www.ietdl.org Published in IET Communications Received on 2nd September 2013 Revised on 27th April 2014 Accepted on 15th May 2014 doi: 10.1049/iet-com.2013.1145
ISSN 1751-8628
Spectrum-sharing broadcast channels using fountain codes: energy, delay and throughput Yuli Yang1, Sonia Aïssa2 1
Electrical and Electronics Engineering Department, Meliksah University, Kayseri 38280, Turkey Institut National de la Recherche Scientifique (INRS-EMT), University of Quebec, Montreal, QC H5A 1K6, Canada E-mail:
[email protected] 2
Abstract: In this study, the authors develop a transmission protocol for cognitive radio networks, whereby fountain codes are exploited in the broadcast channels and secondary users help with the broadcast from the base station (BS) to primary users (PUs). With fountain codes, the BS broadcasts to the secondary transmitter (ST) as well as PUs simultaneously, and stops broadcasting once the ST has received sufficient codeword to decode the original information reliably. Then, the ST will resume the broadcasting to PUs until all of them can decode the original information successfully. While broadcasting, the ST transmits information over its own link, that is, to the secondary receiver, based on dirty paper coding technique. As such, the energy expenditure at the BS is reduced and, moreover, secondary links have more opportunities to access the licensed spectrum band. To evaluate the performance of the developed scheme, they analyse its energy expenditure, broadcast time as well as the throughput over secondary links, and achieve the corresponding closed-form expressions. Compared with the traditional broadcast protocol without the secondary’s help, illustrative numerical results substantiate the validity of the author’s derivations, which also demonstrate the efficiency of the developed scheme both on the energy savings and on the spectrum utilisation.
1
Introduction
Since it emerged, the concept of cognitive radio (CR) has shown tremendous potential to improve the spectral efficiency in licensed bands via realizing dynamic spectrum access [1, 2]. Furthermore, in order to solve the spectrum scarcity problem, regulation bodies, such as the Federal Communications Commission (FCC), have allowed unlicensed users (also known as secondary users, SUs) to operate within the spectrum band allocated to licensed users (also known as primary users, PUs) while ensuring that the PUs’ quality-of-service (QoS) remains unaffected [3], which encouraged the CR technology to be intensively studied [4, 5] and the development of various functionalities in CR design [6, 7]. For the purpose of fully utilizing the licensed spectrum bands, there are three main paradigms for the network design based on the concept of CR, i.e., interweave, underlay and overlay [8]. Amongst them, the interweave paradigm is the original motivation for CR, which activates secondary users (SUs) only when the PUs are absent. Then, in order to further improve the spectrum utilisation efficiency, underlay and overlay paradigms are exploited. They allows SUs’ operation in the PUs’ presence as long as PUs’ quality of service (QoS) is not affected. Specifically, the underlay paradigm mandates SUs to access the licensed spectrum bands as long as the interference they inflict onto PUs remains below a tolerable limit [9, 10]. In the overlay paradigm, SUs would manage their own communications 2574 & The Institution of Engineering and Technology 2014
by utilising the knowledge of PUs’ message and codebook to reduce the interference that PUs will suffer. Comparisons among these paradigms are listed in Table 1, where from interweave to overlay, at the cost of higher operation complexity, SUs may achieve better performance, specifically on obtaining more opportunities to access the licensed spectrum. In this work, the overlay paradigm is considered to break the limitation on SUs’ transmit power and, accordingly, to increase the SUs’ communications opportunities. The fundamental problem in this context is how to efficiently and fairly allocate the radio resources for SUs’ communications while balancing their effects on PUs’ QoS. As the interference from SUs to PUs can be offset by using part of SUs’ transmit power to relay PUs’ information, PUs’ QoS is further guaranteed with more flexible resource allocation [8]. With this paradigm, SUs can be deemed to play a role of helpers in PUs’ communications and the SUs performance has been analysed from an information-theoretic view in [11, 12]. On the other hand, as an information-collection scheme, fountain codes have been widely studied in recent years, see [13] and references therein. It has been proven that the success of fountain codes for erasure channels can be carried over to general binary input memoryless symmetric channels, additive white Gaussian noise (AWGN) channels and Rayleigh fading channels [14–16]. Consequently, fountain codes have been suggested to be exploited in point-to-point links [17, 18] as well as multi-point cooperative communications, including relaying networks IET Commun., 2014, Vol. 8, Iss. 14, pp. 2574–2583 doi: 10.1049/iet-com.2013.1145
www.ietdl.org Table 1 Comparisons among CR paradigms paradigms
required information at SU
SU’s behaviour in PU’s presence
interweave underlay overlay
whether PU is active or silent channel strength from SU to PU PU’s message and codebook
stops operation operates with transmit power limitation operates without power limitation while helping PU
[19, 20] and multicast/broadcast channels [21–23], since they enable the accumulation of information directly instead of energy so as to achieve higher effective throughput, with zero-rate feedback, compared with energy-accumulation transmission with repetition coding. Motivated by this, we develop a spectrum-sharing transmission strategy with fountain codes exploited for the broadcasting from the base station (BS) to PUs, where SUs are leveraged as relaying nodes to improve the broadcasting performance while implementing their own communications. For relays used in broadcast channels, the power and resource allocation, network design as well as diversity-multiplexing tradeoff have been studied in [24– 26], respectively, where different information is broadcast to different users and a single user is scheduled within each resource unit (e.g. time slot or frequency sub-band). In this paper, we focus on the BS broadcasting the same information encoded with fountain codes to multiple PUs simultaneously. In general (i.e. without SUs’ help), for the BS’s broadcast with fountain codes, at a given time, the BS transmits to all PUs in the broadcast group, instead of the PU with the best instantaneous channel state. Hence, no feedback of channel state information (CSI) is required and the utilisation efficiency of licensed spectrum is improved. Furthermore, we will quantify SUs’ help with the broadcast in a CR network from an information theoretical view, in terms of energy expenditure and transmission latency. When it comes to the simultaneous broadcast from a BS to multiple PUs, using fountain codes, the energy expenditure and transmission latency in broadcasting depend on the PU with the worst channel condition, which will be measured by the path loss. When the transmit/receive antennas used are assumed to have unity gain, the ‘path loss’ is generally given by Rappaport [27, Ch.3] PL[dB] = −10 log10
(c/f )2 (4p)2 d 2
(1)
where c = 3 × 108 m/s is the light speed and f is the carrier frequency in Hertz. Besides, d is the distance from the transmitter to the receiver, which is an important determinant of the path loss. As shown in (1), the path loss is proportional to the square of d. Therefore, for the broadcast system under study, the channel power gain in large-scale is increased with the decrease in the distance from the BS to the PUs within the broadcast group. To improve the broadcast performance, a SU located between the BS and the broadcast group should be scheduled to help with the broadcast, so as to perform with higher channel power gains achieved and, accordingly, lead to the BS’s energy expenditure reduced. Herein, our developed broadcast protocol with fountain codes consists of two phases. In the first phase, the BS broadcasts to PUs as well as the scheduled secondary transmitter (ST). Once the ST has finished its decoding process of the fountain coded information, it will feedback an acknowledgement to the BS. Subsequently, this phase will stop and the next IET Commun., 2014, Vol. 8, Iss. 14, pp. 2574–2583 doi: 10.1049/iet-com.2013.1145
