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Soft Information Relaying with Transceiver
Hardware Impairments in Cognitive Networks
Dang Khoa Nguyen∗, Dushantha Nalin K. Jayakody†, and Hiroshi Ochi∗
∗Graduate School of Computer Science and Systems Engineering, Kyushu Institute of Technology, Fukuoka, JAPAN
‡Institute of Computer Science, University of Tartu, ESTONIA
Emails: {khoa, ochi}@dsp.cse.kyutech.ac.jp, nalin.jayakody@ut.ee
Abstract—This paper demonstrates the impact of transceiver
impairments on channel capacity and bit-error-rate (BER) per-
formance of a dual-hop half-duplex cognitive relay network over
AWGN channel. We consider the soft-information-relaying (SIR)
protocol where the relay node computes the reliabilities (soft)
of the received signal from source and then forwards to the
destination. The hardware impairment model of the received
signal via AWGN channel is first introduced. The analysis on
capacity and BER performance are then presented for the
network with binary phase shift keying (BPSK) modulation.
Furthermore, the impacts of hardware impairments on BER
are quantified for the network with SIR and hard decode-and-
forward (DF) protocol. The simulation results on channel capacity
of the network with SIR protocol acknowledge the ceiling capacity
of the realistic transceivers that can not be exceeded by increasing
transmit power. Moreover, we found that the BER performance of
SIR network with the worst hardware impairment level in 3GPP
LTE requirements is on par with the best transceiver level of the
network with hard DF. This concludes that the SIR outperforms
the hard DF on limit the impact of hardware impairments on
BER performance.
I. INT ROD UC TI ON
Cooperative communication is a promising technique to re-
alize spatial diversity and increased spectral efficiency through
user cooperation [1]. There are three basic memoryless re-
lay protocols: amplify-and-forward (AF), decode-and-forward
(DF) and estimate-and-forward (EF). In DF, the error prop-
agation can be avoided using decoder process under good
channel conditions. However, error-prone relays can destroy
the performance of the destination’s decoder when the relay
forwards erroneous signals to the destination. In contrast, the
AF protocol suffers from the problem of noise amplification.
However, estimate and forward (EF) [2]-[7] relay combine the
advantages presented in these two protocols and mitigate the
shortcomings of traditional protocols such as error propagation
to the destination (DF) and noise amplification at the relay
(AF).
In [2]–[7], a soft-input soft-output (SISO) encoder was
implemented at the relay. However, in [2], the recursive
structure of this encoder means that the reliability of the
recursively encoded soft bits depends strongly on the least
reliable input bits, causing a decaying LLR profile. A scheme
for soft parity generation was recently proposed in [3] which
has the advantage that successively generated soft symbols
do not converge to zero as happens with many existing soft
forwarding methods; this method is specific to BPSK.
Cognitive radio is a strong candidate to combat the scarcity
of frequency spectrum. In order to protect quality-of-service
of primary transmission, the transmit power of secondary
users (SUs) should be limited to the maximum interference
allowance of primary users (PUs). To tackle this limitation,
the idea of two-way cognitive relay (TWCR) networks has
been investigated in [8], [9] among others. The cognitive relay
networks exploit the advantages of relaying protocols and
cognitive radios and are able to overcome the transmit power
limits to further boost the system performance.
In [24], the outage probability (OP) of DF cognitive relay
networks was reported with the constraint imposed on the
interference suffered by the primary users. The work in [25]
analyzed the performance of spectrum sharing amplify-and-
forward (AF) in the existence of transmit power constrain
and the interference from a primary transmitter. The OP of
the cognitive DF networks over Nakagami-m fading was per-
formed in [26]. In these literature, the transceiver of the relay
nodes were supposed to be flawless. Nevertheless, the practical
transceiver hardware suffers from several types of impairments;
such as, I/Q imbalance [10], [11], high power amplifier non-
linearities [13]. Recently, the impacts of hardware impairments
to relay networks were provided in [14]. Undoubtedly, those
impairments also degrade the system performances of the CR
networks, especially when the power budget is high.
In this work, we apply the SIR protocol for a cognitive
network and evaluate the impact of transceiver imperfections
by utilizing the generalized impairment model of [17] on
channel capacity and BER performance in compared to hard
DF protocol. The contributions of this paper are:
•We portray SIR protocol for cognitive relay networks and
simplify the impairment model for AWGN channel.
•We provide new analysis results for channel capacity and
BER performance of the network with SIR protocol under
the impact of hardware impairments.
