19th International Conference on Telecommunications (ICT 2012)
Secondary Link Adaptation in Cognitive Radio Networks: End-to-End Performance with Cross-Layer Design Hao Ma† , Yuli Yang† , Sonia Aissa†‡ †
Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal, KSA. ‡ INRS, University of Quebec, Montreal, QC, Canada. Email: {hao.ma, yuli.yang}@kaust.edu.sa;
[email protected]
Abstract—Under spectrum-sharing constraints, we consider the secondary link exploiting cross-layer combining of adaptive modulation and coding (AMC) at the physical layer with truncated automatic repeat request (T-ARQ) at the data link layer in cognitive radio networks. Both, basic AMC and aggressive AMC, are adopted to optimize the overall average spectral efficiency, subject to the interference constraints imposed by the primary user of the shared spectrum band and a target packet loss rate. We achieve the optimal boundary points in closed form to choose the AMC transmission modes by taking into account the channel state information from the secondary transmitter to both the primary receiver and the secondary receiver. Moreover, numerical results substantiate that, without any cost in the transmitter/receiver design nor the end-to-end delay, the scheme with aggressive AMC outperforms that with conventional AMC. The main reason is that, with aggressive AMC, different transmission modes utilized in the initial packet transmission and the following retransmissions match the timevarying channel conditions better than the basic pattern.
I. I NTRODUCTION In the information era, traffic in wireless communication systems is increasing rapidly as more and more services have to be provided with reliable and efficient transmissions. Compared to traditional design approaches, cross-layer design has proved to be a necessity for improving the system spectral efficiency while maintaining the quality of service (QoS) at the desired level. Such design can be implemented for link adaptation purposes by using adaptive modulation and coding (AMC) at the physical layer to match time-varying channel conditions, and truncated automatic repeat request (TARQ) at the data link layer to control packet delays while ensuring the overall reliability by requesting retransmissions for erroneously received packets [1], [2], [3], [4]. In many works, cross-layer combining of AMC with ARQ has been studied. A cross-layer design with constant-power AMC and T-ARQ under delay and error performance constraints is presented in [1]. Optimization of joint implementation of variable-power AMC and T-ARQ is also investigated in [5] and shown to result in an improvement of system performance in terms of spectral efficiency and packet loss rate. Further, aggressive AMC (A-AMC) has been proposed in [2] and analyzed for the simple case with one ARQ retransmission. Later, a generalization of A-AMC combined with multiple ARQ retransmissions was presented in [3] for multiuser multiple-input multiple-output (MIMO) systems.
978-1-4673-0747-5/12/$31.00 ©2012 IEEE
On the other hand, contemporary wireless communication systems are suffering from a shortage of spectrum resources, which prevents further penetration of more services and devices in the wireless market. With the development of cognitive radio (CR), CR-based spectrum-sharing is emerging as a promising method to solve this problem [6], [7]. In this technique, rather than reserving a spectrum band exclusively to licensed users (primary users), unlicensed users (secondary users) are allowed to access this spectrum band under appropriate constraints established in order to maintain the QoS of primary users in the shared spectrum at required levels. Motivated by the above issues, we consider the cross-layer design of AMC and ARQ to be exploited by secondary users in CR networks. In order for the secondary user to take full advantage of the shared spectrum, aiming at maximizing spectral efficiency with a target packet loss rate we derive the optimal boundary points for the secondary user to choose AMC transmission modes under spectrum-sharing resource requirements, by taking into account the channel state information from the secondary transmitter to both the primary and the secondary receivers. The corresponding closed-form expressions are achieved for the designs with basic AMC and with A-AMC. Numerical results provide reference for both designs and, additionally, substantiate the design with A-AMC outperforms that with basic AMC because the former utilizes different AMC transmission modes in the first transmission and the following retransmissions, which matches the timevarying channel conditions better than the latter. The remainder of this paper is organized as follows. Section II presents the considered spectrum-sharing system model as well as the introduction to the cross-layer combining of AMC and ARQ in the secondary link. In Section III, we derive the optimal boundary points for the secondary user to maximize its average spectral efficiency with the cross-layer combining of basic AMC or A-AMC at the physical layer and T-ARQ protocol at the data link layer. Numerical results are provided in Section IV and the paper is concluded in Section V. II. S YSTEM M ODEL A. Spectrum-Sharing Network As shown in Fig. 1, we consider a spectrum-sharing system where a secondary user is scheduled to perform communications in the spectrum band originally allocated to a primary
