A noncooperative spectrum sharing protocolfor multicarrier cognitive sensor networks
Donatella Darsena, Giacinto Gelli, and Francesco Verde
Abstract
In this paper, we consider a broadband cognitive radio network, where both primary and secondary systems employ an orthogonal frequencydivision multiplexing (OFDM) modulation scheme.The proposed scheme is reminiscent of additive superposition coding: speciﬁcally, the secondarytransmitter acts as an amplifyandforward relay that sends a linear weighted combination of thereceived multicarrier primary signal and its own block of multiple symbols. Such a superpositionis performed by the secondary transmitter on the ﬂy, in a single OFDM symbol of the primarysystem. Moreover, the proposed scheme is noncooperative in the sense that no cooperation isrequired between the primary and secondary systems. An informationtheoretic analysis of theproposed scheme is developed, whose results are corroborated by means of numerical Monte Carlosimulations.
I. I
NTRODUCTION
Due to the continuing adoption of tablets, laptops with cellular connections, and smartphones along with their datahungry applications, the actual problem facing telecommunications operators is the socalled “capacity crunch”, i.e., there are too many users demandingtoo much data. A viable way for increasing capacity consists of bringing the access network closer and closer to end users, i.e., in a range of few meters around them. To pursue sucha basic scope, networks have been rapidly turned into heterogeneous mixtures of small basestations (pico and especially femto), remote radio units, lowpower nodes, and relays [1],[2], [3]. This unprecedented escalation has aroused considerable interest in
spectrum sharing
among wireless systems [4].
Cognitive radio
(CR) approaches [5] allow secondary users (SUs) to share a portion of thespectrum with licensed or unlicensed primary users (PUs). The stringent requirement is thattransmissions of SUs should not degrade the quality of service that operators have agreedwith their PUs. CR techniques can be categorized according to the coexistence strategy of theprimary and secondary systems. On the basis of the
overlay
paradigm [6], the SUs transmitby resorting to standard methods of orthogonalization (in space, time, or frequency) with
July 16, 2016 DRAFT
1
respect to the primary transmissions [5]. The temporary spacetimefrequency voids in thetransmission of the PUs are collectively referred to as a
white spaces
(or
spectrum holes
).Implementation of overlay CR schemes requires the accurate and timely knowledge of thewhitespace locations to identify the existence of the primary transmissions.Subsequently, there have emerged CR paradigms that are potentially more efﬁcient than theoverlay one. In the
underlay
paradigm [6], the SU transmissions overlap the signal transmittedby the PUs in space, time, and frequency, provided that the interference level they cause tothe PUs is below a given threshold. In this case, the interfering effect of the secondarytransmissions on the primary receivers should be determined
a priori
. Existing underlay CRapproaches can be distinguished from each other through the degree of
cooperation
that isrequired between primary and secondary systems.The mutual interference between primary and secondary transmissions can be optimally(in the informationtheoretic sense) removed by allowing SUs and PUs to cooperate in a noncausal manner [7], [8], [9], [10]. Such a family of underlay CR techniques rely on encodingtechniques like dirty paper coding [11], which require
a priori
knowledge of the primaryuser’s transmitted data and/or its codebook.A causal cooperation between primary and secondary systems can be obtained by resortingto the concept of
additive superposition coding (SPC)
[12], [13], [14]. In its simplest guise,a SPC scheme can be seen as a speciﬁc modulation technique, which consists of linearcombining multiple coded symbols. The SPC philosophy has been recently used to developcooperative primarysecondary spectrum sharing schemes for ﬂatfading channels [15], [16].According to such papers, the secondary transmitter acts as a decodeandforward (DF) relay,which demodulates the symbols transmitted by the PU on a symbolbysymbol basis and, ineach symbol period of the PU, it remodulate a linear weighted combination of the srcinalprimary symbol and its own secondary symbol, such that the outage performance of theprimary system is not affected. However, besides requiring a strict coordination betweenthe primary and secondary system, which may be difﬁcult to achieve in many cases, theemployment of such a spectrum sharing strategy leads to a
twophase
protocol spanning twotime slots.An underlay spectrum sharing paradigm has been recently proposed in [17], [18] for ﬂatfading channels, whereby cooperation between the PU and SU is
not
