End-to-End HARQ in Cognitive Radio Networks
Weng-Chon Ao, Kwang-Cheng Chen
Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan
Abstract—Cognitive radio networks (CRN) may greatly en- hance the throughput based on a given bandwidth. CRN has a unique feature, consisting of uni-directional opportunistic wireless links, and packets may be cooperatively relayed from source node to destination node through one or multiple paths, while each path consists of multi-hop opportunistic wireless fading links. Effective end-to-end error control is therefore a must to complete transportation of packets in CRN, though not being touched in open literatures. Traditional ARQ cannot generally function over uni-directional opportunistic links. We consequently develop a novel hybrid ARQ based on amplify- and-forward cooperative relay of CRN to reach the purpose of end-to-end error control at session level. Multiple coded sub- packets are sent through multiple paths, and the destination node decodes these received coded sub-packets from different paths. This HARQ for CRN works even missing some coded sub-packets. By the concept of outage, we also study allocation of coded sub-packets on multiple paths in an information theoretical view and develop a coding rate adaptation scheme for CRN such that end-to-end error control is possible.
I. INTRODUCTION
Facing the increasing demands of wireless services and the underutilization of licensed spectrum, cognitive radio (CR) to sense the spectrum and to opportunistically access the spectrum holes of primary (licensed) systems has emerged as a technology to enhance spectrum utilization. Networking CRs and primary system nodes to form a cognitive radio network (CRN) can use cooperative relay to greatly enhance network efficiency given a fixed bandwidth [1]. However, due to opportunistic access, the CRN actually consists of uni- directional opportunistic wireless links [2]. A transmission opportunity may exist in one direction but no warranty in another direction. An effective error control is thus necessary to facilitate reliable packet transmission in the CRN.
Traditional ARQ is a link level error-control method used for packet error detection and retransmission. Error-detection bits (such as CRC bits) are attached with data bits to form a message packet. When transmission errors occur, detected by the receiver, a negative acknowledgement (NACK) is sent back requesting retransmission of the message packet; otherwise an acknowledgement (ACK) is sent back. HARQ combines ARQ with error control coding and has two types in general.
In Type-1 HARQ, FEC (forward-error correction) bits are additionally added with the message packet. Type-1 HARQ reduces the number of retransmissions but a fixed throughput offset always exists due to the fixed FEC redundancy. By introducing FEC redundancy incrementally, Type-2 HARQ adapts to varying channel conditions and achieves higher throughput efficiency. An overview of the recent development of link level HARQ can be found in [3] and references
therein. The above link level ARQ/HARQ schemes based on bidirectional link assumption cannot generally function over uni-directional opportunistic links. We consequently develop a novel end-to-end (session level) HARQ scheme to reach the purpose of end-to-end error control in the CRN.
Packets in the CRN may be cooperatively relayed from the source node to the destination node through one or multiple paths, while each path consists of multi-hop uni-directional opportunistic wireless links. Our proposed end-to-end HARQ scheme is based on coded cooperation among the multiple paths and amplify-and-forward relaying within each path. A coded packet at the source node is divided into multiple coded sub-packets which are sent through multiple paths, and the destination node decodes these received coded sub-packets from different paths. The idea of link level coded cooperation is first introduced in [4]–[6] where partial redundancy is generated through a cooperative relay in order to exploit spatial diversity. We generalize the concept of coded cooperation in a network perspective to realize end-to-end error control in the CRN. In [7] [8], analyses of different cooperative relaying protocols, e.g., amplify-and-forward relaying, and diversity techniques are given.
The remainder of the paper is organized as follows. In Section II, the end-to-end HARQ scheme is presented. By the concept of outage, the coded packet division problem is posed in Section III. In Section IV, performance degradation due to network delay is addressed. In section V, we further discuss a coding rate adaptation scheme. Simulation results are presented in Section VI. Section VII provides the conclusion.
