Opportunistic Spectrum Multichannel OFDMA
Descrição do Produto
Opportunistic Spectrum Multichannel OFDMA Przemysław Pawełczak, R. Venkatesha Prasad and Ramin Hekmat Faculty of Electrical Engineering, Mathematics and Computer Science Delft University of Technology, Mekelweg 4, 2600 GA Delft, The Netherlands Email: {p.pawelczak, vprasad, r.hekmat}@ewi.tudelft.nl
Abstract— Opportunistic Spectrum Access (OSA) is being seriously considered for the future spectrum needs. In this paper we propose a simple and effective multichannel multiple access technique for OSA networks. In our design users of an OSA network must contact the OSA Base Station to gain access to the radio resources. In an OSA environment each of the channels can be arbitrarily occupied by the Primary Users (PUs) of the specific band. Thus the OSA nodes should cause least interference to the PUs while exploiting the voids in the PU usage. We analyze the OSA network where many OSA nodes would be competing amongst themselves and with the PU, using fast retrials. We also propose mechanisms to minimize the probability of collisions and interference caused to the PUs, while maximizing the throughput of the OSA network.
I. I NTRODUCTION Opportunistic Spectrum Access (OSA) is a novel and not fully explored paradigm for wireless radio communications, where secondary (unlicensed) users utilize spectrum only when it is not exploited by primary users (PU), i.e., licensed users of the specific band [1]. The utilization of PU channels by secondary users in an OSA system has to be performed in such a way that it will cause no degradation in service to the PUs [2]. The natural candidate for the radio layer of an OSA networks is Orthogonal Frequency Division Multiplexing (OFDM). This is mainly due to its flexibility, which allows for simple adaptation of sub-carriers to fast changing conditions in radio spectrum and to duty cycles of PUs. For example, OFDM by narrowband carrier adaptation overcomes frequency selective fading and allows for multiuser diversity. The major challenge is to design a resource reservation multiple access protocol that works in the OSA environment using OFDM. CSMA-type protocols, while used broadly in unlicensed channels, viz. IEEE 802.11 a/b/g, are not completely suitable for operation in licensed channels or OSA environment, mainly due to “channel efficiencies that use a licensed band” [3]. One of the solutions for multiple access in licensed bands is to use Slotted Aloha or Packet Reservation Multiple Access (PRMA) [4]. Unfortunately PRMA does not perform well in the case of traffic bursts, and does not scale with increasing number of users [5]. However, instead of random access methods mentioned above, a network can assign unique radio resources to each OSA user. For example, in high data rate CDMA systems each user has a unique code assigned This research was carried out in the Adaptive Ad-Hoc Free Band Wireless Communications (AAF) project funded by the Freeband program of the Dutch Ministry of Economic Affairs and Magnet Beyond project funded by the EU.
for the uplink. However, to efficiently use the radio resources the network should have a dedicated channel for scheduling in which carriers are opportunistically assigned to the users. Using TDMA for scheduling purposes may result in under utilization of spectrum usage, and thus contention based multiple access protocols for this type of channel are inevitable1 . To cope with this issue random access MAC can be used, since control messages are shorter compared to data packets. Also, such a hypothetical MAC can be constructed even on channels which are mostly utilized by the PU. Through these channels, an OSA network can later schedule OFDM carriers that are more stable and match the QoS needs of a particular user of the OSA network. For example, a contention-based MAC can serve as a support for distributed carrier assignment algorithms for OSA networks [6], where the carrier is shared by each node on a TDMA basis. In this paper, we extend the simple Aloha-like protocol for OFDM Access (OFDMA) presented in [3] to the case where carriers are randomly occupied by PU. We provide detailed analysis of packet capture in the presence of Rayleigh fading and give bounds on the performance of the system in the presence of radio regulator constraints [1], [2]. We note that there are already many attempts to design MAC protocols for OSA networks. In [7], authors proposed a secondary medium access control, called AS-MAC, working as an underlay in GSM bands. DOSS protocol is presented in [8], where discussions on the physical radio design for spectrum sensing in the MAC context are presented. In [9], HD-MAC is proposed, where groups of secondary users coordinate cooperatively to decide which channels to utilize. A recent survey on related multi-channel MAC protocols and their specific modifications can be found in [3, Section I] and [10]. The reminder of the paper is organized as follows. Section II introduces system model. Collision analysis for different packet service disciplines are given in Section III, accompanied with numerical results in Section IV. Finally Section V concludes the paper. II. S YSTEM M ODEL Let every Mobile Station (MS) belonging to the OSA network request radio resources from the Base Station (BS). 1 A similar approach is used in IEEE 802.16, where Mobile Stations send control and channel request messages to the Base Station in a random fashion, while collisions are resolved by exponential backoff.