•Finally, we present simulation results which show signif-
icant benefits of the SIR scheme compared to hard DF
protocol.
The reminder of this paper is organized as follows. Sec-
tion II introduces the generalized impairment model and its
simplified model for AWGN channel. Section III describes
the dual-hop half-duplex cognitive relay network and channel
model in this paper. Section IV presents SIR scheme in
detail and provides the analysis on BER performance and
channel capacity for this protocol, while section V presents
the simulation results. Section VI provides the conclusions.
II. HA RDWAR E IMPA IR ME NT S’ MOD EL
In this section, we describe the transceiver hardware im-
pairments model that explained in [17]. It is assumed that the
source transmits a signal x∈Cwith power Pover the wireless
channel to the receiver with AWGN noise ηthat has zero mean
and variance σ2
η=N0. The practical transceiver impairments
at the source distort the signal xbefore it is emitted, whilst
the imperfect transceiver hardware of the receiver distorts the
received signal during the reception phase. Each source of
distortion is represented by a different hardware model. Let
τ1, τ2be the distortion affecting the source and destination,
respectively. The received signal can be succinctly expressed
as
y=√P(x+τ1) + τ2+η. (1)
As in [18], τ1∼ CN(0, κ2
1)and τ2∼ CN(0, κ2
2P), where
κ1, κ2are the impairment levels at the source and destination
transceivers, respectively. Following [18], the distortion powers
caused by transceiver impairments at the source and destination
can be, more compactly, represented by an aggregate distortion
power at the receiver, such that τ∼ CN(0, κ2), where κ,
pκ2
1+κ2
2is the aggregate impairment level. Then, (1) can be
rewritten as
y=√P(x+τ) + η=√P x +√P τ +η, (2)
we define ε=√P τ +ηas the impairment-noise-distortion,
where ε∼ CN (0, κ2P+N0). We can rescript (1) as
y=√P x +ε. (3)
As definition of SNR, Eb
N0=P
σ2
η, then the variance of εis given
by:
σ2
ε=σ2
η+σ2
τ=PN0
Eb
+κ2P. (4)
Fig. 1 illustrates the impact of transceiver hardware impair-
ments on variance of the total noise include AWGN and
impairment-noise-distortion. It can be seen in Fig. 1, σ2
ε
increases as the rise of the impairment level κ2. We note
that the transmit power is kept unchanged as P= 1 in order
to obtain the simulation results in Fig. 1 while the hardware
impairment level in the range κ∈[0.08,0.175] are examined,
which resemble the error vector magnitudes (EVMs) of 3GPP
LTE requirements.
III. SYS TE M AN D CHA NN EL MO DEL
We consider a half-duplex cognitive three-node relay chan-
nel as illustrated in Fig. 2. In this cognitive relay network,
the source node (S) transmits information xto the destination
node (D) with the help of the relay node (R). Rxis a receiver
in the primary network. We assume each node is equipped with
a single antenna and working in half-duplex mode. To protect
Rx from interference signals caused by the transmission of
the cognitive users, we define IPas the maximum tolerance
0 2 4 6 8 10
0
0.2
0.4
0.6
0.8
1
Eb/N0(dB)
Variance of impairment−noise−distortion
κ2 = 0.08
κ2 = 0.1275
κ2 = 0.175
Idea model
Figure 1. Variance of impairment-noise-distortion when transmit power P=
1for difference impairments levels κ2∈[0.08; 0.1275; 0.175]
S
Source
R
Relay
D
Destination
Rx
Primary Receiver
Figure 2. A three-node cognitive relay network.
interference received at Rx. We observe a case where the
cognitive users are allowed to transmit with peak power, hence,
the transmit power at Sand Rare IP.
The information is conveyed in two timeslots; in the first
timeslot, Sbroadcasts xto both Rand D. The received
information ySR is processed using the relay function f(ySR ),
and then it is forwarded to Dvia R. All channels of the
network are assumed to be AWGN channel. Without loss
of generality, the additive noise terms ηi,i∈ {S, R, D},
is assumed to have zero mean and variance σ2
i, such that
ηi∼ CN(0, σ2
i). Moreover, following the discussion in the
previous section, the aggregate impairment level at Rand D
are presented as κ2
Rand κ2
D, respectively. We consider the
BPSK modulation, x∈ {±1}, in this paper, our results can be
easily extended to higher order modulations.