II. END-TO-ENDHARQSCHEME
We generate a coded packet from message packet at the source node and then divide the coded packet into multiple coded sub-packets. These coded sub-packets are sent through multiple forward paths as shown in Fig. 1. A forward (back- ward) path from the source (destination) node to the destina- tion (source) node may consist of uni-directional opportunistic links. Since many different forward and backward paths may exist, we take the advantage of spatial diversity by using multiple paths between the source node and the destination node. Each intermediate node within a path amplifies and forwards the coded sub-packets to its next node. Please note that within a path, link-by-link fully decode-and-forward is not possible due to the uni-directional characteristic of a link and amplify-and-forward is used here. Decoding is only performed at the destination node by combining coded sub-packets gathered from different paths. Under the coded cooperation, when some coded sub-packets missed due to opportunistic
environment, we may still be able to recover the message packet by combing the received coded sub-packets, regarding the missed coded sub-packets as punctured from the coded packet originated at the source node. If the message packet is successfully recovered at the destination node, a session level ACK is generated passing through backward paths to the source node; otherwise a session level NACK is generated.
End-to-end error in the CRN is thus realized through the end- to-end HARQ scheme at session level. Performance analysis is provided subsequently.
A. Link and path model
We assume that there exist L link-disjoint paths between the source node and the destination node as shown in Fig. 1.
Each path i, 1 ≤ i ≤ L, has Mi− 1 intermediate nodes. Each link between a pair of node is modeled as an independent slow flat Rayleigh fading channel. The received signal at node Ri,j
is defined as yi,j = hi,jxi,j−1+ zi,j, where hi,j is denoted as channel gain and is assumed to be Rayleigh distributed. xi,j−1
is denoted as the signal generated from the previous node Ri,j−1and zi,j is denoted as independent zero-mean additive white Gaussian noise with variance N0. Each intermediate node amplifies and forwards the received signal subject to the same signal energy constraint Eb. The signal generated by node Ri,j is given by
xi,j= αi,jyi,j, α2i,j= Eb
h2i,jEb+ N0, (1) where αi,jis the amplifying coefficient. The per node received SNR at node Ri,j is defined as γi,j = h2i,jEb/N0 which is exponential distributed with mean γi,j. The equivalent end-to- end SNR of the path i (or called path SNR) is denoted as γeqi. It can be evaluated as [9],
γeqi =
Mi
Y
j=1
µ 1 + 1
γi,j
¶
− 1
−1
, 1 ≤ i ≤ L (2)
At high SNR, (2) reduces to
γeqi =
Mi
X
j=1
µ 1 γi,j
¶
−1
, 1 ≤ i ≤ L (3)
It is more tractable and can be obtained with the amplifying coefficient αi,j= 1/hi,j. The above equation relates the path SNR with the SNRs of its composed links.
B. Performance analysis of the coding scheme
We assume that the code rate of the FEC code is RC, message packet size is K bits, and coded packet size is N = K/RC bits. We divide the coded packet into L coded sub- packets which are transmitted over L different paths. The L coded sub-packets are received, combined, and decoded at the destination node. Please realize that to combining, each relay node Ri,j needs to include the channel side information γi,j
in the header of its forwarding packet to facilitate calculation of path SNR (c.f. (2)) at the destination node. The header of
h11
RL1 RL2 S
R21
R11 R12
R22 h21 D
hL1
h12
h22
hL2
1M1
h
LM2
h
LML
h
Fig. 1. CRN network topology
a coded sub-packet is assumed to be protected by a separated powerful low rate code and can be recovered individually.
The pairwise error probability (PEP) between two code- words can be evaluated as
P (d|γeq) = Q³p
2d1γeq1+ 2d2γeq2+ ... + 2dLγeqL
´ , (4) where γeq= (γeq1, γeq2, ..., γeqL), d is the Hamming distance between the transmitted codeword and the codeword obtained after decoding, di is the portion of Hamming distance con- tributed from the i’th coded sub-packet, 1 ≤ i ≤ L, and d = d1 + d2 + ... + dL. The unconditional pairwise error probability can be written as
P (d) = Z
γeq
P (d|γeq)f (γeq)dγeq, (5)
f (γeq) = f (γeq1)...f (γeqL) is the probability density function of γeq. In high SNR, using the parameterization method introduced in [10], (5) can be derived as
P (d) ≈ QL
i=1(2i − 1) L2L+1
YL i=1
1di Mi
X
j=1
1 γi,j
(6)
We can realize that diversity gain of order L is achieved. Also, the denominator of (6) has a termQL
i=1di corresponding to the coding gain. It is maximized when di ≈ d/L, i.e., the total Hamming distance is distributed evenly among coded sub-packets.
