VS = fS .

(6a)
(6b)

A. Beamforming Design
If the space of the desired signal is linearly independent from that of the interference signal,
then the desired signal can be easily decoded from the received one. Hence, the design of
precoding matrices should be in such a way that interference in all receivers need to span to
one another. Thus, in the first time period, the interference at R1 , R2 and R can be spanned as






[1]
[1]
[1]
[1]
[1]
span H1,2 V2 = span (H1,S VS ), span H2,1 V1 = span (H2,S VS ) and span HR,1 V1 =


[1]
span HR,2 V2 , respectively, where span(X) is the vector space spanned by the column vectors
[1]

[1]

of X. After spanning all interference, the precoding matrices V1 , V2 and VS can be obtained

as [15]
[1]

[1]

V2 = (HR,2 )−1 HR,1 V1 ,
[1]

[1]

VS = (H2,S )−1 H2,1 V1 ,

(7a)
(7b)

−1

[1]
[1]
[1]
[1]
where V1 is derived using V1 = eig (Z), with Z = (HR,1 )−1 HR,2 H1,2
H1,S (H2,S )−1 H2,1
and eig(X) are the eigenvectors of X.

[k]

Interference suppression matrices Uj during two time slots, need to be orthogonalized to
the interference at Rj to meet conditions in (5). Similarly, UR needs to be orthogonalized to the
interference at R in S-R transmission period. Derivations of those matrices can be written as
h
iH 
[k] [k]
= null Hj,i Vi
, j 6= i,
h
iH 
[1]
UR = null HR,1 V1
.

[k]
Uj

(8a)
(8b)

In the 2nd time period, S stays silent, while R establishes its own communication. The design
of precoding and interference suppression matrices for this time period can be done by following
the same step in (7)-(8).
B. Imperfect CSI
The assumption of perfect CSI in wireless networks is highly idealistic due to channel
estimation error. Thus, the following model can be deployed for an imperfect CSI estimation [4]
Ĥ = H + E,

(9)

where Ĥ is the observed mismatched channel, H ∼ CN (0, I) represents the real channel matrix
and E is the error matrix which represents an inaccuracy degree in the estimated CSI. It is
also assumed that E is independent of H. Considering the signal-to-noise ratio (SNR), θ, E is
described as
E ∼ CN (0, λI) with λ = ψθ−κ ,

(10)

where λ is an error variance, κ ≥ 0 and ψ > 0 determine various CSI scenarios. Finally, the
real channel matrix, conditioning on Ĥ, [16], can be described as
H=

1
Ĥ + H̃,
1+λ

(11)

λ
where H̃ ∼ CN (0, 1+λ
I) is independent of Ĥ.

T

PN
SN

T/2

T/2

Data transmission (TS 1)

Data transmission (TS 2)

Energy harvesting

R → D data transmission

S → R data transmission

Fig. 2. Time frame structure of PSR.

III.

P OWER -S PLITTING R ELAYING

The PSR for SWIPT is shown in Fig. 2, where the total time is split into two equal portions,
one for the S-R and the rest for R-D data transmissions [?]. Within the 1st time fraction, an
energy portion of ρ, with 0 < ρ < 1, at R is allocated for EH, while the remaining power of
(1 − ρ) is conveyed to data transmission purpose.
Hence, the R obtains the following signal for EH
s
s
2
X
ρP
ρPi
√
S
[1]
EH
yR
=
ρnR .
τR,S HR,S VS sS +
τR,i HR,i Vi si +
dR,S
d
R,i
i=1

(12)

The power harvested from the noise is insignificant which can be neglected. Thus, the
instantaneous harvested energy at R can be derived from (12) as [7]
2

PR = ηρ

X Pi
PS
2
||H
V
||
+
R,S S
τR,S
τ
dR,S
d R,i
i=1 R,i

[1]

HR,i Vi

2

!

,

(13)

where || · || denotes the Euclidean norm. Then, by using (11), the received information signal
with power (1 − ρ) at R can be derived as (14) at the top of the next page.
The corresponding signal-to-interference-noise ratio (SINR) for R from (14) is derived by

IT
yR

p
= 1 − ρUH
R

s

PS
τR,S
dR,S



!
s



2
X
1
1
Pi
[1]
ĤR,S + H̃R,S VS sS +
ĤR,i + H̃R,i Vi si + nR
τR,i
1+λ
1+λ
dR,i
i=1
(14)

following
τ

γR =

PS (1−ρ)

Pi (1−ρ)
τR,i
dR,i

P2

2
||UH
R ĤR,S VS ||

2
2
||UH
R H̃R,S VS || + IP N + σñR

τR,S
dR,S

where IP N =

PS (1−ρ)

R,S
(1+λ)2
dR,S

,

(15)

[1]

i=1

2
||UH
R H̃R,i Vi || defines the interference from primary transmitters.

Then, the received signal at D can be written as
s


PR
1
yD =
ĤD,R + H̃D,R VR sR + nD .
τD,R
1+λ
dD,R

(16)

and SINR from (16) can be derived as
PR
||ĤD,RVR ||2
τD,R
(1+λ)2
dD,R

γD =

PR
τD,R
dD,R

2
||H̃D,RVR ||2 + σD

,

(17)

2
where σD
is the noise power.