required. In this scheme,the arithmetic operation of
multiplication
is used to superimpose a single SU symbol on aframe of multiple PU symbols, through an amplifyandforward (AF) protocol. As a result,
July 16, 2016 DRAFT
2
under reasonable conditions [17], [18], the SU can transmit without a power constraint, whilekeeping the desirable property of not degrading (but even improving) the PU performance.However, the main limitation of the approach in [17], [18] is that only lowdata rates canbe achieved by the secondary system, due to the fact that the SU transmits only one symbolper PU frame. The extension of the scheme proposed in [17], [18] to the case in which theSU transmits multiple symbols within a symbol interval of a primary multicarrier system isconsidered in [19], where the SU convolves its blockprecoded symbols with the receivedPU signal in the timedomain. To improve the achievable data rate of the secondary systemwith AF spectrum sharing, another strategy is to use SPC, as an alternative to
convolutive
superposition. This is pursued in [20], where SPC is employed to perform a symbolbysymbol additive superposition of the SU information on the PU received signal in a ﬂatfading channel scenario. Similarly to [15], [16], besides introducing a substantial amount of cooperation between the primary and secondary systems, the price to pay is to spread thetransmission of one primary symbol over two time slots.Contrary to [17], [18], [15], [16], [20], we consider a broadband CR system where modulation is based on
orthogonal frequencydivision multiplexing (OFDM)
[21], due to its advantages in multipath resistance, performance, spectral efﬁciency, ﬂexibility, and computationalcomplexity. We propose a
noncooperative
spectrum sharing scheme where the secondarytransmitter acts as an AF relay
1
: speciﬁcally, the secondary transmitter forwards a linearweighted combination of the received PU signal and its own block of multiple symbols.This scheme offers the following advantages: compared to [17], [18], it allows the SU totransmit multiple symbols within a single OFDM symbol interval of the primary system,by jointly exploiting both white spaces (i.e., unused subcarriers of the PU signal) and dirtyspaces (i.e., subcarriers used by the PU), thereby attaining larger transmission rates; withrespect to [15], [16], [20], no cooperation is required between the primary and secondarysystems and, moreover, only a single slot is required to superimpose the SU data on the PUsignal on the ﬂy, thus doubling the network throughput. The theoretical performance analysisof the proposed scheme is based on inputoutput mutual information and ergodic capacityof both the primary and secondary systems. Numerical results are also reported, aimed atcorroborating our theoretical ﬁndings.
1
This work has been partially presented in
July 16, 2016 DRAFT
3
OFDM RX sqrt _a sqrt _b OFDM TX
u_2(t)
OFDM TX OFDM RX
Theta s1
u_1( t ) r_2( t ) h_12/ t) h_13/ t) h_14/ t) h_23/ t) h_24/ t) z_2( t ) r_3( t ) r_4( t )
node 1 node 2 PTx STx PRx node 3 node 4 SRx
Figure 1. The wireless network model: in blue, the PU transmitting/receiving nodes, in red the SU transmitting/receivingnodes.
II. T
HE SYSTEM MODEL
We consider the wireless cognitive sensor network depicted in Fig. 1, composed by aprimary user (PU) system (in red) and a secondary user (SU) system (in blue). The PUsystem, comprising a primary transmitterreceiver pair (nodes PTx and PRx), is authorizedto operate in a certain portion of the spectrum; the SU system, comprising a secondarytransmitterreceiver pair (nodes STx and SRx), can operate on the same spectrum, providedthat its operation does not degrade the PU performance. In the sequel, the PTx, STx, PRx,and SRx will be also referred to as nodes
1
,
2
,
3
, and
4
, respectively.Both PTx and STx employ OFDM modulation, with
M
subcarriers and a cyclic preﬁx(CP) of length
L
cp
, and experiment independent and quasistatic frequencyselective Rayleighfading. In particular, for each
i
∈{
1
,
2
}
and
j
∈{
2
,
3
,
4
}
, with
i
=
j
, we model the discretetime channel corresponding to the
i
→
j
link as a ﬁniteimpulse response system, whoseimpulse response
h
ij
(
)
has order
L
ij
. The channel coefﬁcients
h
ij
(
)
, for
∈{
0
,
1
,...,L
ij
}
,are supposed to be constant over one OFDM symbol, but can independently change from onesymbol to another. We denote with
θ
ij
≥
0
the integer time offset on the
i
→
j
link, whichencompasses both the propagation delay of the wireless link and the processing time at node
i
2
. In the sequel, we assume that the condition
L
ij
+
θ
ij
≤
P
−
1
holds, such that the block received at each node in the network is contaminated only by the interblock interference(IBI) of the previous transmitted block. We also assume that channel state information (CSI)
2
The fractional time offset is incorporated as part of
{
h
ij
(
)
}
L
ij
=0
.