user. The secondary transmitter (ST) operates as long as the average interference power to the primary receiver (PR) does not exceed a given interference limit. In order to take full advantage of the shared spectrum, the ST adapts its transmission mode according to both the channel power gains from it to the secondary receiver (SR), hss , and from it to the PR, hsp . Under the assumption of discrete-time block fading channels, both hsp and hss are assumed to follow independent and identically distributed Nakagami-m model with unit variance and their probability density functions (PDFs) are expressed as sp
fsp (hsp ) =
msp −1
(msp )m (hsp ) Γ (msp )
exp (−msp hsp )
(1)
primary user, defined as Z Z P (hss , hsp )hsp fsp (hsp )fss (hss )dhsp dhss ≤ Imax , hss
hsp
(4) where P (hss , hsp ) is the ST’s transmit power, function of both channel gains [8]. Here, Imax is the upper bound of the average interference power exerted by the ST on the PR, to promise the QoS requirements of the primary user remain satisfied. Since the interference constraint in (4) relies on the ratio of both channel gains, a new random variable v = hss /hsp is defined, with PDF [9] given by: sp
ss
(mss )m (hss ) fss (hss ) = Γ (mss )
ss
v m −1 ρ−m , fv (v) = β(msp , mss ) (v + ρ1 )msp +mss
and mss −1
exp (−mss hss ),
(2)
respectively, where msp and mss represent the Nakagami fading parameters for channel gains hsp and hss , respectively, and Γ(·) is the Gamma function. In addition, the noise power spectral density and the signal bandwidth are denoted by N0 and B, respectively. Without loss of generality, it is assumed that N0 B = 1.
Figure 1: Spectrum-sharing system model.
where ρ=
mss msp
In the above-mentioned spectrum-sharing system with Nakagami-m fading channels, we consider a cross-layer combination of AMC and ARQ in the secondary link. At the data link layer, once the SR detects a received packet to be erroneous, it sends a feedback to the ST requesting the latter to perform T-ARQ up to a maximum number of retransmissions Nr . After Nr retransmission attempts, the packet loss probability should be no larger than the maximum allowable packet loss rate Ploss which, in turn, constrains the packet error rate (PER) of each transmission to be less than a physical layer target, Ptgt . In detail, the relationship between Ploss and Ptgt is given by Nr +1 Ploss = Ptgt . (3) At the physical layer, the ST determines its adaptive power as a function of the channel gains hss and hsp , by considering the average interference power constraint imposed by the
and β(msp , mss ) =
Γ(msp )Γ(mss ) . Γ(msp + mss )
In order to implement AMC in the secondary link, the total range of the ratio v is divided into N + 1 non-overlapping consecutive intervals, [vn , vn+1 ), n = 0, 1, . . . , N , based on which AMC mode n is chosen when v ∈ [vn , vn+1 ) and transmission is performed with a power of Pn (hss , hsp ). All AMC transmission modes are arranged in ascending rate order, and no transmission occurs when v < v1 so as to avoid deep channel fading, namely in the case that hss is too weak compared to hsp . Thus, the secondary’s received SNR is given by γ v = Pn (hss , hsp )hsp v (6) and the average interference constraint given in (4) transforms to [9, (6)]: N Z vn+1 X Pn (hss , hsp )hsp fv (v)dv ≤ Imax . (7) n=1
B. Cross-Layer Design of AMC and ARQ
(5)
vn
The PER of each transmission mode n is a function of γ v , according to ( 1 0 ≤ γ v < γnb P ERn (γ v ) = (8) ss sp sp an e−gn Pn (h ,h )h v γnb ≤ γ v where an , gn and γnb are mode-dependent fitting parameters. For example, these fitting parameters are provided in [1] for different transmission modes in a system with a packet length Np = 1080 bits. Accordingly, the ST’s power allocated to AMC transmission mode n can be expressed in terms of the instantaneous PER, P ERins , as [9] 1 an Pn (hss , hsp ) = ln . (9) gn vhsp P ERins III. P ERFORMANCE OF C OMBINING AMC WITH T-ARQ UNDER S PECTRUM -S HARING C ONSTRAINTS In this section, we derive the optimal boundary points for the secondary user to choose AMC transmission modes by
maximizing the average spectral efficiency under spectrumsharing requirements. Both basic AMC and aggressive AMC are considered in the cross-layer designs with truncated ARQ.