Also, the received SINR for Rj is shown as
τ

[k]

γj =

[k]H

Pj

j,j
dj,j
(1+λ)2

||Uj

[k]

[k]

Ĥj,j Vj ||2

B [k] + C [k] + σñ2 j

[k]

,

(18)

where the intra-network interference of the PN due to the CSI mismatch is given by B [k] =
[k]H

Pj
τ

j,j
dj,j

||Uj

[k]

[k]

H̃j,j Vj ||2 +

[k]H [k] [k] 2
Pi
H̃j,i Vi ||i6=j
τj,i ||Uj
dj,i

SN is expressed by
C

[k]

=









PS
τj,S
dj,S

[k]H

||Uj

while the inter-network interference from the

H̃j,S VS ||2, if k = 1,

[k]H
PR
H̃j,RVR ||2 ,
τj,R ||Uj
dj,R

(19)

if k = 2.

The BER of symbol sm for binary phase shift keying (BPSK) can be derived as [17]
√
BERm = Q( γm ), m ∈ {1, 2, R, D},

(20)

√ R∞
where Q(x) = 1/ 2π x exp(−t2 /2)dt is the Gaussian-Q function.
IV.

S IMULATION R ESULTS

This section presents the simulation results for the proposed system model in Rayleigh fading
channels with BPSK modulation. The system parameters are as follows: dm,n = 3 and τm,n =
2.7 ∀m ∈ {1, 2, R, D}, ∀n ∈ {1, 2, S, R} and equal transmit power at Ti and S. The calculated
optimal values of ρ = 0.75 with η = 0.8 in [18] is considered. Furthermore, the following values
of (κ, ψ) such as (0, 0.001), (0, 0.05), (0.75, 10), (1, 10) and (1.5, 15) are used to investigate
the impact of CSI mismatch.
10

10

10

-1

10

BER

BER

10

0

-2

10

0

-1

-2

S-R
R-D
10

PU

-3

10

-3

R-D
S-R
PU

Perfect CSI
10

-4

10
0

5

10

15

20

25

30

SNR (dB)

(a) BER performance for perfect CSI and SNR-independent
CSI mismatch ((0, 0.001) and (0, 0.005)).

-4

0

5

10

15

20

25

30

SNR (dB)

(b) BER performance for SNR-dependent CSI mismatch
((0.75, 10), (1, 10) and (1.5, 15)).

Fig. 3. BER vs. SNR of the primary user, the relay and the destination node operating in the
PSR protocol under different CSI scenarios.

Fig. 3 shows how imperfect CSI parameters impact on the BER performance of the PU and
SUs. For the case of SNR-independent CSI mismatch (when κ = 0, Fig. 3a), the BER degrades
as ψ increases because the channel error variance does not depend on the SNR and the BER
curves saturate after some SNR values, e.g. at 15 dB and 21 dB for 0.05 and 0.001, respectively.
Furthermore, it is worth to note that the BER performance is not affected by ψ in the low SNR
region, i.e. ψ starts playing a role at 3 dB and 6 dB for the BER of PU and SUs, respectively.
This can be explained by the fact that small values of ψ do not increase much the error rate of
the received signal at low SNR.

10

-1

BER

10

0

10

10

-2

-3

0

1

2

3

4

5

0

5

10

15

Fig. 4. BER vs. the CSI mismatch parameters κ and ψ of SU at 20 dB.

In general, BER performance of PU outperforms those of R and D because of the power
portion 1 − ρ devoted for data transmission at R. The less the value of the allocated power
for data transmission is, the higher the probability of the incorrect data detection becomes. To
compare the performance of R and D at low SNR, R performs better than D because R transmits
its data with a certain number of errors which in turn affects the error rate of D. However, the
BER performances of SUs match after 10 dB due to the fact that R harvests more energy at
high SNR and D consequently receives a strong signal to detect. When κ 6= 0, the channel
error variance becomes SNR-dependent (see Fig. 3b), which implies no saturation of the BER
performance. An increase of κ leads to the BER improvement. At 30 dB, the BER performance
of SUs obtains 0.0353, 0.0079 and 0.0005 for (0.75, 10), (1, 10) and (1.5, 15), respectively.
A more deeper analysis on the impact of κ and ψ on the BER performance can be obtained
from Fig. 4, where the BER performance of SUs is built up as a function of different values
of κ and ψ at 20 dB. It can be noticed that the BER performance improves as κ increases,
while an increase of ψ results in the BER degradation. In the first subfigure, the BER curves for
different values of ψ approach 0.0019 at certain κ values. Meanwhile, in the second subfigure,
the BER performance for different κ degrades as ψ increases. It is observed that small values
of κ correspond to more abrupt BER degradation, and vise versa.

V.

