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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 1, NO. 4, AUGUST 2012

Achievable Data Rate in Spectrum-Sharing Channels with Variable-Rate Variable-Power Primary Users Yuli Yang, Member, IEEE, and Sonia Aissa, Senior Member, IEEE Abstract—In this work, we propose a transmission strategy for secondary users (SUs) within a cognitive radio network where primary users (PUs) exploit variable-rate variable-power modulation. By monitoring the PU’s transmissions, the SU adjusts its transmit power based on the gap between the PU’s received effective signal-to-noise power ratio (SNR) and the lower SNR boundary for the modulation mode that is being used in the primary link. Thus, at the SU’s presence, the PU’s quality of service (QoS) is guaranteed without increasing its processing complexity thanks to no interference cancellation required in the PU’s operation. To demonstrate the advantage of our proposed transmission strategy, we analyze the secondary user’s achievable data rate by taking into account different transmission capabilities for the secondary transmitter. The corresponding numerical results not only prove the validity of our derivations but also provide a convenient tool for the network design with the proposed transmission strategy. Index Terms—Cognitive radio (CR), spectrum sharing, adaptive modulation, data rate.

I. I NTRODUCTION HE concept of cognitive radio has attracted a lot of interest in both academia [1] and industry [2] as it offers a promising solution to the problem of spectrum scarcity for wireless applications. On the other hand, adaptive modulation has become a regular setting in current wireless networks to realize robust and spectrally efficient communications [3]. As is known, in order for secondary users to increase their transmission opportunities within a cognitive radio network, any available knowledge on the primary users’ transmissions has to be fully exploited [4]. Motivated by this philosophy, we consider a spectrum-sharing channel where variable-rate variable-power modulation is adopted in the primary link. With the adaptive modulation, each modulation mode corresponds to an interval of the received signal-to-noise power ratio (SNR), given a target bit error rate (BER). According to the interval where the received SNR at the primary user (PU) falls, the corresponding modulation mode is activated. As such, the gap between the lower boundary of the SNR interval and the PU’s actually received SNR forms an interferencetolerable zone and, consequently, this setting may avail the secondary user (SU) more opportunities to access the licensed spectrum while maintaining the PU’s quality-of-service (QoS). Based on said gap, this paper proposes a transmission strategy for the SU to accommodate its transmit power and achieve good performance under the requirements of the PU’s QoS. With this strategy, no interference cancellation is involved in

T

Manuscript received March 18, 2012. The associate editor coordinating the review of this paper and approving it for publication was S. Sun. Y. Yang is with the Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal, KSA (email: [email protected]). S. A¨ıssa is with the Institut National de la Recherche Scientifique (INRS), University of Quebec, Montreal, QC, Canada (e-mail: [email protected]). Digital Object Identifier 10.1109/WCL.2012.042512.120198

ST

gps

gs

SR

gsp

gp PR

PT Fig. 1.

Spectrum-sharing system model.

the primary link so that the PU’s processing complexity is not increased while maintaining its QoS. The cognitive radio channel capacity has been formulated in [5], [6], and [7] by imposing instantaneous or average interference constraints at the PU. Moreover, the capacity is analyzed in [8] with imperfect channel information. In this paper, to illustrate the advantage of the proposed transmission strategy, we derive the achievable data rate in the secondary link by taking into account different capabilities of the secondary transmitter (ST), namely with or without the peak transmit power constraint imposed on the ST. Furthermore, numerical results will substantiate the validity of our derivations. In the following, we detail the design of the proposed transmission strategy and demonstrate its performance by presenting the SU’s achievable data rate obtained in closed form as well as in the corresponding numerical results. II. S YSTEM M ODEL Consider a spectrum-sharing system, where a primary transmitter-receiver pair uses adaptive rate and power allocation to perform communications in between. Meanwhile, a secondary transmitter (ST) is trying to access the licensed spectrum and transmit information to its own receiver by taking into account the impact of its transmissions on the QoS in the primary link. As shown in Fig. 1, let gp , gps , gs and gsp denote the instantaneous channel power gains from the primary transmitter (PT) to the primary receiver (PR), from the PT to the ST, from the ST to the secondary receiver (SR), and from the ST to the PR, respectively. All the channel states are assumed to be flatfading, following the independent and identically distributed (i.i.d.) complex Gaussian distribution with zero-mean and unitvariance. Accordingly, all these channel power gains follow the i.i.d. unit-mean exponential distribution with probability density function (PDF) fgX (gX ) = e−gX ,