PU network type 3
Channel 1 Channel 2 Channel 3
OSA MS
PU MS
PU network type 1 BS PU network type2
Fig. 1. Symbolic representation of the OSA network system model, where multiple MSs contend on multiple channels (here M = 3) for the access to the OSA network’s BS, normally used by PUs of these bands. We note that PU networks can be ad-hoc or infrastructure based.
Every MS has no packet buffering [4], is synchronized with other MSs and the channel is slotted. The total traffic generated by the OSA network expressed in packets per slot, is Poisson distributed with parameter λ. All packets have equal length. Also, each node obtains immediate feedback whether transmission was successful on a dedicated broadcast channel [4], [11]. We assume that the broadcast channel is always available to the OSA network (such a channel could be constructed using, e.g., Ultra-Wide Band communication). The OSA network havs access to a set of M channels (corresponding to OFDM carriers), while each of the channels is also randomly occupied by the proprietary PU of that channel (Fig. 1 shows an example system model for M = 3). By PU, we mean an ad-hoc or infrastructure based network consisting of a number of MS, operating on channel m ∈ M licensed exclusively to PU by the radio regulator. Here, we also assume that channel occupancy by the PU is described by a Poisson process with parameter λp,m , its transmission is slotted, and the OSA network is synchronized with the PU (a similar assumption was made in [12]). Nota bene it has been shown through analysis of channel occupancy measurements [13], that in analogue data transmission radio channels, i.e. public trunking on channels 420-430 MHz of Dutch spectrum [14], periods of channel occupancy of almost fixed size are observed, while periods between consecutive channel occupancies are exponentially distributed. We can thus approximate PU’s operation as a slotted system, with Poisson arrival traffic, where the slot length is equal to the occupancy period of the PU. Finally, we assume that λp,m is known to each of the OSA MSs. According to the algorithm proposed in [3], each OSA user, before transmitting a request packet, chooses randomly on which OFDM carrier to transmit2 . Whenever there is collision in a slot k, an OSA MS immediately chooses another carrier randomly, and in slot k + 1 tries to transmit the packet (this procedure is called fast retrial in [3]). If the packet is still not transmitted, after S successive tries it is backlogged for a random amount of time. The value of S is given a priori to the 2 We
note that the algorithm analyzed here can also be applied to classical FDMA networks. However we follow the naming from [3], thus we use the term OFDMA throughout this paper.
network and is specific to the network operation environment, e.g. level of frequency reuse in cellular-type OSA. Since an OSA network has to operate under the shadow of the PU network, it should behave in such a way that it will not cause excessive interference to the PU on a channel m [1]. The interference for PU will occur, in the OFDMA scenario described here, when both PU and the OSA users try to transmit simultaneously in a slot. A radio regulator allowing operation of an OSA network in a specific channel, can restrict users to transmit such that the probability of interference, Im , to the PU on channel m is Im = pa,m pm ≤ Ψm ,
(1)
where pm = 1 − exp(−λp,m ) is the probability of channel occupancy by the PU on channel m, pa,m is the probability of gaining slot access on channel m by an OSA network user, and Ψm is the interference limiting factor on a channel m. This paper aims to analyze performance of a single OSA network under these circumstances. We note however that the analysis presented here can easily be extended to a multiple OSA systems. III. C OLLISION A NALYSIS Let us assume that the total arriving traffic on channel m, λT,m , is the sum of newly generated traffic, fast retrial traffic and backlogged traffic from the OSA network. Although fast retrial traffic does not follow a Poisson distribution, we will assume it is distributed in Poisson manner, since such an assumption is the norm in the analysis of Aloha-type protocols [4]. The total arrival rate at slot k is then [3], λT,m (k) = λm + pc,m γλT,m (k − 1), where pc,m is the ratio of collisions to total trials of the OSA network on channel m (OSA network user collision 0 is the traffic splitting probability), λm = ρm λ, ρm > M coefficient on channel m, such that i=1 ρi = 1, and S−1 k pc,m γ = k=0 S k k=0 pc,m is the ratio of fast retrials to the number of collisions in the previous slot. Therefore, we can write λT,m for the steady state in compact form as λT,m =
λm 1−
1−pS c,m 1−pS+1 c,m
pc,m
= λm
1 − pS+1 c,m . 1 − pc,m
(2)
Because operation on each channel is independent and utilization of channels by the PU is nonuniform, the total OSA network throughput is defined, using [15, eq. 1] as T =
M
λT,i (1 − pc,i ).