The above result can be shown in an alternative way by noticing that in high SNR, the performance of the weakest link dominates the path,
γeqi ≈ γbi≡ min (γi,1, γi,2, ..., γi,Mi), 1 ≤ i ≤ L (7) γbi is exponential distributed with mean
γbi = 1
1 γi,1 +γ1
i,2 + ... + γ1
i,Mi
, 1 ≤ i ≤ L (8)
Using the moment generating function method, (5) can be
simplified and bounded as P (d) = 1
π Z π
2
0
µ
1 + d1γb1
sin2θ
¶−1 ...
µ
1 +dLγbL
sin2θ
¶−1 dθ
≤ 1
2
µ 1
1 + d1γb1
¶ ...
µ 1
1 + dLγbL
¶
< 1 2
YL i=1
1di Mi
X
j=1
1 γi,j
(9)
It is the same as (6) with a scaling factor.
For convolutional code, the packet error rate can be bounded as [11]
PP ER≤ 1 − Z
γeq
1 − min
1, X∞ d=df
X∞ w=1
aw,dP (d|γeq)
B
f (γeq)dγeq, (10)
where df is the free distance of the code, aw,dis the number of codewords corresponding to input weight w and output weight d, and B is the number of trellis stages in the codeword.
III. CODED PACKET DIVISION PROBLEM
We discuss how to decide the fraction of a coded packet allocated to each path (i.e., the time-sharing ratio among the paths). Our objective is to choose a division strategy to minimize the outage probability given a source information rate. The strategy we use depends on how much side in- formation (i.e., path statistics) available at the source. First, we consider the case that the source does not have any information about the statistics of paths. A reasonable strategy is to divide the coded packet evenly into L coded sub-packets which then allocated to the L paths (refer to Fig. 1). In other words, the source uses the L paths in an equal time- sharing fashion. The end-to-end capacity of path i is denoted as log2(1 + γeqi), 1 ≤ i ≤ L, and the source is assumed to have information rate R. In the high SNR regime, the outage probability Pout can be expressed as
Pout = P Ã L
X
i=1
1
Llog2(1 + γeqi) < R
!
≥ P ÃL
\
i=1
{log2(1 + γeqi) < R}
!
= YL i=1
P (log2(1 + γeqi) < R)
≈ YL i=1
(2R− 1)
Mi
X
j=1
1 γi,j
(11)
In the low SNR regime, it can be written as Pout = P
à L X
i=1
1
Llog2(1 + γeqi) < R
!
≈ P Ã L
X
i=1
γeqi< LR log2e
!
(12)
Next, we consider the case that each source has side information of the mean statistics of paths between itself and its destination. Here, we present this exploration in a network perspective with multiple source-destination pairs using the network utility maximization framework [12]. Each source s is assumed to have fixed information rate Rs and utility Us(ρs) which is a concave function in ρs. ρs is denoted as the reliability of s and equals 1 − Psout. wisis denoted as the fraction of a coded packet of s allocated to its ith path (i.e., the time-sharing ratio of its ith path),P
iwsi = 1, and is decision variable we attempt to find such that the sum utility of sources is maximized.
The network is described to have E links, 1 ≤ e ≤ E, N source-destination pairs, 1 ≤ s ≤ N , and each source s has Ls paths, 1 ≤ i ≤ Ls, between itself and its destination. (We do not assume link-disjoint paths here.) A matrix Heis is defined for each source s, Heis = 1 when path i of source s uses link e, otherwise it equals 0.