Thus, the received signals in the first timeslot at Rand D
with transmit power PScan be respectively expressed as
ySR =pIPx+εR=pPSx+εR,(5)
ySD =pIPx+εD=pPSx+εD,(6)
where the impairment-distortion-noise at Rand Dare εj∼
CN(0, κ2
jPk+N0), where j∈ {R, D}and k∈ {S, R}. In the
second timeslot, the received signal at Dcan be written as
yRD =pPRf(ySR ) + εD=pPRxR+εD.(7)
IV. SOF T INF OR MATI ON RE LAYING
In this paper, we employ the soft information relaying (SIR)
protocol in the cognitive relay network while the hard decode-
and-forward (DF) protocol is used as a bench mark to evaluate
the benefits of the SIR protocol under hardware impairments.
A. Calculation of Soft Information at the Relay
In the first timeslot, source transmits signal xto relay.
The relay calculates and forwards the minimum mean-square
error (MMSE) value of this received signal ySR to D. The
conditional expectation of xis (E[x|ySR]), which is calculated
as
exR=E[x|ySR ] = tanh LR
2,(8)
where LR= ln p(ySR|x=1)
p(ySR|x=−1) is a log-likehood ratio (LLR) of
the received symbol xwith BPSK modulation and tanh(t) =
e2t−1
e2t−1is the hyperbolic tangent function. Therefore, the relay
function can be expressed as
f(ySR ) = tanh !LR
2
qEtanh !LR
2=βexR,(9)
where β=qEtanh !LR
2. In practice the factor βis chosen
to satisfy the transmit power constraint at the relay, i.e.,
β=s1
1
NPN
i=1 ˜x2
i
,(10)
where Nis the number of symbols.
B. Calculation of LLR at the Destination
In the second timeslot, the relay forwards the soft informa-
tion of the received signal in the first timeslot to the destination.
Hence, the destination receives two different signals via two
independent channels, i.e., ySD and yRD . First, the LLR value
of the received signal ySD is calculated as
LSD = ln p(ySD |x= 1)
p(ySD |x=−1) =2ySD
σ2
εD
.(11)
Assume that the received version of the soft symbol xRat the
destination is exR. From (7), the soft information at Dcan be
rewritten as
yRD =pPRβexR+εD.(12)
The transmit power PRis selected to satisfy PR≤IP
β2. The
relationship between the soft symbol at R,exR, and the correct
symbol xR, is modeled in [2] as
exR=xR(1 −eη),(13)
where eηis the soft noise random variable whose mean and
variance are measured offline and respectively given by
µeη=1
N
N
X
k=1 |exk
R−xk
R|,(14)
σ2
eη=1
N
l
X
k=1
(1 −exk
Rxk
R−µeη)2.(15)
We denote that µeηand σ2
eηare priorly computed and stored at
Dfor calculating LLR in real time transmission. Hence, (12)
can be recast as
yRD =pPRβ[xR(1 −eη+µ−µ)] + εD
=pPRβxR(1 −µ)−pPRβxR(µ+eη) + εD
=pPRβxR(1 −µ) + ¯ηD(16)
In (16), ¯ηD=−√PRβxR(µ+eη) + εDis the noise term of
the received signal at Dform Rin the second timeslot. This
equivalent noise is not a Gaussian random variable. However,
its distribution has zero mean and variance is derived as
σ2
¯n=PRβ2(µ+eη)2+ε2
D.(17)
Therefore, the LLR of the received signal yRD can not be
obtained as (11) because the probability density function of
the soft symbol is unknown. The LLR of yRD is approximated
using the soft noise model as follows
LRD = ln p(x= 1|yRD)
p(x=−1|yRD)=2(1 −µeη)
PRσ2
eηβ2+σ2
εD
yRD.(18)
From (11) and (18), the total LLR of the received signal at D
in two different channel routes is computed as
LD=LSD +LRD .(19)
The decoded signal at Dis
ˆxD=sign(LD).(20)
V. NU ME RI CA L RES ULTS A ND DI SC US SI ON
In this section, we present the performance of the SIR
protocol for the three-node cognitive relay network under the
impact of transceiver hardware impairments.
A. Simulation Parameters
We consider the cognitive relay network where data is trans-
mitted using BPSK modulation. The interference allowance
power is assumed to be satisfy where transmit power at source
and relay are assumed to be PS=PR= 1. Encoders and
decoders are supposed to be ideal hardware, however wireless
transceivers are modeled with hardware impairment level is in
the range [0.08,0.175]. Unless otherwise states, the aggregate
impairment levels of the relay and destination are similar, i.e.