(3)
i=1
As we noted earlier, channel occupancy by each PU is different, thus the coefficient ρm allows access to PU channels nonuniformly (in contrast to the uniform random channel selection
analyzed in [3]) minimizing the probability of collision with PU traffic. We observe that throughput is maximized only when (see the proof in Appendix) 1 − pm . ρm = M i=1 1 − pi
(4)
In (2), total traffic is affected by the ratio of collisions to total trials. In the following paragraphs we will analyze pc,m depending on the procedures used to transmit packets of the OSA network during multiple transmissions in a slot, i.e., packet capture and spectrum sensing. A. Collision Probability without Packet Capture With the assumption of slotted access and synchronization between primary and secondary system, the OSA network will experience collisions not only due the channel occupancy by PU but also as a result of to its own traffic. Ratio of collisions to total trials can be defined as [3] pc,m = 1 −
E[|Q|] = 1 − exp(−λT,m − λp,m ), (5) E[|Q|] + E[|R|]
where operator E[|X|] denotes expected number of event X, Q denotes success and R denotes collision. For the OSA network E[|Q|] = λT,m exp(−λT,m ) exp(−λp,m ), i.e., one arrival from OSA user and no arrivals from PU, while E[|Q|]+ E[|R|] = λT,m , i.e., total expected arriving traffic by OSA network3 . Now solving λT,m using (1) with pa,m = pc,m taking into account Ψm ≤ pm we get exp(λp,m )(1 − Ψm ) − 1 λT,m ≤ − log = λR,m , (7) exp(λp,m ) − 1 which defines the maximum traffic that can be offered on PU channel m for the OSA network. Whenever the offered traffic is higher, then each node can randomly discard each newly generated packet with a probability pα = λT,m /λR,m − 1. Such a handling of packets allows for saving its Poisson behavior [4, problem 3.11]. The value of pα is transmitted to each MS by BS on a feedback channel, based on the knowledge of total number of OSA users and λ. B. Collision Probability with Packet Capture Due to the fading phenomenon even if i > 1 users were transmitting in a slot, receiver is able to receive the packet when interference caused by i − 1 transmitting nodes was smaller than the predefined threshold. Such packet capture increases the throughput, possibly minimizing fast retrial and backlogged traffic. 3 Since the arrivals of the PU and packet generation by the OSA network are independent, the ratio of packet collisions to total trials will be equal to, according to inclusion-exclusion formula,
pc,m = 1 − (1 − pc,m )(1 − pm ) = 1 − exp(−λT,m − λp,m ), where pc,m = 1 − exp(−λT,m ), and thus (5) is equivalent to (6).