C ONCLUSION

In this paper, we analyzed the BER performance of EH-based DF CRN with PS relaying
protocols and embedded IA technique. The five special scenarios of the imperfect CSI given by
(0, 0.001), (0, 0.05), (0.75, 10), (1, 10) and (1.5, 15) were studied to analyze the impact of the
CSI quality on the BER performance of PU and SUs. The presented results with ρ = 0.75 showed
that the BER of PU outperforms those of SUs in perfect and imperfect SCI cases. Moreover,
the BER curve degraded as ψ increased while rise of κ leaded to the BER improvement.
R EFERENCES
[1]

A. Goldsmith, S. Jafar, L. Maric and S. Srinivasa, “Breaking spectrum gridlock with cognitive radios: an information
theoretic perspective,” IEEE Proceedings, vol. 97, no. 5, pp. 894–914, May 2009.

[2]

S. Arzykulov, G. Nauryzbayev and T. A. Tsiftsis, “Underlay Cognitive Relaying System Over α - µ Fading Channels,”
IEEE Commun. Lett., vol. 21, no. 1, pp. 216–219, Jan. 2017

[3]

G. Nauryzbayev and E. Alsusa, “Enhanced Multiplexing Gain Using Interference Alignment Cancellation in Multi-cell
MIMO Networks,” IEEE Trans. Inf. Theory, vol. 62, no. 1, pp. 357–369, Jan. 2016.

[4]

G. Nauryzbayev and E. Alsusa, “Interference Alignment Cancellation in Compounded MIMO Broadcast Channels with
General Message Sets,” IEEE Trans. Commun., vol. 63, no. 10, pp. 3702–3712, Oct. 2015.

[5]

M. Amir, A. El-Keyi and M. Nafie, “Constrained Interference Alignment and the Spatial Degrees of Freedom of MIMO
Cognitive Networks,” IEEE Trans. Inf. Theory, vol. 57, no. 5, pp. 2994–3004, May 2011.

[6]

J. Tang, S. Lambotharan and S. Pomeroy, “Interference cancellation and alignment techniques for multiple-input and
multiple-output cognitive relay networks,” IET Signal Process., vol. 7, no. 3, pp. 188–200, May 2013.

[7]

A. Nasir, X. Zhou, S. Durrani, and R. Kennedy, “Relaying protocols for wireless energy harvesting and information
processing,” IEEE Trans. Wireless Commun., vol. 12, no. 7, pp. 3622–3636, Jul. 2013.

[8]

G. Nauryzbayev, K. M. Rabie, M. Abdallah and B. Adebisi, “Ergodic Capacity Analysis of Wireless Powered AF Relaying
Systems over α - µ Fading Channels,” in Proc. IEEE Global Commun. Conf. (GLOBECOM), Singapore, pp. 1–6, Dec.
2017.

[9]

N. Zhao, F. R. Yu and V. C. M. Leung, “Wireless energy harvesting in interference alignment networks,” IEEE Commun.
Mag., vol. 53, no. 6, pp. 72-78, June 2015.

[10]

S. Park, H. Kim and D. Hong, “Cognitive radio networks with energy harvesting,” IEEE Trans. Wireless Commun., vol.
12, no. 3, pp. 1386–1397, Mar. 2013.

[11]

G. Zheng, Z. Ho, E. A. Jorswieck and B. Ottersten, “Information and energy cooperation in cognitive radio networks,”
IEEE Trans. Signal Process., vol. 62, no. 9, pp. 2290–2303, Sept. 2014.

[12]

F. Wang and X. Zhang, “Resource Allocation for Multiuser Cooperative Overlay Cognitive Radio Networks with RF
Energy Harvesting Capability,” IEEE Global Commun. Conf. (GLOBECOM), Washington, DC, pp. 1–6, 2016.

[13]

G. Nauryzbayev and E. Alsusa, “Identifying the Maximum DoF Region in the Three-cell Compounded MIMO Network,”
IEEE WCNC, pp. 1–5, Doha, Qatar, Apr. 2016.

[14]

G. Nauryzbayev, E. Alsusa, and J. Tang, “An Alignment Based Interference Cancellation Scheme for Multi-cell MIMO
Networks,” IEEE VTC, pp. 1–5, Glasgow, UK, May 2015.

[15]

H. Sung, S. H. Park, K. J. Lee and I. Lee, “Linear precoder designs for K-user interference channels,” IEEE Trans.
Wireless Commun., vol. 9, no. 1, pp. 291–301, Jan. 2010.

[16]

S. Kay, “Fundamentals of statistical signal processing: Estimation theory” in Englewood Cliffs NJ: Prentice-Hall 1993.

[17]

S. Ohno and K. A. D. Teo, “Universal BER Performance Ordering of MIMO Systems over Flat Channels,” IEEE Trans.
Wireless Commun., vol. 6, no. 10, pp. 3678-3687, Oct. 2007.

[18]

S. Arzykulov, G. Nauryzbayev, T. A. Tsiftsis and M. Abdallah, “On the Capacity of Wireless Powered Cognitive Relay
Network with Interference Alignment,” in Proc. IEEE Global Commun. Conf. (GLOBECOM), Singapore, pp. 1–6, Dec.
2017.