phase is launched. In the second phase, the ST will resume the broadcast to PUs and simultaneously transmit to its own receiver based on dirty paper coding (DPC). As the ST, with DPC-based technique, can make the additive interference pre-subtracted from broadcast codewords as if there were no interference of secondary information [28–30], the secondary link has more opportunities to access the licensed spectrum band while improving the QoS for PUs in the broadcasting. Given the proposed protocol, the main objective of this paper is to investigate how a scheduled ST can help the BS’s broadcast of the fountain coded information to multiple PUs, in the view of energy saving and latency reduction for primary links, as well as throughput improvement for secondary links. Specifically, our main contributions are 3-fold: † We propose a transmission strategy by using fountain codes for the BS’s broadcast to multiple PUs under a scheduled ST’s help, where no CSI feedback is required and high spectrum efficiency is achieved. Moreover, a statistical framework is developed to investigate how the scheduled ST can help the BS’s broadcast in a CR network. † To quantify the scheduled ST’s help with the BS’s broadcast service, we compare the proposed scheme to its counterpart without the ST’s help in terms of the BS’s energy expenditure and broadcast time. For these metrics, closed-form expressions are achieved. † To evaluate the ST’s performance, we firstly obtain an approximation of the ST’s transmission time to each PU so as to scale the effects of the related channel power gains and the information entropy to be broadcast on it. Since it is difficult to achieve the statistics of the ST’s broadcast time from the probability density function (PDF) of its transmission time to each PU, we then process the calculation by handling the cases pertaining to the worst channel-case PUs in the first and second phases separately. In this way, closed-form expressions are reached for the ST’s broadcast time and the throughput in secondary link. In detailing the above-mentioned contributions, the remaining of the paper is organised as follows. In the next section, we introduce some preliminaries on fountain codes and detail the proposed broadcast protocol within spectrum-sharing networks, based on which we analyse the broadcast data rate, the energy expenditure, the broadcast time and the throughput over secondary links in Section 3. In Section 4, the broadcast data rate and the energy expenditure are derived for the BS’s broadcast without the secondary’s help. In Section 5, numerical results are provided to substantiate the validity of our analysis and derivations as well as to demonstrate the efficiency of the proposed broadcast protocol. Finally, concluding remarks are presented in Section 6. Notations: Hereafter, fX(x) and FX(x) are used to denote the PDF and the cumulative distribution function (CDF) of a random variable X, respectively. In addition, E {·} denotes 2575
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www.ietdl.org the expectation operator x and the exponential integral function is given by Ei(x) = −1 et /t dt.
2
Broadcast using fountain codes
In a broadcast system using fountain codes, the BS encodes the data packet to be broadcast with a fountain code and transmits it to all users in the broadcast group. While listening to the BS, the users accumulate received information. Each user will transmit an acknowledgement to inform the BS about its successful reception as soon as it has acquired sufficient entropy to reliably decode the broadcast information. Until the BS receives all users’ acknowledgements, it will stop transmitting the data packet of the moment and start to broadcast the next packet. To simplify the analysis of the proposed protocol, it is assumed that fountain codes used are perfect at all desired rates. That is, all users are capable of decoding their received information correctly as long as the receiving time multiplied with the instantaneous channel capacity is equal to the entropy of the codeword [17–23]. 2.2
fg (g) = 1/ g exp −g/ g,
System model
In this section, we firstly present some preliminaries on fountain codes exploited in broadcast systems and then detail the proposed broadcast protocol within spectrum-sharing networks. 2.1
amplitudes. Thus, their channel power gains follow independent exponential distributions with the PDFs given by
BS’s broadcast with secondary assistance
Consider a spectrum-sharing broadcast channel as shown in Fig. 1, where the BS needs to transmit an information codeword with bandwidth normalised entropy, Ht, in the unit of [nats/Hz], to N PUs. A ST, specifically located between the BS and the broadcast group of PUs, is scheduled to help with the broadcast and simultaneously transmit the information to its receiver, that is, the secondary receiver (SR), over its own link. The ST operates in half-duplex mode, that is, it either transmits or receives, but cannot do both at the same time. Let gpn, gs, μn and β, n = 1, 2, …, N, denote the instantaneous channel power gains from the BS to PU n, from the BS to ST, from the ST to PU n and from the ST to SR, respectively. All these channels are modelled to be frequency-flat and block-fading, following independent complex Gaussian distributions with Rayleigh-distributed
g.0
(2)
where the random variable γ refers to the channel power gains, that is, gpn, gs, μn and β, n = 1, 2, …, N, and where = E g represents the mean power gain of the channel. g As a common assumption for the analysis with fountain codes, perfect CSI can be obtained at the receivers to guarantee the decoding quality [13–23], whereas no CSI is fed back to the transmitters for lowering feedback load and realisation complexity. As the scheduled ST is located between the BS and PUs, usually we have gs ≥ gpn and m n ≥ gpn , for n = 1, 2, …, N, according to the philosophy in (1). That is, the presence of ST results in better channel qualities in the broadcasting. The broadcast with the ST’s help is composed of two phases: the BS’s broadcast and the ST’s broadcast. In the first phase, the BS broadcasts to the ST as well as the PUs in the broadcast group concurrently. The ST and the PUs will feedback an acknowledgement to the BS once they have collected enough information to decode the broadcast codeword reliably. Feedback channels are assumed to be error free and have no latency. Therefore all the feedback is instantaneous. Owing to gs ≥ gpn , normally it takes shorter time for the ST than the PUs to acquire sufficient information for the decoding. As such, the first phase will stop as long as the ST indicates to the BS that it has reliably decoded the broadcast codeword. Subsequently, the second phase is initiated, where the ST broadcasts to the PUs and the BS keeps silent. The ST uses different fountain codes from the BS’s broadcast codeword, which can smoothen the PUs to resume their information collection. In addition, based on DPC, the ST transmits its own information to the SR over the secondary link while broadcasting to PUs. The second phase (i.e. the whole broadcast process) ends up with all PUs’ acknowledgement of their successful decoding. In the following analysis, and without loss of generality, it is assumed that the AWGN components as well as the BS’s and ST’s transmit powers for the broadcast are normalised to unity, so that channel gains and signal-to-noise power ratios (SNRs) become synonymous [17–23]. Although this assumption facilitates the analysis, it can be easily generalised to the cases of AWGN and transmit powers with any other values. Moreover, since the transmit power is normalised to unity, the energy expenditure and transmission time become synonymous as well.