(6)
Let us assume that signal amplitude received by BS from PU on channel m is Rayleigh distributed, with average received power P¯m = Pm,t /dδ , where transmitted power Pm,t decays with factor δ on distance d from OSA BS. We assume that thermal noise can be neglected (i.e., “ideal” contention-limited design [11]), since the dominating interference in each slot comes from transmitted packets by the OSA and PU network users. Moreover let us assume that distance d between the OSA network and PU transmitters is such that each user of the OSA network observes the same average received power P¯m . Received amplitude of the transmitted packet by a OSA network user to the BS is also Rayleigh distributed, with the same average power for each user, equal to P¯0 . This network model is equivalent to the case when all MS of the OSA network were placed on a ring around BS of the OSA. For an arbitrary fading scenario, ratio of collisions to total trials in presence of packet capture is defined as [11, eq. 4] ∞ Pt λnx exp(−λx ) Pr pc,m,¯x (z0 ) = < z0 , (8) n! Pn,¯x n=1 where z0 is the threshold level4 and the Pt /Pn,¯x is the ratio of the power of the test packet to the interference power of n users each transmitting with an average power of x ¯, and generating Poisson traffic with the parameter λx . Assuming incoherent addition of n Rayleigh distributed phasors we have [11, eq. 20] z0 ∞ Pt Pr < z0 = fPt (xy)fx¯,n (x)xdxdy, (9) Pn,¯x 0 0 where −x 1 xn−1 exp fx¯,n (x) = n (10) x ¯ (n − 1)! x ¯ denotes gamma PDF with shape parameter n − 1 and the scale parameter x ¯ of X Pn,¯x – sum of n interferers powers (denoted also as X ∼ G(n − 1, x ¯)). While fPt (y) denotes PDF of Y Pt ∼ G(1, P¯0 ) – power of test packet of the OSA network. 1) Packet Capture without Spectrum Sensing: It has to be noted that even if the incoming OSA traffic has been limited artificially by pα , still OSA network can experience collision due to the presence of PU MSs. Since the independence of the PU and the OSA network operation is assumed, we analyze only two types of packet collisions in the presence of packet capture: one in the presence of OSA sources only, denoted as pc,m,P¯0 (z0 ), and in the presence of PU network only, denoted as pc,m,P¯m (z0 ). Using (9) we have −n nP¯m +P¯0 z0 nP¯ m Pt P¯0 < z0 = dx Pr ¯ Pn,P¯m xPm + P¯0 0 n P¯0 . (11) =1− z0 P¯m + P¯0 4 In [16] authors have noticed that capture probability depends on the threshold level z0 = z(n) , which is a function of the number of interfering sources, i.e., it has to be adaptive to the number of interfering sources. However throughout this paper we will refer to a fixed threshold z0 for simplicity.
Now applying (11) to (8) to compute pc,m,P¯m (z0 ) and to compute pc,m,P¯0 (z0 ) using (11) with P¯m = P¯0 in (8), we get, after some calculations, pc,m = 1 − (1 − pc,m,P¯0 (z0 ))(1 − pc,m,P¯m (z0 )) z0 z0 P¯m − λp,m ¯ = 1 − exp −λT,m , (12) z0 + 1 z0 Pm + P¯0 which for the case of z0 → ∞ reduces to (6) as expected. 2) Packet Capture with Spectrum Sensing: To preserve system from random packet discarding while λT,m > λR,m , the OSA network can detect when the PU was present before transmitting a packet. This allows for proper packet scheduling at each OSA node, i.e., having more control over the packets to remove from the queue to satisfy (1). Specifically in every slot of length L, each node will observe the PU signal for l < L time (thus reducing T in comparison to no detection case by M l/L). After carrier observation the OSA node will decide whether the PU user was present or not. The OSA users will claim no slot whenever PU is transmitting. Throughout this paper we assume that each OSA node performs energy detection to find the PU5 . For generality of our analysis we assume detection of signals in the presence of AWGN with known parameters. Moreover we assume that the signal from the PU is deterministic and unknown. Let us also assume that each node is individually detecting the presence of PU. For a given decision threshold νm of channel m, the probability of false alarm when the PU is absent can be computed with the help of [17, eq. 12] as pf,m = (1 − pm )F (u, νm /2), where u = lW , W is the bandwidth of each detected PU channel, and F (., .) is the regularized incomplete lower gamma function. Thus the ratio of collisions total trials due to the presence of the PU, the OSA packets and the ‘imaginary’ collision due to false alarm is given by, pc,m = 1 − (1 − pc,m,P¯0 (z0 ))(1 − pc,m,P¯m (z0 ) − pf,m ). Let us now focus on the analysis of the interference introduced to the PU by the OSA network. In this case probability of misdetection can be computed as, pξ,m = 1 − p−1 m where
∞ λnp,m exp(−λp,m )Pd,m,n , n! n=1
Pd,m,n =
0
∞
(13)
√ Qu ( 2η, νm )fη¯,n (η)dη,
¯ 2 PNm0 ,
η¯ = η is instantaneous SNR, N0 is the one sided noise PSD, and Qx (., .) is the regularized Marcum Q function. Because in this case distribution of fη¯,n (η) has integer shape 5 The offset in timing information and turnaround time [7] (time of switching from transmission to sensing) for spectrum sensing can be accommodated by guard bands, which we assume here as negligible in comparison to spectrum sensing phase and packet length.