κ2
R=κ2
D=κ2.
0 20 40 60 80 100
0
1
2
3
4
5
6
7
Power (P)
Capacity (C) [bit/sec/1Hz]
3.5983
3.0484
2.6793
Idea model
κ2 = 0.08
κ2 = 0.1275
κ2 = 0.175
Figure 3. Capacity performance of the network when the bandwidth
B= 1 (Hz), variance noise σ2
η= 1 and impairment level κ2=
[0,0.08,0.125,0.175].
B. Channel Capacity in AWGN Performance
From (6) and (16), we have the SNR of the received signals
at Dfrom two timeslots are respectively given by
γSD =PS
σ2
εD
=IP
σ2
εD
, γSR =PS
σ2
εR
=IP
σ2
εR
,(21)
γRD =PRβ2
σ2
¯nD
=IP
σ2
¯nD
=IP
IPσ2
eη+σ2
εD
.(22)
The end-to-end SNR of the network is obtained as
γD= max (min(γSR, γRD ), γSD ).(23)
The capacity of AWGN channel with bandwidth Bis given
by Shannon’s well-know formula
C=Blog2(1 + γD
B).(24)
Fig. 3 demonstrates the capacity of the cognitive relay net-
work with SIR protocol versus transmit power Pfor different
transceiver impairment levels κ2. It can be seen that the capac-
ity of the channel for ideal transceiver (κ2= 0) is theoretically
unlimited when P→ ∞. However, for the network with
realistic transceiver (κ26= 0), the ceiling capacity is established
as the growth of transmit power. This is fundamental limit
for the network spectral efficiency. As we observe, the ceiling
capacity decreases when the impairment levels increase. In
particular, it is about 0.9(bit/sec/1Hz) lost as κ2rises from
0.08 to 0.175.
C. Bit-Error-Rate Performance
Fig. 4 compares the BER performance of the cognitive relay
network over AWGN channel of the SIR relaying scheme with
0 2 4 6 8 10
10−3
10−2
10−1
100
Eb/N0(dB)
BER
DF ideal (κ2 = 0)
SIR ideal (κ2 = 0)
DF (κ2 = 0.175)
SIR (κ2 = 0.175)
Figure 4. BER performance for the SIR protocol in compared to DF protocol
over AWGN channel for ideal transceiver and realistic transceiver model with
hardware impairment level κ2= 0.175.
that of hard DF protocol. The SNRs of S→R,S→Dand
R→Dwireless link are assumed to equal and rise in the range
[0,10] dB to represent both poor and good channel conditions.
Overall, the network with SIR scheme outperforms that with
DF scheme in term of BER; BER increases as the growth of
hardware impairment level κ2, especially when SNR is high.
It is noticed that BER of the network with SIR protocol with
κ2= 0.175 is on par with that of the DF network with ideal
transceiver and just under the performance of the SIR network
with perfect transceiver. In particular, BER of the DF network
falls sharply in the high SNR regime, from 7×10−4to 20 ×
10−4when κ2increases from 0(idea transceiver) to 0.175;
whereas it reduces gradually by 4.5×10−4for the network
with SIR relaying protocol.
This explains that the the SIR protocol is more effective to
remove the impact of noise that the DF protocol albeit at the
expense of implementation complexity of the noise variance
computation circuit. This evidence claim that cognitive relay
network with SIR scheme outperforms the network with the
DF protocol; moreover, SIR protocol is able to discard the
impact of transceiver impairment when compared with the DF
protocol.
VI. CO NC LU SI ON
The paper presented the simulation results on BER and ca-
pacity performance under the impact of hardware impairments
of a cognitive relay network using SIR protocol. Our numerical
results demonstrated that the SIR protocol outperforms hard
DF scheme. In particular, the BER of the SIR network with
hardware impairment level κ2= 0.175 and the DF protocol
with perfect transceiver κ2= 0 are of the same parity.
Furthermore, we confirm the fundamental limit of realistic
transceiver hardware on the achievable capacity. The ceiling
capacity is established even when the transmit power increase
to infinity, while it decrease as the hardware impairment level
increases.
ACK NOW LE DG ME NT
This work is supported (in part) by the Norwegian-Estonian
Research Cooperation Programme through the grant EMP133,
by the Estonian Research Council through the research grants
PUT405 and IUT2-1 and by the European Regional Devel-
opment Fund through the Estonian Center of Excellence in
Computer Science, EXCS.
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