3 Broadcast with the help of secondary transmitter In this section, we investigate the broadcast data rate, the energy expenditures as well as the throughput in secondary links, with the proposed broadcast protocol, that is, the BS’s broadcast with the assistance of the secondary transmitter. 3.1 Fig. 1 Spectrum-sharing broadcast channel ST helps with the BS’s broadcast 2576 & The Institution of Engineering and Technology 2014
Broadcast data rate and energy expenditures
As the proposed broadcast protocol is divided into two phases, we will analyse the performance therein one by one. IET Commun., 2014, Vol. 8, Iss. 14, pp. 2574–2583 doi: 10.1049/iet-com.2013.1145
www.ietdl.org 3.1.1 First phase – BS’s broadcast: In this phase, the BS broadcasts to ST and PUs simultaneously (cf. Fig. 1). As long as ST has acquired sufficient information to reliably decode the broadcast codeword, this phase will stop and the second phase is initiated. Accordingly, the transmission time and the BS’s energy expenditure in this phase depend only on the data rate from the BS to the ST. Theorem 1: To broadcast the information of entropy Ht under the secondary’s help, the BS’s mean energy expenditure and average transmission time in the first phase are given by
H 1 P P1 = E tP1 = t e1/gs Rz ,0 gs gs
(3)
where the subscript ‘P1’ represents the first phase in the broadcast under the ST’s help. Thus, P P1 and tP1 stand for the BS’s energy expenditure and instantaneous transmission time in this phase, respectively. Proof: Based on the concept of Shannon capacity, the instantaneous time required by the ST for successfully decoding the information of entropy Ht, in the first phase, can be expressed as
tP1 =
Ht ln (1 + gs )
(4)
The PDF of tP1 is given by (5)
As a result, the BS’s mean energy expenditure and the average time for the ST to decode the broadcast information of entropy Ht in the first phase can be formulated by 1 0
tP1 ftP1 tP1 dtP1
Ht 1 H eHt /tP1 = exp + t − dtP1 s tP1 gs tP1 gs 0 g 1
1 1 x (a) Ht = exp exp − dx gs 1 ln x gs gs
Ht 1 1 Rz ,0 = exp gs gs gs 1
3.1.2 Second phase – secondary’s broadcast: In the first phase, the data rate from BS to PU n is given by Un = ln(1 + gpn) [nats/s/Hz], n = 1, 2, …, N. In the second phase, the data rate form ST to PU n is given by Wn = ln(1 + μn) [nats/s/Hz], n = 1, 2, …, N. After receiving the BS’s broadcast during the period of tP1 in the first phase, each PU n achieves an entropy of tP1Un. Therefore for the ST’s broadcast in the second phase, the instantaneous time required by PU n is expressed as
Ht − tP1 Un Ht − tP1 ln 1 + gpn (7) tP2,n = = Wn ln (1 + mn ) where subscript ‘P2’ stands for the second phase of the broadcast under the ST’s help, and the time required for the broadcast from BS to ST in the first phase, tP1, is given in (4). In practice, those users near to each other are grouped for broadcast service so as to militate in favour of antenna directivity and power allocation for the transmitter [31, 32]. Thus, without loss of generality, the average channel power gains from the BS to PUs are assumed to be the same [33–35], that is, gpn = gp , and so do those from the ST to PUs, that is, m n = m , ∀n ∈ {1, 2, …, N}. Lemma 1: The PDF of tP2,n is given by (see (8))
Ht 1 Ht eHt /tP1 exp + − ftP1 tP1 = gs tP1 gs gs t2P1
P P1 = E tP1 =
transmitted and is reduced with the increase in the mean channel power gain over the BS–ST link.
(6)
where the equality (a) holds by substituting x = eHt /tP1 and Rz (p, 0) is defined as a member of the family functions 1 Rz (p, m) = 1+z xm e−px / ln x dx with m = 0, ζ → 0 [19]. Consequently, the right-hand side of (3) is obtained. □ As shown in (3), in the first phase of the broadcast under the ST’s help, the BS’s energy expenditure obtains higher with the increase in the information entropy to be
ftP2,n tP2,n ≃
where the parameter B = Aμ(Ap + As)/Ap, with Ap, As and Aμ defined as Ap = 1/ gp −1, As = 1/ gs −1 and Am = 1/ − 1, respectively. m Proof: From (7), tP2,n can be expanded as
Ht 1 − ln 1 + gpn / ln 1 + gs tP2,n = ln (1 + mn ) H 1 − Un /V = t Wn where we define the variable V = ln(1 + gs).