We address that, even in the limited SNR regime, the outage probability Psoutof s is not jointly convex in wsi, 1 ≤ i ≤ Ls. In the high SNR regime,
Psout = P ÃLs
X
i=1
wsilog2(1 + γeqsi) < Rs
!
≈ P ÃLs
Y
i=1
(γseqi)wsi < 2Rs
!
(13) In the low SNR regime,
Psout ≈ P ÃLs
X
i=1
wisγeqsi < Rs log2e
!
(14)
The network optimization problem can be formulated as,
maximize X
s
Us(1 − Psout)
subject to Psout = P ÃLs
X
i=1
wislog2(1 + γeqsi) < Rs
! , ∀s X
s
X
i
Heiswsi ≤ 1, ∀e X
i
wis= 1, ∀s 0 ≤ wsi ≤ 1, ∀s, i
1 ≤ s ≤ N, 1 ≤ i ≤ Ls, 1 ≤ e ≤ E (15) where the second constraint is the capacity constraint. The optimization problem can be solved only numerically such that each source s uses its paths in time-sharing with weight wsi∗, 1 ≤ i ≤ Ls, which are solutions of (15).
IV. NETWORK DELAY
We analyze the impact of network delay with a single source-destination pair (refer to Fig. 1). Each multi-hop path between the pair is modeled as M/M/1 tandem queues. Sup- pose that there exists an information flow with Poisson arrival
rate λ between the pair, which is divided into L sub-flows passing through L paths with Poisson rate λi = wiλ, 1 ≤ i ≤ L, P
iwi= 1. wi can be chosen as described in section III.
Each intermediate node Ri,j, 1 ≤ i ≤ L, 1 ≤ j ≤ Mi, is as- sumed to have its own background traffic with Poisson arrival rate bi,j and its processing time is assumed to be exponential distributed with mean 1/µi,j. The probability density function of link delay τi,j(queueing time plus processing time) of Ri,j
can be derived as
fτi,j(t) = µi,j(1 − ρi,j)e−µi,j(1−ρi,j)t, (16) where ρi,j = (λi+Pj
k=1bi,k)/µi,j. The probability density function of end-to-end delay τi of path i is the Mi-fold convolution of fτi,j(t), 1 ≤ j ≤ Mi,
fτi(t) = fτi,1+...+τi,Mi(t) =
"M Yi
l=1
µi,l(1 − ρi,l)
#
×
Mi
X
j=1
e−µi,j(1−ρi,j)t QMi
k=1,k6=j(µi,k(1 − ρi,k) − µi,j(1 − ρi,j))(17) The probability that the end-to-end delay of path i is smaller than t can be computed as Fτi(t) ≡ P (τi≤ t) =Rt
0fτi(x)dx.
Suppose that there exists an end-to-end delay threshold Tthat the destination node, a coded sub-packet is considered lost when the end-to-end delay is greater than the threshold which happens with probability 1 − Fτi(Tth). Due to network delay, the expected number of received coded sub-packets reduces to PL
i=1Fτi(Tth) causing performance degradation.
V. CODING RATE ADAPTATION SCHEME
If simply only one out of L coded sub-packets is forwarded at a time; we then wait an end-to-end round trip time (RTT) to see if decoding succeeds and decide whether we should forward next coded sub-packet; the decoding delay would be multiple end-to-end RTTs facilitating successful decoding (re- fer to Fig. 1). Such long decoding delay may not be favorable in applications. Our proposed coding rate adaptation scheme works in a “backward” sense that all coded sub-packets are transmitted at the first transmission. The coding rate changes successively according to the information piggybacked along the acknowledgement packet of the previous transmission.
The scheme has two phases, the “probe” phase and the
“settling” phase. In the “probe” phase, the source node has no idea of the conditions of paths between itself and the destination node which may be due to the first attempt of transmission or abrupt changes of conditions of paths indicated by previous decoding failure. The source node transmits all L coded sub-packets to probe the paths. This initial setting leads to high probability of successful decoding and thus low decoding delay.