parameter we can evaluate (13) with the help of [17, eq. 18-23] as u−1 (νm /2)i η¯νm Φ n, i + 1, Pd,m,n = α ζ + β , 2i! 2¯ η+2 i=1 where Φ(., ., .) = 1 F1 (., ., .) denotes confluent hypergeometric function, α = ((n − 1)!¯ η 2n−1 )−1 , β = (n − n η /(¯ η + 1)) , and 1)! exp(−νm /2) (2¯ νm η¯n+1 ζ = 2n−1 (n − 1)! exp − η¯ + 1 2¯ η+2 n−1 1 i η¯νm
k Li − × , 1 + η¯ 2¯ η+2 i=0 where Ln (.) is a Laguerre polynomial of degree n, and k = 1 η otherwise. for i < n − 1 and k = 1 + 1/¯ With energy detection capability nodes canreduce their M traffic splitting coefficients to ρm = (1−pξ,m )/ i=1 1−pξ,i , which in the limiting case, ρm =
1 − pξ,m 1 , = M ∀i pξ,i →0 M i=1 1 − pξ,i lim
implying that in case of perfect detection of the PU on the channels the OSA user can randomly choose a channel for transmission. Having computed pd,m we can observe the gain ΓR,m = λR,m − λR,m in introducing energy detection mechanism with λR,m which is the maximum allowed traffic computed using (7) with pa,m = pm pξ,m . We get
exp(λp,m )(pd,m Ψm −pd,m )+pd,m log , pd,m = 0 exp(λp,m )(Ψm −pd,m )+pd,m ΓR,m = . ∞, pd,m = 0 IV. N UMERICAL R ESULTS We performed a set of numerical experiments to study the performance of the proposed protocol. In Fig. 2 we have plotted the throughput in the case of packet capture. System configuration is mimicking the real OSA network scenario, where some channels are free of PU, while others are occupied, but each of them to a different degree. As expected throughput is decreasing with the increase of z0 . In Fig. 3 we have compared throughput of the OSA network using the uniform channel selection and traffic splitting coefficients. We have varied number of PU channels to which OSA network has access to, where for each channel we fixed λp,i < λp,i+1 . As expected, splitting the traffic between channels depending on the arrival rate of the PU gives a substantial increase in the throughput T , especially when the number of channels is larger and if arrivals of the PU vary highly between channels. We have also plotted throughput of the OSA network in the case of packet capture and spectrum sensing (see Fig. 4). We clearly observe the decrease in throughput when the timebandwidth product u becomes small. This implies that for a fixed OFDM subcarrier bandwidth W , with the decrease of integration time we observe very high probability of false
20 z = 0 dB
0.8
0
18
z0 = 11 dB
16
z0 = 18 dB
M=15, uniform M=15, splitting M=10, uniform M=10, splitting M=5, uniform M=5, splitting
0.7
z0 = 23 dB 14
0.6 0.5
10 T
T
12
0.4
8 0.3
6 4
0.2
2
0.1 0
5
10
15 λ
20
25
30
Fig. 2. Throughput T in the presence of the OSA network packet capture. Configuration: P¯0 = 23 dB, P¯m = 16 dB, M = 20, where first 10 channels are PU free and the rest is occupied non-uniformly by PU, with the rates given by vector Λm = [2, 4, . . . , 20], where Λm (i) = λp,i , for the corresponding channels m = {11, ...20}.
alarm, e.g., for W = 1 kHz and l = 1 ms (u = 1) and νm = 5 dB probability of false alarm is 0.9179. In the next step we plotted the curves for probability of PU detection (1 − pξ,m ), in the function of the threshold (see Fig. 5). We observe an increase in probability of detection with the increase of offered traffic (i.e., increase of collision) by PU. This leads to an interesting conclusion that the higher the offered traffic by PU, the higher is the probability of interference, but lower the throughput of the OSA network on that OFDM carrier. Also interestingly, probability of detection of colliding packets transmitted according to the Poisson traffic for a given threshold and η¯ is much higher in comparison to one signal only being transmitted. We also plotted ΓR,m in function of Ψm for fixed value of λp,m (see Fig. 6). As expected ΓR,m → ∞ as 1 − pξ,m → 0. We also observe that for relatively high value of Ψm even for low detection probability the OSA network can gain from energy detection.