□
Based on (2), the PDFs of the data rate from the BS to PU n in the first phase, Un = ln(1 + gpn), and the data rate from the ST to PU n in the second phase, Wn = ln(1 + μn), are obtained by 1 eu − 1 u fUn (u) = exp − (10) e gp gp and w
1 e −1 w e fWn (w) = exp − m m
−Ht Ht B Ht B Ht B Ei 1 − + 1 exp − tP2,n tP2,n tP2,n A2p t2P2,n m gp gs
IET Commun., 2014, Vol. 8, Iss. 14, pp. 2574–2583 doi: 10.1049/iet-com.2013.1145
(9)
n = 1, 2, . . . , N
(11)
(8)
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www.ietdl.org respectively, n = 1, 2, …, N. Then, fromthe PDF of V given by fV (v) = (1/ gs ) exp −(ev − 1)/ gs +v , the PDF of Y = Un/ V can be expressed as [36, 3.351]. As such v
v eyv − 1 yv 1 e −1 v fY (y) = exp − exp − e dv e p gp gs gs 0 g
1 (a) 1 yv v ≃ v exp − + yv exp − + v dv gp gs 0 gp gs 1
=
1
2 gp gs Ap y + As (12)
where (a) follows the Maclaurin series expansion of exponential function and, for simplicity, ex ≃ 1 + x is used. In addition, the parameters Ap and As are defined as Ap = 1/ gp −1 and As = 1/ gs −1, respectively. Accordingly, the PDF of Z = Ht(1 − Y ) is found as
fZ (z) =
1 2 gp gs Ht Ap 1 − z/Ht + As
(13)
As a result, the PDF of tP2,n = Z/Wn can be calculated using [37, 2.1.3] ftP2,n tP2,n =
1 0
w
w/ m · e−(e −1)/m ew dw 2 gp gs Ht 1 − wtP2,n /Ht Ap + As
H ≃ 2 2 t Ap tP2,n m gp gs (a)
=
−Ht 2 2 Ap tP2,n m gp
1
gs
we−Am w dw
2
w − Ht (Ap + As )/(Ap tP2,n )
Ht B Ht B Ht B Ei 1− +1 exp − tP2,n tP2,n tP2,n
0
(14) where (a) follows ex ≃ 1 + x for simplicity, and we have Am = 1/ m − 1 and B = Aμ(Ap + As)/Ap. Therefore the right-hand side of (8) is achieved. In high-SNR regimes, that is, when the mean channel power gains gp 1, gs 1 and m 1, we have the parameters Ap = As = Aμ = −1 and, accordingly, B = −2. Hence, the PDF of tP2,n in high-SNR cases can be approximated to
−Ht 2Ht 2H 2H exp Ei − t 1 + t (15) ftHP2,n (t) = 2 tm gp gs t t t where the superscript ‘H’ pertains to the high-SNR cases. Subsequently, the mean time required by each PU n for its 2578 & The Institution of Engineering and Technology 2014
successful decoding in high-SNR cases can be calculated as
−Ht 1 1 2Ht 2H 2H E tP2,n = exp Ei − t 1 + t dt m gp gs 0 t t t t 1 x e (a) −Ht = Ei( − x)(1 + x)dx m gp gs 0 x =
−Ht S, m gp gs
n = 1, 2, . . . , N (16)
1 where (a) holds by substituting t = 1/x and S = 0 ex /x Ei( − x)(1 + x)dx is a constant. As shown in (16), the mean time required by every PU to decode the broadcast information from the ST in the second phase obtains higher with the increase in the information entropy to be transmitted and is reduced with the increase in the mean power gains of the BS–ST, BS–PU and ST–PU channels. As the second phase will stop until all PUs feedback their acknowledgements to indicate the successful decodings, the ST’s instantaneous broadcast time in this phase can be found by
tP2 = max {tP2,1 , tP2,2 , . . . , tP2,N }
(17)
Although some insights, for example, linear scaling expression in (16), can be figured out from the approximated PDF of tP2,n in (8), it is quite difficult to achieve the statistics of tP2 from (8). Thereby, we will consider an upper bound on the transmission time in the second phase, which depends on the data rates pertaining to the worst channel-case users in both phases. The instantaneous data rate from the BS to the worst channel-case PU in the first phase is denoted by U = min{U1, U2, …, UN}, where Un = ln(1 + gpn) is the data rate from the BS to PU n in the first phase, n = 1, 2, …, N. Lemma 2: After the BS’s broadcast in the first phase, the upper bound on the remaining information entropy to be broadcasted by the ST in the second phase is given by U HP2 = Ht − tP1 E{U }
(18) Ht 1 1 N N , 0 exp + Ei − = Ht + Rz gs gs gp gp gs
Proof: Based on the PDF of Un, fUn (u) given in (10), the CDF of Un is expressed as 1 ex − 1 x FUn (u) = fUn (x)dx = exp − e dx p gp 0 0g eu 1 t−1 (a) = dt exp − p gp 1 g eu − 1 = 1 − exp − , n = 1, . . . , N gp u
u
(19)
where (a) holds by substituting t = ex. Accordingly, the CDF IET Commun., 2014, Vol. 8, Iss. 14, pp. 2574–2583 doi: 10.1049/iet-com.2013.1145
www.ietdl.org of U = min{U1, U2, …, UN} can be obtained by N eu − 1 1 − FUn (u) = 1 − exp −N FU (u) = 1 − gp n=1
phase are calculated using PU P2
and then the PDF of U is given by (21)
As such, using [36, 4.331], the expectation of U = min{U1, U2, …, UN} can be calculated by 1 1 Nu eu − 1 u ufU (u)du = exp −N E {U } = e du p gp 0 0 g 1 N ln t t−1 (a) (22) = exp −N dt g g 1 p p
= − exp N / gp Ei −N / gp □
where (a) holds by substituting t = eu.