A. Scheme with Basic AMC To begin with, the combining of basic AMC with T-ARQ is considered for the cross-layer design in the secondary link, i.e., the same transmission strategy is used in the first transmission and potential retransmissions. We investigate Nr = 1 retransmission in the T-ARQ protocol, which can be generalized into the case with more retransmissions following the approach in [3]. For one transmission, the average spectral efficiency achieved at the physical layer is the weighted sum of data rates from different modes, given by SE =
N X
Rn P r(n),
(10)
n=1
where P r(n) is the probability that the nth transmission mode is chosen in the transmission from ST, defined by [9] Z vn+1 fv (v)dv P r(n) = vn ss
ρ−m = ss × m β(msp , mss ) h ss ivn+1 , v m ×2 F1 ([mss , mss + msp ]; [1 + mss ]; −vρ) vn (11) where 2 F1 ([a, b]; [c], z) denotes the Gaussian hypergeometric function. According to (8), the optimization problem for maximizing the overall average spectral efficiency in this case is formulated as follows: maximize
P ERins ,{vn }N n=1
subject to :
S ef f
C1 :
N X
Z
vn+1
Sn
n=1
vn
1 fv (v)dv ≤ Imax (12) v
C2 : P ERins ≤ Ptgt ,
# Z vn+1 N X 1 1 an +η log fv (v)dv − Imax , g P ERins v vn n=1 n (13) where η is the Lagrangian multiplier. According to the Karush-Kuhn-Tucker (KKT) conditions [10], the optimal parameters {vn? }N n=1 should satisfy the following equations: ∂L (v1 , v2 , . . . , vN , η) = 0 n = 1, . . . , N ∂vn Z vn+1 N X 1 1 an log fv (v)dv = Imax g P ER v ins vn n=1 n P hsp vn > γnb ,
S ef f =
(1 − P ERins )(2 + P ERins ) SE, 2
and we have Sn =
1 log gn
an P ERins
1
and
2 Ptgt = Ploss .
To solve the optimization problem above, we define its Lagrangian as: L(v1 , v2 , . . . , vN , η) Z vn+1 N (1 − P ERins )(2 + P ERins ) X Rn fn (v)dv 2 vn n=1
(14)
n = 1, . . . , N,
where P is the secondary’s average transmit power. As such, the optimal boundary points {vn? }N n=1 can be solved as 2ηS1 v1? = [(1 − P ERins )(2 + P ERins )] R1 (15) 2η(Sn−1 − Sn ) vn? = [(1 − P ERins )(2 + P ERins )] (Rn−1 − Rn ) where n = 2, . . . , N . The optimal η can be obtained numerically. B. Scheme with Aggressive AMC In order for the secondary user to achieve higher spectral efficiency, aggressive AMC is considered in the cross-layer design. In the combination of A-AMC and T-ARQ, the selection thresholds of the AMC modes may be different in the first transmission and the following retransmissions, because the mode selection process depends on the ratio between the instantaneous channel power gains, hss and hsp , and both gains vary during different transmissions. With Nr = 1 in the T-ARQ protocol, we denote the selecN tion thresholds by {vn,T X }N n=1 and {vn,RT }n=1 for the first transmission (TX) and the retransmission (RT), respectively, and use PT X and PRT to represent the instantaneous PER for the first transmission and the retransmission, i.e., TX and RT, respectively. Therefore, the packet loss rate constraint with Nr = 1 A-AMC is given by PT X · PRT ≤ Ploss ,
where
=
"
(16)
where Ploss is the maximum allowable packet loss probability. Based on [3], the overall average spectral efficiency in this case can be calculated as follows: (1 − PRT )PT X S ef f = (1 − PT X )SE T X + 1 , (17) + SE1 SE TX
RT
where SE T X and SE RT denote the average spectral efficiency achieved in the first transmission and the retransmission, respectively, expressed as Z vn+1,T X N X SE T X = Rn fv (v)dv, n=1
vn,T X
SE RT =
N X
vn+1,RT
Z Rn
? N Thus, the optimal boundary points, denoted {vn,T X }n=1 and ? N {vn,RT }n=1 , can be found using:
fv (v)dv. vn,RT
n=1
Then, to maximize the overall average spectral efficiency of the cross-layer combination of A-AMC and T-ARQ, the optimization problem is formulated as maximize
N PT X ,{vn,T X }N n=1 ,PRT ,{vn,RT }n=1
s.t.