(1)

where the subscript X refers to the channel power gains of the links shown in Fig. 1, i.e., p , ps , s and sp .

c 2012 IEEE 2162-2337/12$31.00 

YANG and AISSA: ACHIEVABLE DATA RATE IN SPECTRUM-SHARING CHANNELS WITH VARIABLE-RATE VARIABLE-POWER PRIMARY USERS

Here, the variable-rate variable-power M QAM in [9] is adopted by the PU. With a pilot protocol, for a constant pilot ¯ the PR’s instantaneous received SNR in the absence power S, of a SU can be expressed as ¯ p, γp = gp S/N

(2)

where Np is the additive white Gaussian noise (AWGN) power received at the PR. Assuming S¯ = 1, the PDF of γp is given by (3) fγp (γp ) = Np e−Np γp . For each symbol to be transmitted in the primary link, an M QAM constellation from N candidates is selected according to γp . The N candidates are arranged in an ascending order of the data rate and the j th constellation is activated if γp ∈ [Mj γ ∗ , Mj+1 γ ∗ ), j = 0, 1, · · · , N , where Mj is the number of points in the j th M QAM constellation with M0 = 0 and MN +1 = ∞. The parameter γ ∗ > 0 can be optimized using numerical search to maximize the spectral efficiency. To avoid deep channel fading in the primary link, choosing the M0 constellation corresponds to no data transmission once γp < M1 γ ∗ . When γp ∈ [Mj γ ∗ , Mj+1 γ ∗ ), j = 1, · · · , N , and the j th constellation is activated, the data rate is log2 Mj bits and the PT’s transmit power Sj is adapted relative to γp , as specified by (4) Sj = (Mj − 1)/(Kγp ), where K = −1.5/ ln(5BER) is a parameter pertaining to the target BER of the adaptive modulation scheme. Thus, with the variable-rate variable-power modulation, for each M QAM constellation, the PR’s received SNR is a constant, given by γj = (Mj − 1)/K,

j = 1, · · · , N.

(5)

Since the pilot protocol is used in the primary link, the ST is supposed to have the knowledge of the pilot via the broadcast channel in the system that it is trying to access. Hence, the channel state gps may be estimated at the ST by overhearing the pilot transmitted by the PT through this channel [10] and, consequently, the ST can obtain the PT’s instantaneous transmit power Sj as well as deduce the constellation that is being used in the primary link. In the presence of the ST’s transmission, the PR’s effective received SNR with each modulation mode is found at γj , j = 1, · · · , N, (6) γe,j = 1 + gsp Tj /Np where Tj is the ST’s transmit power as the j th constellation is active in the primary link. Hence, in order to guarantee the QoS of primary communications, it is obligatory upon the ST to control its transmit power Tj to satisfy γe,j  Mj γ ∗ when the PU is employing the j

th

(7)

constellation.

313

strategy, where no peak transmit power constraint is imposed on the ST, and the other is with the peak power constraint considered at the ST, which is upper bounded by the first case. It should be noted that the noise plus interference at the SR is assumed to be AWGN, as the ST may get the waveforms of the PT’s transmissions by overhearing the pilot via the channel gps , thereby exploiting precoding techniques to alleviate the impact of the PT’s transmissions on the SR [10]. A. ST without Peak Transmit Power Constraint As above-mentioned, the modulation mode M0 is activated (i.e., no data transmission) in the primary link once a deep channel fading emerges with γp ∈ [0, M1 γ ∗ ), where the ST may transmit with a power as high as possible within its power budget. In the scenario without transmit power constraint at the ST, the SU’s achievable data rate, with M0 constellation activated by PU, can be expressed in [nats/sec/Hz] as  M1 γ ∗  ∞ C0 = fγp (γp ) dγp ln (1 + gs PM /Ns ) fgs (gs ) dgs 0 0  M1 γ ∗  ∞ = Np e−Np γp dγp ln (1 + gs PM /Ns ) e−gs dgs 0 0  ∗ = e−Np M1 γ − 1 eNs /PM Ei (−Ns /PM ) , (8) where PM represents the ST’s transmit power with an arbitrarily high value once there is no data transmission in the primary link, and Ns denotes the SR’s received AWGN power. The PDFs of γp and gs , fγp (γp ) and fgs (g  xs ), are given in (3) and (1), respectively. Besides, Ei(x) = −∞ (et /t) dt is the exponential integral function. When it comes to the modulation modes other than M0 activated by the PU, the ST is required to control its transmit power based on (7) so as to guarantee the QoS of the primary communications is unaffected. Without loss of generality, if the j th constellation is being used in the primary link, j = 1, · · · , N , the ST’s transmit power should be specified as a function of the channel power gain from the ST to the PR, gsp , according to   Np (Mj − 1)/K Np −1 = μj , Tj = (9) ∗ gsp Mj γ gsp where the parameter μj 