= Ht − tP1 E{U }, we By substituting (3) and (22) into have
Ht 1 1 N N U , 0 exp + HP2 = Ht + Rz Ei − (23) gs gs gp gp gs
U , Ht because of Ei −N / gp , 0. Note that, HP2 Hence, the right-hand side of (18) is obtained. Thus, the upper bound on the ST’s broadcast time in the U U second phase can be expressed by tU P2 = HP2 /W , where HP2 is given in (18) and W = min{W1, W2, …, WN} is the instantaneous data rate from the ST to the worst channel-case PU in the second phase, with Wn = ln(1 + μn) denoting the data rate from the ST to PU n. Theorem 2: The upper bounds on the ST’s mean energy expenditure and the mean transmission time in the second phase are given by (24)
Proof: Similarly with deriving the PDF of U = min{U1, U2, …, UN} in (21), we have the PDF of W as
N ew − 1 w (25) e fW (w) = exp −N m m U Consequently, the PDF of tU P2 = HP2 /W is formulated by
ftU (tU P2 ) = P2
U U HP2 /tP2
U U NHP2 N HP2 Ne + U − U 2 exp m m t m tP2 P2
3.1.3 Total broadcast time: In summary, with the assistance of the ST during the broadcast, the BS broadcasts in the first phase and its energy expenditure is P P1 given in (3), whereas the ST broadcasts in the second phase and the upper bound on its energy expenditure is P P2 given in (24). Based on Theorems 1 and 2, the mean of total broadcast time in the two phases of the proposed protocol is given by E tbc = E tP1 + E tU P2
U H 1 NHP2 N = t e1/gs Rz ,0 + eN /m Rz ,0 gs gs m m (28)
IET Commun., 2014, Vol. 8, Iss. 14, pp. 2574–2583 doi: 10.1049/iet-com.2013.1145
U = Ht + (Ht / gs )Rz (1/ gs , 0)e1/ gs +N / gp Ei( − N / where HP2 gp ) is shown in Lemma 2, that is, (18).
3.2
Throughput in secondary links
In the second phase, the ST transmits its own information to the SR while broadcasting to the PUs, on the basis of DPC technique implemented in [28–30]. With this technique, the ST first picks a codeword for its own information and, then, chooses a codeword for the broadcast information to PUs. Thus, PUs do not see the codeword for the ST’s own information as interference, and they can decode the broadcast information from the ST as if there were no interference because of the secondary’s information [38, 39]. However, the SR’s decoding is interfered by the broadcast information to PUs. By setting the power ratio of the ST’s broadcast information for PUs to the information over the secondary link as η, the SU’s achievable data rate in the unit of [nats/s/Hz] can be calculated by Prudnikov and Brychkov [37, 2.5.2]
1 RSU = E ln 1 + 1/b + h 1 )e−b/b db ln (1 + (h + 1)b) − ln (1 + hb) (1/b = 0
=e
As a result, the upper bounds on the ST’s mean energy expenditure and the mean transmission time in the second
P2
As such, the right-hand side of (24) is obtained.
) (1/hb
(26)
tUP2 ftU (tUP2 )dtUP2
U U U U NHP2 N HP2 NeHP2 /tP2 = + U − dtU P2 U exp m m m t t 0 P2 P2 1
U N 1 Nx (a) NHP2 = exp − dx exp m m m 1 ln x
U NHP2 N N exp ,0 (27) Rz = m m m U U where the equality (a) holds by taking x = exp HP2 /tP2 . □
1
U HP2
U U NHP2 N N / m PU = = E t e R , 0 z P2 P2 m m
1 0
(20) d N eu − 1 u e fU (u) = FU (u) = exp −N du gp gp
= E tU P2 =
1 1 ) (1/(h+1)b Ei − − e Ei − (h + 1)b hb (29)
Accordingly, the throughput over the secondary link in the second phase (i.e. in the whole broadcast process), 2579
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www.ietdl.org expressed in the unit of [nats/Hz], is obtained by
U NHU N m P2 N / e Rz ,0 CSU = E tP2 · RSU = m m
1 1 × e(1/hb) Ei − − e(1/(h+1)b) Ei − (h + 1)b hb (30) where the upperbound on the mean transmission time in the second phase, E tU P2 , is shown in (24).
4 Broadcast without the help of secondary transmitter Based on the statistical framework developed in the previous section, we now analyse the broadcast data rate and the BS’s energy expenditure for the case of the BS’s broadcast without the ST’s help, that is, traditional fountain coded broadcasting [21–23], in order to evaluate the scheduled ST’s help within the BS’s broadcast by comparing the network performance between the proposed broadcast protocol and its counterpart without the ST’s help. Theorem 3: To broadcast the information of entropy Ht to N PUs with no help from the secondary, the BS’s mean energy expenditure and the mean broadcast time are given by
P BS = E tBS
NHt N /gp N e Rz ,0 = gp gp
(31)
Proof: Without the ST’s help, the BS broadcasts to PUs and stops the broadcasting until all PUs indicate their successful decodings. Consequently, the broadcast data rate depends on the worst channel-case PU, which is expressed as U = min{U1, U2, …, UN} with Un = ln(1 + gpn) denoting the data rate from BS to PU n, n = 1, 2, …, N. Thus, the broadcast time of the traditional protocol without the ST’s help is given by tBS = Ht/U. □ Based on the PDF of U given in (21), the PDF of tBS = Ht/U can be formulated by NHt N Ht NeHt /tBS ftBS (tBS ) = exp + − gp tBS gp gp t2BS
(32)
Thus, the BS’s energy expenditure and the mean broadcast time, without the ST’s help, are given by P BS = E tBS =
1 0
tBS ftBS (tBS )dtBS
NHt N Ht NeHt /tBS dtBS = exp + − p tBS gp gp tBS 0 g 1 N 1 Nx (a) NHt exp − = exp dx gp 1 ln x gp gp NHt N N exp ,0 = Rz gp gp gp 1
where (a) follows x = eHt /tBS . 2580 & The Institution of Engineering and Technology 2014
(33)
As a consequence, the right-hand side of (31) is obtained. From Theorem 3, that is, (31), we may observe that the BS’s energy expenditure in the broadcast without the ST’s help, P BS , (i.e. equivalent to the BS’s mean broadcast time tBS) is enhanced with the increase in the information entropy to be transmitted, Ht. Moreover, it obtains larger with the increase in the total number of PUs, N, while it is varying inversely as the mean channel power gain over the BS–PU link, gp . The insight from this equation dovetails completely with the intuition, that is, as the information entropy to be transmitted or the number of PUs increases, the BS is expected to spend more energy for the broadcast. On the contrary, the BS’s energy expenditure is reduced if the channel power gain is improved. Compared with P BS without the ST’s help in (31), the BS’s mean energy expenditure in the proposed protocol with the ST’s help, P P1 shown in (3), is not affected by the number of PUs. That is, with the ST’s help in the proposed broadcast protocol, the BS’s energy expenditure can be dramatically decreased.