N X
C1 :
n=1 N X
C2 :
S ef f
vn+1,T X
Z
1 fv (v)dv ≤ Imax v
Sn,T X vn,T X vn+1,RT
Z Sn,RT
vn,RT
n=1
1 fv (v)dv ≤ Imax v
PT X · PRT ≤ Ploss ,
C3 :
(18) where 1 an log , gn P T X an 1 = log , gn PRT
Sn,T X = Sn,RT
(19)
S ef f = (1 − PT X )SE T X +
(1 − PRT )PT X . 1 + SE1 SE TX
RT
The Lagrangian for this problem can be stated as L(v1 , v2 , . . . , vN , λ, µ) Z X = (1 − PT X ) Rn 1
P
Rn
"
R vn+1,T X
N X
vn,T X
fv (v)dv
PT X (1 − PRT ) 1 + P R vn+1,RT
fv (v)dv
Z
Rn
vn,RT
vn+1,T X
1 an +λ log g P n TX vn,T X n=1 "N Z vn+1,RT X 1 an log +µ g PRT vn,RT n=1 n
fv (v)dv
# 1 fv (v)dv − Imax v # 1 fv (v)dv − Imax , v
(20) where λ and µ are the Lagrangian multipliers. According to the KKT conditions, the optimal v’s should satisfy the following equations: ∂L (v1 , v2 , . . . , vN , λ, µ) = 0 ∂vn,T X ∂L (v1 , v2 , . . . , vN , λ, µ) = 0 ∂vn,RT
n = 1, . . . , N (21) n = 1, . . . , N
with the constraints: Z vn+1,T X N X 1 an 1 log fv (v)dv ≤ Imax , g P v n T X v n,T X n=1 Z vn+1,RT N X 1 1 an log fv (v)dv ≤ Imax , g P v RT vn,RT n=1 n P hsp vn > γnb PT X · PRT ≤ Ploss .
λS1,T X [(1 − PT X ) + 41 PT X (1 − PRT )]R1 λ(Sn−1,T X − Sn,T X ) v˜n,T X = [(1 − PT X ) + 14 PT X (1 − PRT )](Rn−1 − Rn ) µS1,RT v˜1,RT = 1 4 PT X (1 − PRT )R1 µ(Sn−1,RT − Sn,RT ) v˜n,RT = 1 , 4 PT X (1 − PRT )(Rn−1 − Rn ) (25) where n = 2, . . . , N . The optimal λ, µ can be obtained numerically. v˜1,T X =
vn+1,T X
vn,T X
+
λS1,T X [(1 − PT X ) + A PT X (1 − PRT )]R1 λ(Sn−1,T X − Sn,T X ) ? vn,T X = [(1 − PT X ) + A PT X (1 − PRT )](Rn−1 − Rn ) µS1,RT ? v1,RT = [B PT X (1 − PRT )]R1 µ(Sn−1,RT − Sn,RT ) ? vn,RT = , [B PT X (1 − PRT )](Rn−1 − Rn ) (23) where n = 2, . . . , N , and we have 2 2 SE T X SE RT , B= , A= SE T X + SE RT SE T X + SE RT 1 an 1 an Sn,T X = log , Sn,RT = log . gn PT X gn PRT (24) The optimization results should satisfy 41 < A < 1 and 0 < B < 14 because the key assumption in A-AMC is that the transmission mode selection is more daring in the first transmission than in following retransmissions [2], [3]. One good approximation can be achieved by setting both A and B to 41 , and the approximation formulas can be derived as ? v1,T X =
n = 1, . . . , N,
(22)
IV. N UMERICAL R ESULTS Now, we present numerical results based on the theoretical analysis developed in Section III, to quantify the performance gain of the secondary link when utilizing cross-layer combining of AMC, basic or aggressive, with T-ARQ in terms of the overall average spectral efficiency within cognitive radio networks when transmissions are performed over Nakagamim block fading channels. For illustration purpose, the shape parameters m are set to m = 1 and m = 2. We consider two sets of candidate transmission modes as detailed in [1] where the corresponding PER fitting parameters in (4) are also introduced. The first set, referred to as TM1, contains 7 uncoded M-QAM modulation modes, and the second set, TM2, contains 6 convolutionally coded modulation modes. Without loss of generality, the packet length is set to Np = 1080 bits. We remark that the packet length is chosen according to the channel fading speed in the system design, and therefore,
Average Spectral Efficiency (bps/Hz)
1.5
AMC A−AMC approximation A−AMC optimization
1
TM2
TM1
0.5
0 −15
−10
−5 0 Average Interference Limit (dB)
5
Figure 2: Overall average spectral efficiency in Nakagami fading channels with m = 1 (Rayleigh fading). V. C ONCLUSION In this paper, we investigated the end-to-end performance of a secondary link exploiting cross-layer design of AMC and ARQ in cognitive radio networks. Taking into account the spectrum-sharing constraints, we obtained the optimal
Average Spectral Efficiency (bps/Hz)