At the destination node, we consider the case that it receives, combines all L coded sub-packets, then decodes. We are going to inference the number of coded sub-packets actually required to facilitate the successful decoding. We first try to combine and decode the coded sub-packets from the top L − 1 paths
with highest path SNR. If decoding succeeds, we combine and decode the coded sub-packets from the top L − 2 paths with highest path SNR. The process continues until decoding fails at combining the coded sub-packets from the top M − 1 paths with highest path SNR. We now know that combining the coded sub-packets from the top M paths with highest path SNR is just enough, corresponding to coding rate RC×ML with the assumption of equal-size coded sub-packets, and the remaining L − M coded sub-packets are not actually needed.
The destination node would generate an ACK to the source node attached with the information of the combining ratio ML and the corresponding M paths. The source node can use the attached information to adapt the coding rate and choose the appropriate paths for successive packet transmission. That is, the source sends M out of L coded sub-packets through the reporting M paths. Here comes the beginning of the “settling”
phase in which we continue to try to reduce the number of coded sub-packets at each successive transmission.
The “settling” phase ends when decoding fails at the desti- nation node which may be due to abrupt changes of conditions of paths. A NACK is generated requesting transmission of all remaining coded sub-packets at the source node. After that, the destination node receives, combines all L coded sub-packets, then decodes, and returns to the “probe” phase to operate as described before. In our coding rate adaptive scheme, there are regeneration points corresponding to the beginning of the
“probe” phase. The regenerative cycle is assumed to have average period W (in unit end-to-end RTT) consists of the interlacing “probe” phase and “settling” phase with length 1 and W −1 (in unit end-to-end RTT) respectively. If conditions of paths change abruptly within one RTT, we are always in the
“probe” phase (W = 1), i.e., we always use the lowest coding rate corresponding to total L coded sub-packets transmission.
A. Performance analysis
In high SNR, we use the approximation (7) in the following derivation and assume that γb1, .., γbL have equal mean γb for simplicity. In the “probe” phase, the PEP can be derived as (9).
In the “settling” phase, the joint probability density function of the top M paths with highest path SNR is f¡
γb(1), ..., γb(M )
¢, the upper M order statistic of γb1, ..., γbL, γb(1) ≥ ... ≥ γb(L). The PEP can be evaluated as
PM(dM|γb(1), ..., γb(M )) = Q
³q
2d1γb(1)+ ... + 2dMγb(M )
´ (18) where dM = d1+ ... + dM. With the change of variables [13],
xi = γb(i)− γb(i+1), i = 1, ..., L − 1 xL = γb(L)
or, γb(i) = xi+ ... + xL, i = 1, ..., L, (19) where xi, i = 1, ..., L, are independent and distributed as exponential with mean γib. Substitute (19) in (18), it becomes
PM(dM|γb(1), ..., γb(M ))
= Q³p
2d1x1+ 2(d1+ d2)x2+ ... + 2(d1+ ... + dM)xL
´
The unconditional PEP can be computed as PM(dM)
= Z
PM(dM|γb(1), ..., γb(M ))f (γb(1), ..., γb(M ))dγb(1)...dγb(M )
= 1 π
Z π
2
0
µ
1 + d1γb
sin2θ
¶−1Ã
1 + (d1+ d2)γ2b sin2θ
!−1 ...
× Ã
1 + (d1+ d2... + dM)γLb sin2θ
!−1
dθ
≤ 1 2
µ 1
1 + d1γb
¶ Ã 1
1 + (d1+ d2)γ2b
! ...
× Ã
1
1 + (d1+ d2... + dM)γLb
!
(20) We can observe that diversity gain of order L is still achieved.
For convolutional code, the packet error probability com- bining coded sub-packets from the top M paths with highest path SNR can be bounded as
PPER(M ) ≤ 1−
Z
1 − min[1, X∞ dM=dMf
X∞ w=1
aw,dPM(dM|γb(1), ..., γb(M ))]
B
f (γb(1), ..., γb(M ))dγb(1)...dγb(M ), (21) where dMf is the free distance of the punctured code with coding rate RC×ML.