5
Numerical results and discussions
Now, we illustrate the performance of our proposed broadcast protocol, specifically on the BS’s energy savings, broadcast time and throughput over secondary links. For the case without ST’s help, the analysis results pertaining to Theorem 3 demonstrate the BS’s energy expenditure and broadcast time. For the proposed protocol with ST’s help, the analysis results will focus on Theorems 1 and 2 in the first and second phases, respectively. That is, the BS’s and ST’s energy expenditure as well as broadcast time are taken into account with respect to the worst channel-case PUs in both phases, and the corresponding Monte Carlo simulations will be performed. Hereafter, and without loss of generality, the entropy of information to be broadcast is normalised to unity, that is, Ht = 1. For the location of the scheduled ST, we consider two scenarios as shown in Fig. 2: (i) the distances from the BS to PUs, from the BS to the ST and from the ST to PUs are the same, that is, dbp = dbs = dsp, where the average channel power gains are accordingly equal to each other, that is, gp = gs = m √ ; (ii) relation among the considered the √ distances is dbp = 2dbs = 2dsp , such that the relation among the corresponding channel power gains is approximated as m = gs = 2 gp . To begin with presenting energy savings with the ST’s help, the BS’s energy expenditures are depicted in Fig. 3 as a function of the average channel power gain over each PU, gp , for the proposed broadcast protocol and its counterpart without the ST’s help in the scenarios (i) and (ii), where N = 20 PUs are in the broadcast group. As shown in this figure, corresponding Monte Carlo simulation results are exactly coincident with analytical results, which substantiates the validity of our derivations. Moreover, the ST’s energy expenditures are also shown for the sake of comparison. It is observed from this figure that the BS’s energy expenditure is saved significantly with the ST’s help in the broadcast. As gp increases, the energy saving for the BS is reduced, because the BS’s energy expenditure in the traditional scheme without the ST’s help is decreased. By comparing the energy expenditures between scenarios (i) and (ii), we may find that the ST’s energy expenditure in scenario (i) is higher than that in scenario (ii) because of lower channel power gains in gs and m . With lower gp in IET Commun., 2014, Vol. 8, Iss. 14, pp. 2574–2583 doi: 10.1049/iet-com.2013.1145
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Fig. 4 Broadcast time against gp : comparisons between the proposed and traditional broadcast protocols for scenarios (i) and (ii) with N = 20 PUs in the broadcast group
Fig. 2 Network topologies of two scenarios considering the ST’s location
scenario (i), the ST’s energy expenditure is almost the same as the BS’s without the ST’s help in the broadcast. However, in this scenario the reduction in the ST’s energy expenditure is faster than the BS’s with the increase in gp . Then, in Fig. 4, we compare the broadcast time against gp between the cases with and without the ST’s help in the BS’s broadcast for scenarios (i) and (ii) with N = 20 PUs in the broadcast group, where the broadcast time with the ST’s
Fig. 3 BS’s energy expenditures versus the average channel power gain over each PU, gp , compared for the proposed and traditional broadcast protocols in scenarios (i) and (ii) with N = 20 PUs in the broadcast group Also shown are ST’s energy expenditures in the corresponding conditions IET Commun., 2014, Vol. 8, Iss. 14, pp. 2574–2583 doi: 10.1049/iet-com.2013.1145
help is much lower than that without the ST’s help in scenario (ii). On the other hand, in scenario (i), the broadcast time with the ST’s help is the same as that without when gp = 6 dB. At low channel power gains (i.e. gp , 6 dB), the total broadcast time with the ST’s help is slightly higher than that without the ST’s help, and it obtains lower than that without the secondary’s help for the channel power gain increased further as gp . 6 dB. This phenomenon illustrates that the latency reducing in two-phase broadcasting is faster than that in one-phase direct broadcasting as the channel power gains increase in each phase. Subsequently, the broadcast time is plotted in Fig. 5 as a function of the number of PUs, N, for the proposed and traditional protocols in scenarios (i) and (ii), where the average channel power gain over each PU link is set to
Fig. 5 Broadcast time against the number of PUs, N, for the proposed and traditional protocols in scenarios (i) and (ii) with gp = 3 dB and 8 dB 2581
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Fig. 6 Secondary throughput against its average channel power gain m for scenarios (i) and (ii) in the proposed scheme with N = 20 and 30 PUs in the broadcast group while setting gp = 6 dB and the ratio of the ST’s broadcast information for PUs to the information over its own link η = 0.5