0
0
5
10
15
20 λ
25
30
35
40
Fig. 3. Throughput comparison between uniform channel usage by the OSA network and using traffic splitting coefficients. Configuration: no packet capture, M = 20, where all PU channels are occupied according to Λm = [1, . . . , M ] (see notation from Fig. 2).
0.9 u=3 u=4 u=5 u=6 u=7
0.8 0.7 0.6 0.5 T
0
0.4 0.3 0.2 0.1 0
0
5
10
15
20 λ
25
30
35
40
Fig. 4. Throughput T in the presence of the OSA network packet capture and spectrum sensing for different values of u. Configuration: P¯0 = 10 dB, P¯0 = 5 dB, z0 = 30 dB, M = 10, Λm = [0.15, 0.3, . . . , 1.5] (see notation from Fig. 2), and threshold value νm = 5 dB. We assume here that l L.
V. C ONCLUSIONS 1 η=10 η=20 η=5 η=1 η=25
0.9 0.8 0.7 0.6 1−pξ,m
We analyzed an OSA network in the presence of PU and with fast retrial capability under the OFDMA setting. OSA network nodes harness the holes in the spectrum usage under the shadow of the activity of the PUs. We analyzed our mechanism of spectrum sharing with and without packet capture capability and with spectrum sensing. We applied recently proposed OFDMA-based Slotted Aloha protocol, for accessing the PU channels which is simple and easily implementable. We have given a simple way to avoid and control collisions when the traffic generated by the OSA is higher. The contributions of this paper also includes the effective use of the PU channel by using the spectrum sensing. We proved that scheduling the OSA traffic to the least used PU channel reduces the collision and increases the OSA throughput. We note that our assumption that threshold in sensing is independent of the threshold used in the packet capture which
0.5 0.4 0.3 0.2 0.1 0
0
10
20
30
40 νm
50
60
70
80
Fig. 5. Probability of detection for u = 2, λp,m = 0.5, for different values of η¯ as a function of νm .
We note that while ρi → 1/M or M → ∞, gain from introducing access scheme for OSA network based on PU activity is negligible, in comparison to random access scheme.
7
6
R EFERENCES
5
Ψm=0.1
Ψm=0.9
λ
R,m
4
3
2
1
0
0
0.2
0.4
0.6
0.8
1
1−p
ξ,m
Fig. 6. ΓR,m as a function of 1 − pξ,m for λp,m = 7. Curves from left to right are plotted for Ψm = {0.1, 0.2, . . . , 0.9}.
may not be so in reality. We therefore plan to investigate this issue in the future. We also plan to focus on the analysis, holistically, of the proposed scheme in cellular environment with different channel sharing values. A PPENDIX Lemma 1: Channel access procedure in multichannel multiaccess protocols based on the arrival rates of the PU minimizes collision probability, in comparison to uniform channel selection. M Proof: First we introduce the metric M i=1 pA,i pi where pA,i is the observed probability of choosing a channel i by OSA network using channel access procedure of type A, and pi is the probability of arriving PU user on channel i. Knowing pm for each PU on its channel m, one can express the normalized channel M arrival probability for each PU as pm , and ρm = M i=1 ρi = 1. Let us take ρ1 ≤ . . . ≤ ρM , i=1 pi and analyze two access schemes here. In the random access scheme, A = RND, the OSA user chooses each channel uniformly randomly with probability pRND,i = 1/M . In the Least Used First scheme6 , A = LeU, OSA user chooses 1−pm = ρ˜i , each channel with probability pLeU,i = M i=1 1−pi M ˜i = 1, such that ρ˜1 ≥ . . . ≥ ρ˜M Therefore we only i=1 ρ need to prove using M that M i=1
ρ˜i ρi ≤
M 1 ρi . M i=1
(A.14)
Using Chebyshev’s sum inequality [19] n n n n ai bi ≤ ai bi , i=1
i=1
i=1
for a1 ≤ . . . ≤ an and b1 ≥ . . . ≥ bn replacing n = M , bi = ρi and ai = ρ˜i we get (A.14). 6 This algorithm is similar to the channel assignment scheme proposed for optical switches in All-Optical Networks [18].
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