(Mj − 1)/K − 1 is defined for a Mj γ ∗

simple expression. Subsequently, based on the ST’s transmit power given by (9), in the case of no peak transmit power constraint imposed on the ST, the SU’s achievable data rate in the unit of [nats/sec/Hz] can be calculated using (10) (see at the top of next page), where C0 is given by (8) and the parameter λj  μj Np /Ns is introduced for simplicity, with μj defined in (9).

III. S ECONDARY U SER ’ S ACHIEVABLE DATA R ATE In this section, we derive the achievable data rate in the secondary link by considering two scenarios with respect to the ST’s transmission capabilities. The first is a general one to demonstrate the full benefit of the proposed transmission

B. ST with Peak Transmit Power Constraint To better protect the PU’s communications, the peak transmit power of a ST is constrained when the ST accesses to a spectrum-sharing channel. Assuming that the peak transmit

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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 1, NO. 4, AUGUST 2012



gs Tj ln 1 + fgs (gs ) fgsp (gsp ) dgs dgsp Ns ∗ 0 0 j=1 Mj γ

 ∞ ∞ N  Mj+1 γ ∗  gs Tj −Np γp = C0 + Np e dγp ln 1 + e−gs e−gsp dgs dgsp N ∗ s 0 0 M γ j j=1 N   ∞  g

 sp −Np Mj γ ∗ −Np Mj+1 γ ∗ gsp /λj e −e Ei − = C0 + −e e−gsp dgsp λ j 0 j=1 = C0 +

N  

Mj+1 γ ∗



fγp (γp ) dγp







e−Np Mj γ − e−Np Mj+1 γ





j=1

power constraint imposed on the ST is PC , when the j th constellation is selected by the PU (j = 0), the ST’s transmit power will be adapted from (9) to Np μj /gsp , gsp > Np μj /PC C Tj = (11) PC , 0  gsp  Np μj /PC j = 1, · · · , N, where the superscript C is used to represent the case that a peak transmit power limit is imposed on the ST. As a result, if the ST’s peak transmit power is limited by PC , the SU’s achievable data rate with the proposed transmission strategy is calculated in [nats/sec/Hz] as shown in (12) on the top of next page, where C0C is the SU’s achievable data rate, with the ST’s peak transmit power constrained, once there is no data transmission in the primary link. In detail, C0C can be found as follows:  M1 γ ∗  ∞ C −Np γp Np e dγp ln (1 + gs PC /Ns ) e−gs dgs C0 = 0 0   ∗ = e−Np M1 γ − 1 eNs /PC Ei (−Ns /PC ) . (13) IV. N UMERICAL R ESULTS AND D ISCUSSIONS Based on the analysis and derivations presented in the above, the performance of the proposed transmission strategy is illustrated numerically in this section. Variable-rate variablepower M QAM [9] is exploited in the primary link with N = 4 constellations as the candidates to be selected. The number of constellation points for each modulation mode Mj = 0, 2, 4, 16, 64 as the mode order j varies from 0 to N = 4. The target BER is set to 10−3 . For the pilot power S¯ = 1, the parameter γ ∗ is optimized as 1.22 and 1.685 when the PR’s received AWGN power Np = −10dBw and −20dBw, respectively. In addition, for the case that no peak transmit power constraint is imposed on the ST, the latter sets its transmit power to PM = 15dBw when constellation M0 is activated in the primary link. To begin with, the SU’s achievable data rate is plotted as a function of the SR’s received AWGN power Ns in Fig. 2. Two examples are considered for the PR’s received AWGN power: Np = −10dBw and −20dBw. The peak transmit power constraint imposed on the ST is set to PC = 10dBw and, moreover, the case with no peak transmit power constraint



(10)

λj ln λj λj − 1

4.5 SU’s Achievable Data Rate [nats/sec/Hz]

Cs = C0 +

N  

no Pc, N = −10dBw p

4

Pc = 10dBw, N = −10dBw p

3.5

no Pc, N = −20dBw p

Pc = 10dBw, N = −20dBw

3

p

2.5 2 1.5

Np = −10dBw N = −20dBw p

1 0.5 0 −20

−15 −10 −5 SR’s Received AWGN N [dBw]