gp = 3 dB and 8 dB. As observed, the broadcast time increases almost linearly with the number of PUs. The increasing slope with the ST’s help in scenario (i) is the same as that without the ST’s help, which are both higher than the increasing slope with the ST’s help in scenario (ii). In addition, with the proposed broadcast protocol, the throughput in the secondary link against its average channel power gain m is reported in Fig. 6 for scenarios (i) and (ii) with N = 20 and 30 PUs, where gp is set to 6 dB for the same broadcast time achieved there with the proposed scheme as that with the traditional scheme. Moreover, the ratio of the ST’s broadcast information for PUs to the information over its own link η is set to 0.5 and, thus, the ST’s total transmit power in the second phase is three times of the unity. From this figure, we observe that the secondary throughput is improved with the increase in the number of PUs, and the secondary throughput in scenario (i) is higher than that in scenario (ii) with the same conditions. The main reason behind this phenomenon is that the ST’s increased broadcast time in the second phase results in higher secondary throughput. Furthermore, we present the relation between secondary throughput and the ST’s total energy expenditure in Fig. 7 = 10 dB, for scenarios (i) and (ii) with gp = 6 dB and b where the cases of N = 20 and 30 PUs in the broadcast group are investigated. For each case, the power ratio η varies from 2 to 0.1. As the secondary’s transmit power for the broadcasting is fixed, the ST’s total energy expenditure is enhanced with the increase in η. This figure reveals that the secondary throughput is improved significantly at high values of η, where the ST’s transmit power for its own information is relatively low. However, as η decreases, that is, the ST spends more transmit power for its own information, the increments in the secondary throughput is not dramatically enhanced. As such, the value of η needs to be chosen carefully for improving the secondary throughput with a reasonable energy expenditure at the ST. Other important insights reached from these analysis results are summarised as follows: 2582 & The Institution of Engineering and Technology 2014
Fig. 7 Secondary throughput against the ST’s total energy expenditure for scenarios (i) and (ii) in the proposed scheme with N = 20 and 30 PUs in the broadcast group while setting = 10 dB gp = 6 dB and b
† With the ST’s help, the BS’s energy expenditure in the proposed broadcast protocol is much lower than that in the traditional broadcast without the ST’s help. † If an ST located between the BS and PUs is scheduled to help with the broadcasting, both the BS’s energy expenditure and the broadcast time can be reduced dramatically. † If the distances from the BS to PUs, from the BS to the ST and from the ST to PUs are the same, the broadcast time with the ST’s help is slightly longer than that without the ST’s help at low channel power gains. However, as channel power gains increase further, the broadcast time with the ST’s help will become shorter than that without the ST’s help. Based on this issue, to increase the BS’s or the ST’s transmit power and accordingly to improve the channel power gains in the broadcasting is an option to balance the broadcast time and the energy expenditure. † The tradeoff between the broadcast time and the throughput over secondary links needs to be considered in the network design, as increasing the broadcast time results in higher secondary throughput and, however, lower QoS in primary links because of longer latency. † The power ratio of the ST’s broadcast information for PUs to the information transmitted over its own link should be determined by the tradeoff between the secondary throughput improvements, the primary QoS requirements and the ST’s energy expenditures.
6
Conclusions
In this paper, we proposed a broadcast protocol in spectrum-sharing networks, where a ST is scheduled to help the BS’s broadcast using fountain codes. With the proposed scheme, instead of broadcasting to all PUs, the BS’s transmission is only required to promise the ST reliably decoding the fountain coded information. Once the ST receives sufficient codewords and feeds back an acknowledgement, the BS will stop broadcasting. Therefore, the BS’s energy expenditure is dramatically reduced compared with its broadcasting to all PUs. After the BS IET Commun., 2014, Vol. 8, Iss. 14, pp. 2574–2583 doi: 10.1049/iet-com.2013.1145
www.ietdl.org stops, the ST resumes the broadcasting to PUs and, simultaneously, transmits information over its own link based on DPC technique so as to improve the secondary throughput. To evaluate the performance of the proposed scheme, we analysed the corresponding transmission rates, the energy expenditures, the broadcast time and the throughput in secondary links. Subsequent analytical results and Monte Carlo simulations illustrated the validity of our derivations as well as substantiated the efficiency of the proposed broadcast protocol. In addition, based on the analysis, the philosophy of network design is established from the view of energy-delay-throughput tradeoff with the ST’s help in spectrum-sharing broadcast channels.
7
Acknowledgment
The authors would like to thank the editor and the anonymous reviewers for their valuable comments to improve the presentation of this paper.
8
References