B. Throughput analysis
We define the normalized throughput as T = K
lavg, (22)
where lavg is the average number of transmitted bits per K information bits. Since the interlacing “probe” phase and
“settling” phase have length 1 and W − 1 (in unit RTT) respectively, lavg can be expressed as
lavg= 1
Wlpavg+W − 1
W lsavg, (23) where lpavg and lsavg contributed from the “probe” phase and the “settling” phase respectively. In the “probe” phase, we have lpavg= N since the (lowest) coding rate is RC= K/N . In the “settling” phase, the average number of transmitted bits depends on the number of coded sub-packets facilitating successful decoding. PPER(i) is the packet error probability combining coded sub-packets from the top i paths with highest path SNR defined in (21), lsavg can be derived as
lsavg=N
L(1 − PPER(1)) + XL j=2
jN
L (1 − PPER(j))
j−1Y
i=1
PPER(i)
+N YL i=1
PPER(i) (24)
7 8 9 10 11 12 13 14 15 16
10−4 10−3 10−2 10−1 100
γ (dB)
PER
2 paths 4 paths 6 paths 8 paths 10 paths
Fig. 2. Packet error rate with different order of path diversity, L = 2, 4, 6, 8, 10.
6 7 8 9 10 11 12 13 14
10−5 10−4 10−3 10−2 10−1 100
γeq (dB)
PER
two loss one loss no loss
Fig. 3. Packet error rate with coded sub-packet loss, L = 10.
VI. SIMULATIONRESULTS
We assume that message packet size is 120 bits. Convolu- tional code with coding rate 1/2 is used in Fig. 2 and with coding rate 1/3 is used in other simulations. The constraint length of the code is 7, modulation scheme is BPSK, and links are i.i.d. slow flat Rayleigh fading channels.
In Fig. 2, the coded packet is divided evenly into L coded sub-packets which are transmitted over L different paths, L = 2, 4, 6, 8, 10 (refer to Fig.1). We can realize that when L increases, packet error rate decreases due to having higher order of path diversity. The number of relay nodes within a path is uniformly distributed between 1 and 3, γ is the average per node received SNR. In Fig. 3, performance degradation due to coded sub-packet loss is shown with L = 10, γeq is the average path SNR. In Fig. 4, we can realize that when γeq
increases, to maintain a fixed packet error rate at 10−3, only subset of received coded sub-packets from paths with highest path SNR are actually required. For example, at PER=10−3,
6 7 8 9 10 11 12 13 14 10−5
10−4 10−3 10−2 10−1 100
γeq (dB)
PER
best 8 paths best 9 paths 10 paths
Fig. 4. Subset of received coded sub-packets from paths having highest path SNR are combined, L = 10.
7 8 9 10 11 12 13 14
7 8 9 10 11
γeq (dB)
Number of coded sub−packets
Fig. 5. The number of coded sub-packets required to combine to maintain PER=10−3, L = 10.
7 8 9 10 11 12 13 14
0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43
γeq (dB)
Normalized throughput
Fig. 6. Throughput increases due to the coding rate adaptation.
we only need to combine the top eight coded sub-packets from
paths with highest path SNR with L = 10, γeq = 11(dB). In Fig. 5, to achieve PER=10−3, the number of coded sub-packets required decreases with increasing average path SNR. In Fig. 6, throughput increases due to the coding rate adaptation.
VII. CONCLUSION
In this paper, we propose, in a unified fashion, an end-to- end HARQ scheme in the cognitive radio network consisting of unidirectional opportunistic links. End-to-end error control is developed based on coded cooperation among paths and amplify-and-forward relaying within a path. Decoding is only performed at the destination node by combining (subset of) coded sub-packets from paths. Through simulations, we show that the performance of coded cooperation can be improved by exploiting path diversity. Facing the opportunistic and dynamic environment, performance degradation due to coded sub- packet loss is also shown. The allocation of coded sub-packets on multiple paths is modeled as an optimization problem.
A coding rate adaptation scheme is provided to improve the end-to-end error control efficiency, such that reliable packet transmission in CRN is feasible.
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