0

s

Fig. 2. Achievable data rate in the secondary link versus the received AWGN power at the SR, Ns , for the PR’s received AWGN Np = −10dBw and −20dBw.

imposed on the ST is investigated as well. From this figure, we observe that the SU’s achievable data rate is reduced with the increase in Ns and, however, improved with the increase in Np . The former phenomenon is intuition-compliant. The main reason behind the latter is that the impact of the interference from the ST to the PR’s effective received SNR becomes more and more ignorable as the PR’s received AWGN power increases. Therefore, the ST is allowed to transmit with a relatively higher power in the case of higher Np , which can be perceived from the ST’s transmit power adaptation as shown in (9) and (11). Furthermore, to demonstrate the effect of the ST’s peak transmit power constraint, PC , on the performance of the secondary link, we depict the SU’s achievable data rate versus PC in Fig. 3 for Np = −10dBw and −20dBw, where the SR’s received AWGN power Ns = −10dBw and the case with no peak transmit power constraint on the ST is also provided for the sake of comparison. As is shown in this figure, the case with no peak transmit power constraint at the ST is an upper bound on that with the peak transmit power constraint at the ST. As PC is enhanced, the achievable data rate in the secondary link with the peak transmit power constraint increases and approaches that without the peak transmit power constraint, which substantiates the validity of our derivations.

YANG and AISSA: ACHIEVABLE DATA RATE IN SPECTRUM-SHARING CHANNELS WITH VARIABLE-RATE VARIABLE-POWER PRIMARY USERS

CsC

=

C0C

+

N   j=1

= C0C +

Mj+1 γ ∗

Mj γ ∗

N   ∗ e−Np Mj γ j=1

= C0C +

N   ∗ e−Np Mj γ j=1





gs ln 1 + λ e−gs e−gsp dgs dgsp j Np g sp 0 μ PC j

 ∞  ∞ g s + N e−gsp dgsp ln 1 + PC e−gs dgs p N s 0 μ j PC   ∞   g

∗ sp gsp /λj −e Ei − − e−Np Mj+1 γ e−gsp dgsp Np λ j PC μj

 ∞ Ns Ns −gsp PC + N e dgsp · e Ei − p PC PC μj

    Ns ∗ λj Ns Np −(λ −1) P C Ei − e−Np Mj+1 γ μj − e j − Ei − λj − 1 PC PC N



Ns Ns − pμ + e PC j − 1 e PC Ei − PC

Np e

−Np γp







dγp

(12)

of cognitive broadcast and multi-access channels presented in [11] and [12], future work includes the extension of our proposed scheme into the scenario with multiple secondary users.

1.5 SU’s Achievable Data Rate [nats/sec/Hz]

315

N = −10dBw p

1

ACKNOWLEDGEMENT

no Pc, N = −10dBw p

The authors would like to thank the anonymous reviewers for bringing [4] and [12] to their attention.

Np = −10dBw no Pc, N = −20dBw p

0.5

N = −20dBw Np = −20dBw

0 0

p

5 10 Peak Transmit Power Constraint on the ST [dBw]

R EFERENCES

15

Fig. 3. Achievable data rate in the secondary link versus the peak transmit power constraint imposed on the ST, Pc , for the SR’s received AWGN Ns = −5dBw. Also shown is the case with no peak transmit power constraint at the ST.

V. C ONCLUSIONS In general, secondary users (SUs) should stop their communications in a cognitive radio network once primary users (PUs) emerge to occupy the licensed spectrum. For the purpose of increasing the SUs’ transmission opportunities, in this work we proposed a transmission strategy for SUs within a spectrum-sharing context where PUs adopt variablerate variable-power M QAM modulation. Even when a PU is communicating, the SU can adjust its transmit power based on the gap between the PU’s received SNR and the lower SNR boundary for the modulation mode of the moment in the primary link, so as to promise the PU’s QoS. Considering different transmission abilities of the secondary transmitter (ST), we derived achievable data rates in the secondary link and obtained corresponding closed-form expressions. From numerical results provided here, the validity of our derivations is substantiated and we may get a conclusion that, with the proposed transmission strategy, the SU’s performance improves with the decrease in the SR’s received AWGN power, while with the increase in the PR’s received AWGN power or the peak transmit power constraint value at the ST. Finally, in light

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