1 Mitola, J., Maguire, G.: ‘Cognitive radio: making software radios more personal’, IEEE Pers. Commun., 1999, 6, (4), pp. 13–18 2 Weiss, T., Jondral, F.: ‘Spectrum pooling: an innovative strategy for the enhancement of spectrum efficiency’, IEEE Commun. Mag., 2004, 42, (3), pp. S8–S14 3 Federal Communications Commission (FCC): ‘Promoting more efficient use of spectrum through dynamic spectrum use technologies’, 2010, pp. 1–31 4 Haykin, S.: ‘Cognitive radio: brain-empowered wireless communications’, IEEE J. Sel. Areas Commun., 2005, 23, (2), pp. 201–220 5 Ghasemi, A., Sousa, E.: ‘Fundamental limits of spectrum-sharing in fading environments’, IEEE Trans. Wirel. Commun., 2007, 6, (2), pp. 649–658 6 Akyildiz, I., Lee, W., Vuran, M., et al.: ‘A survey on spectrum management in cognitive radio networks’, IEEE Commun. Mag., 2008, 46, (4), pp. 40–48 7 Yang, Y., Aissa, S.: ‘Achievable data rate in spectrum-sharing channels with variable-rate variable-power primary users’, IEEE Wirel. Commun. Lett., 2012, 1, (4), pp. 312–315 8 Goldsmith, A., Jafar, S., Maric, I., et al.: ‘Breaking spectrum gridlock with cognitive radios: an information theoretic perspective’. Proc. of the IEEE, 2009, vol. 97, no. 5, pp. 894–914 9 Gastpar, M.: ‘On capacity under receive and spatial spectrum-sharing constraints’, IEEE Trans. Inf. Theory, 2007, 53, (2), pp. 471–487 10 Yang, Y., Ma, H., Aissa, S.: ‘Cross-layer combining of adaptive modulation and truncated ARQ under cognitive radio resource requirements’, IEEE Trans. Veh. Tech., 2012, 61, (9), pp. 4020–4030 11 Devroye, N., Mitran, P., Tarokh, V.: ‘Achievable rates in cognitive radio channels’, IEEE Trans. Inf. Theory, 2006, 52, (5), pp. 1813–1827 12 Jovicic, A., Viswanath, P.: ‘Cognitive radio: an information-theoretic perspective’, IEEE Trans. Inf. Theory, 2009, 55, (9), pp. 3945–3958 13 Bonello, N., Yang, Y., Aissa, S., et al.: ‘Myths and realities of rateless coding’, IEEE Commun. Mag., 2011, 49, (8), pp. 143–151 14 Etesami, O., Shokrollahi, A.: ‘Raptor codes on binary memoryless symmetric channels’, IEEE Trans. Inf. Theory, 2006, 52, (5), pp. 2033–2051 15 Eswaran, K., Sarwate, A., Sahai, A., et al.: ‘Zero-rate feedback can achieve the empirical capacity’, IEEE Trans. Inf. Theory, 2010, 56, (1), pp. 25–39
IET Commun., 2014, Vol. 8, Iss. 14, pp. 2574–2583 doi: 10.1049/iet-com.2013.1145
16 Orozco, V., Yousefi, S.: ‘Trapping sets of fountain codes’, IEEE Commun. Lett., 2010, 14, (8), pp. 755–757 17 Castura, J., Mao, Y.: ‘Rateless coding over fading channels’, IEEE Commun. Lett., 2006, 10, (1), pp. 46–48 18 Fan, Y., Lai, L., Erkip, E., et al.: ‘Rateless coding for MIMO fading channels: performance limits and code construction’, IEEE Trans. Wirel. Commun., 2010, 9, (4), pp. 1288–1292 19 Molisch, A., Mehta, N., Yedidia, J., et al.: ‘Performance of fountain codes in collaborative relay networks’, IEEE Trans. Wirel. Commun., 2007, 6, (11), pp. 4108–4119 20 Gong, C., Yue, G., Wang, X.: ‘Analysis and optimization of a rateless coded joint relay system’, IEEE Trans. Wirel. Commun., 2010, 9, (3), pp. 1175–1185 21 Jenkac, H., Stockhammer, T.: ‘Asynchronous media streaming over wireless broadcast channels’. Proc. IEEE Int. Conf. Multimedia Expo., Amsterdam, Netherlands, July 2005, pp. 1318–1321 22 Cataldi, P., Grangetto, M., Tillo, T., et al.: ‘Sliding-window raptor codes for efficient scalable wireless video broadcasting with unequal loss protection’, IEEE Trans. Image Process., 2010, 19, (6), pp. 1491–1503 23 Luby, M., Gasiba, T., Stockhammer, T., et al.: ‘Raptor codes for reliable download delivery in wireless broadcast systems’. Proc. IEEE Consumer Commun. and Networking Conf., Las Vegas, US, January 2006, pp. 192–197 24 Shaqfeh, M., Alnuweiri, H.: ‘Joint power and resource allocation for block-fading relay-assisted broadcast channels’, IEEE Trans. Wirel. Commun., 2011, 10, (6), pp. 1904–1913 25 Joda, R., Lahouti, F.: ‘Network code design for orthogonal two-hop network with broadcasting relay: a joint source-channel-network coding approach’, IEEE Trans. Commun., 2012, 60, (1), pp. 132–142 26 Abouelseoud, M., Nosratinia, A.: ‘Opportunistic wireless relay networks: diversity-multiplexing tradeoff’, IEEE Trans. Inf. Theory, 2011, 57, (10), pp. 6514–6538 27 Rappaport, T.: ‘Wireless communications principles and practice’ (Pretice-Hall Inc., 1995) 28 Costa, M.: ‘Writing on dirty paper’, IEEE Trans. Inf. Theory, 1983, 29, (3), pp. 439–441 29 Yang, Y.: ‘Half-duplex relay-help transmission with dirty paper coding’. Proc. IEEE Veh. Tech. Conf., Barcelona, Spain, April 2009, pp. 1–5 30 Yang, Y., Aissa, S.: ‘On the coexistence of primary and secondary users in spectrum-sharing broadcast channels’. Proc. IEEE Int. Conf. Commun., Budapest, Hungry, June 2013, pp. 3085–3089 31 Hartung, F., Horn, U., Huschke, J., et al.: ‘Delivery of broadcast services in 3G networks’, IEEE Trans. Broadcast., 2007, 53, (1), pp. 188–199 32 Ma, X., Chen, X.: ‘Performance analysis of IEEE 802.11 broadcast scheme in Ad Hoc wireless LANs’, IEEE Trans. Veh. Tech., 2008, 57, (6), pp. 3757–3768 33 Kokalj-Filipovic, S., Soljanin, E., Spasojevic, P.: ‘Low complexity doped wireless broadcast for multimedia applications’, IEEE Trans. Commun., 2013, 61, (8), pp. 3462–3471 34 Xie, B., Courtade, T., Wesel, R.: ‘Optimal encoding for discrete degraded broadcast channels’, IEEE Trans. Inf. Theory, 2013, 59, (3), pp. 1360–1378 35 Zhan, C., Lee, V., Wang, J., Xu, Y.: ‘Coding-based data broadcast scheduling in on-demand broadcast’, IEEE Trans. Wirel. Commun., 2011, 10, (11), pp. 3774–3783 36 Gradshteyn, I., Ryzhik, I.: ‘Table of integrals, series, and products’ (Academic Press, 1965, 6th edn. 2000) 37 Prudnikov, A., Brychkov, Y.: ‘Integrals and series (Volume 4): direct Laplace transforms’ (Gordon & Breach Science Publishers, 1992) 38 Viswanath, P., Tse, D.: ‘Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality’, IEEE Trans. Inf. Theory, 2003, 49, (8), pp. 1912–1921 39 Vishwanath, S., Jindal, N., Goldsmith, A.: ‘Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels’, IEEE Trans. Inf. Theory, 2003, 49, (10), pp. 2658–2668
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