the phenomena revealed by our numerical results will not be affected by this setting. Furthermore, the maximum allowed packet loss probability is set to Ploss = 10−4 . The overall average spectral efficiency of the cross-layer design versus the average interference limit is depicted in Figs. 2 and 3, for Nakagami fading channels with parameters m = 1 and m = 2, respectively. In each figure, the cases of AAMC optimization, A-AMC approximation and basic AMC are compared for systems with TM1 and TM2. We observe that, either for TM1 or for TM2, the gap between the approximation and the numerical optimization of the A-AMC cases are negligible, which indicates that the approximation is reasonable. Moreover, both figures reveal that the cross-layer design with A-AMC outperforms that with basic AMC by 0.05-0.2 bits/symbol (around 13%) when the average interference limit at the PR ranges from -15dB to 5dB. Hence, an additional 0.5-2Mbps of bandwidth becomes available if the symbol rate in the secondary link is 10Msymbols/sec. Besides, as the average interference limit increases, the gain obtained by the design with A-AMC over that with basic AMC increases marginally. Thus the overall average spectral efficiency can be improved without any cost in the transmitter/receiver design, by changing the AMC in the crosslayer design from the conventional scheme to the aggressive one. Further, with T-ARQ, the end-to-end delay of the A-AMC is the same as that of the basic AMC. In addition, in both figures, it is confirmed that the system with TM2 can achieve higher spectral efficiency than that with TM1, but at the cost of the complexity of channel coding. However, once the average interference limit of the primary user is lower than -10dB, the difference between cases with TM1 and TM2 gets much smaller, which makes operation of the system with TM1 preferable due to its simplicity.
1.5
AMC A−AMC approximation A−AMC optimization
TM2
1
TM1
0.5
0 −15
−10
−5 0 Average Interference Limit (dB)
5
Figure 3: Overall average spectral efficiency in Nakagami fading channels with m = 2.
boundary points to choose the transmission modes at the physical layer that maximize the overall spectral efficiency of the cross-layer combination with basic or aggressive AMC, while taking into account a target packet loss rate with TARQ at the data link layer. Numerical results illustrate that the design with aggressive AMC outperforms that with basic AMC in terms of the overall average spectral efficiency. Indeed the aggressive scheme allows different transmission modes in the first transmission and following retransmissions, which makes the design more daring to perform the first transmission with a higher data, while keeping the packet loss rate after retransmissions no larger than the target. More importantly, compared to basic AMC, aggressive AMC can be realized without any cost in equipment change nor the end-to-end delay. R EFERENCES [1] Q. Liu, S. Zhou, and G. Giannakis, “Cross-layer combining of adaptive modulation and coding with truncated ARQ over wireless links,” IEEE Trans. Wireless Commun., vol. 3, no. 5, pp. 1746–1755, Sep. 2004. [2] C. Gonz´alez, L. Szczeci´nski, and S. A¨ıssa, “Throughput maximization of ARQ transmission protocol employing adaptive modulation and coding,” in Proc. IEEE/IEE ICT, Fortaleza, Brazil, Aug. 2004, pp. 607–615. [3] J. Qi and S. A¨ıssa, “Cross-layer design for multiuser MIMO MRC systems with feedback constraints,” IEEE Trans. Vehicular Tech, vol. 58, no. 7, pp. 3347–3360, Sep. 2009. [4] A. Maaref and S. A¨ıssa, “Combined adaptive modulation and truncated ARQ for packet data transmission in MIMO systems,” in Proc. IEEE Global Telecommun. Conf., Dallas, TX, Nov. 2004, pp. 3818–3822. [5] J. Harsini and F. Lahouti, “Adaptive transmission policy design for delay-sensitive and bursty packet traffic over wireless fading channels,” IEEE Trans. Wireless Commun., vol. 8, no. 2, pp. 776–786, Feb. 2009. [6] J. Mitola III and G. Maguire Jr, “Cognitive radio: making software radios more personal,” Personal Communications, IEEE, vol. 6, no. 4, pp. 13– 18, 1999. [7] S. Haykin, “Cognitive radio: brain-empowered wireless communications,” Selected Areas in Communications, IEEE Journal on, vol. 23, no. 2, pp. 201–220, Feb. 2005. [8] L. Musavian and S. A¨ıssa, “Adaptive modulation in spectrum-sharing systems with delay constraints,” in Proc. IEEE International Conference on Communications (ICC’09), Dresden, Germany, Jun. 2009, pp. 1–5. [9] K. Nehra, A. Shadmand, and M. Shikh-Bahaei, “Cross-layer design for interference-limited spectrum sharing systems,” in Proc. IEEE Global Communications Conference (Globecom’10), Miami, USA, Dec. 2010. [10] S. Boyd and L. Vandenberghe, Convex optimization. Cambridge University Press, 2004.