July 16, 2016 DRAFT
4
is not available at both the PTx and STx; therefore, both the PU and SU systems uniformlyallocate the available transmit power across all the data subcarriers. Finally, perfect frequencysynchronization at each node is assumed.In the
n
th symbol period (
n
∈
Z
), the PTx (node
1
) transmits its baseband block
u
1
(
n
) =
T
cp
W
IDFT
s
1
(
n
)
∈
C
P
, with
P
M
+
L
cp
and
s
1
(
n
)
Θ
1
s
1
(
n
)
∈
C
M
, where
s
1
(
n
)
[
s
1
,
0
(
n
)
,s
1
,
1
(
n
)
,...,s
1
,M
1
−
1
(
n
)]
T
∈
C
M
1
is the informationbearing symbol vector, whoseentries are modeled as independent and identically distributed (i.i.d.) zeromean circularlysymmetric complex random variables (RVs), with variance
E
[

s
1
,m
(
n
)

2
] =
σ
2
PU
for any
m
∈{
0
,
1
,...,M
1
−
1
}
, the matrix
Θ
1
∈
R
M
×
M
1
models subcarrier mapping,
W
IDFT
∈
C
M
×
M
denotes the unitary symmetric IDFT matrix [22], and
T
cp
[
I
cpT
,
I
M
]
T
∈
R
P
×
M
, with
I
cp
∈
R
L
cp
×
M
obtained from
I
M
by picking its last
L
cp
rows, represents the CP insertion matrix.The entries of
u
1
(
n
)
are, ﬁnally, subject to digitaltoanalog (D/A) plus radiofrequency (RF)conversion for transmission over the wireless channel.The RF signal transmitted by the PTx is received both by STx and PRx. After analogtodigital (A/D) conversion, the baseband signal received by the STx (node
2
) is given by
r
2
(
n
) =
H
(0)12
u
1
(
n
) +
H
(1)12
u
1
(
n
−
1) +
w
2
(
n
)
(1)where
w
2
(
n
)
∈
C
P
is thermal noise,
H
(0)12
∈
C
P
×
P
is a Toeplitz lowertriangular channelmatrix with ﬁrst column
[
h
12
(
−
θ
12
)
,...,h
12
(
−
θ
12
+
L
12
)
,
0
,...,
0]
T
and
H
(1)12
∈
C
P
×
P
is aToeplitz uppertriangular matrix with ﬁrst row
[0
,...,
0
,h
12
(
−
θ
12
+
L
12
)
,...,h
12
(
−
θ
12
+1)]
.The STx wants to transmit towards the SRx its baseband signal block given by
u
2
(
n
) =
T
cp
W
IDFT
s
2
(
n
)
, with
s
2
(
n
)
Θ
2
s
2
(
n
)
∈
C
M
, where the entries of the vector
s
2
(
n
)
[
s
2
,
0
(
n
)
,s
2
,
1
(
n
)
,...,s
2
,M
2
−
1
(
n
)]
T
∈
C
M
2
are modeled as i.i.d. zeromean circularly symmetriccomplex RVs, with variance
E
[

s
2
,m
(
n
)

2
] =
σ
2
SU
, for any
m
∈ {
0
,
1
,...,M
2
−
1
}
, whereas
Θ
2
∈
R
M
×
M
2
is the subcarrier mapping matrix of the secondary system. To this aim,it superimposes its transmission over the received signal
r
2
(
n
)
by transmitting a linearcombination of the received signal and its own signal
z
2
(
n
) =
√
α
r
2
(
n
) +
√
1
−
α
u
2
(
n
)
(2)where
0
≤
α
≤
1
represents the power allocation factor.It is worth noting that the STx actually performs the operations of SPC and relaying
directly
on the RF version of (1), without requiring its down conversion or ADC (see Fig. 1); weconsider the discretetime model (2), and not its continoustime counterpart, only for clarity
July 16, 2016 DRAFT