IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 3, NO. 5, OCTOBER 2014 481

Opportunistic Hybrid ARQ—Enabler of Centralized-RANOver Nonideal Backhaul

Peter Rost, Member, IEEE, and Athul Prasad, Student Member, IEEE

Abstract—Centralized radio access networks rely on transportnetworks with very high throughput and very low latency. In thecase of nonideal backhaul, it may be necessary to only centralizeparts of the radio access network. This implies several timingand protocol constraints, e.g., predefined timing of retransmissionsdue to hybrid ARQ. In this paper, an opportunistic hybrid-ARQapproach is introduced, which estimates the decoding error prob-ability at the radio access points and directly provides feedback tomobile terminals, while actual decoding is performed at the centralprocessor. Furthermore, an effective signal-to-noise ratio (SNR) isderived, which allows for the use of a single mapping curve.

Index Terms—Flexible centralized RAN, hybrid ARQ, errorprobability analysis.

I. INTRODUCTION

CURRENTLY, a multitude of technologies is investigatedto enable the required data rate increase foreseen in 4G

and 5G mobile networks. One such technology is CentralizedRadio Access Network (RAN) [1], [2] which is illustrated inFig. 1. Centralized RAN shifts all digital baseband processingtowards a central processor while only analog processing anddigital-to-analog conversion is performed at the remote radioheads (RRHs). The exchange of I/Q samples between the cen-tral processor and RRHs requires backhaul technologies whichsupport very high throughput and very low latency.

A. Problem Statement

4G and 5G deployments, in particular if based on small cells,will utilize heterogeneous backhaul technologies. This requiresa more flexible assignment of RAN functionality to the centralprocessor and RRHs [3]. Such a flexible assignment will reducethe requirements on the transport network while retaining amajor part of the centralization benefits. One such split wouldbe applied within the physical (PHY) layer as illustrated inFig. 2, i.e., forward error correction (FEC), hybrid automaticrepeat-request (HARQ), and anything above including mediumaccess (MAC), Radio Link Control (RLC), and Packet DataConvergence Protocol (PDCP) layer are centralized. FEC refersto both channel encoding in the downlink as well as decodingin the uplink, e.g., turbo-decoding in the case of 3GPP LTE(Long Term Evolution). HARQ refers to a stop-and-wait feed-

Manuscript received May 9, 2014; accepted May 27, 2014. Date of publi-cation July 29, 2014; date of current version October 9, 2014. This work wassupported by the European Union Seventh Framework Programme (FP7/2007-2013) under Grant 317941. The associate editor coordinating the review of thispaper and approving it for publication was L. Le.

The authors are with NEC Laboratories Europe, Heidelberg 69115, Germany(e-mail: peter.rost@ieee.org; athul.prasad@ieee.org).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LWC.2014.2327982

Fig. 1. Partly centralized radio access network architecture.

Fig. 2. Typical protocol stack.

back protocol where an acknowledgement (ACK) or negativeacknowledgement (NACK) indicates whether or not the lasttransmission was successfully decoded.

The mentioned split of RAN functionality allows for imple-menting advanced decoding algorithms at the central processorand would centralize a major part of computational complexity.However, in this case stringent latency requirements must befulfilled, e.g., HARQ requires that all uplink processing mustbe finished within 3 ms after receiving a subframe (in 3GPPLTE frequency division duplexing (FDD)). These 3 ms includeboth the round-trip delay between central processor and RRH,as well as the actual decoding operation. Nonideal backhaulmay imply significantly higher latencies. In addition, deployinggeneral purpose hardware at the central processor will lead tocomputational jitter violating real-time constraints.

Hence, we need a solution which is applicable to nonidealbackhaul (latency in the order of milliseconds), which allowsfor centralizing the computationally intense part of the PHYlayer, which meets the stringent timing requirements imposed

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482 IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 3, NO. 5, OCTOBER 2014

by HARQ, and which does not impose significant performancepenalties. If we were applying currently available technology,only the backhaul round-trip delay would already exceed theHARQ timing requirements and therefore lead to RAN protocolerrors. The solution must be standards compliant as any changeparticularly to mobile terminals should be avoided. Preferably,the solution only applies to deployed radio access points and istransparent to mobile terminals.

B. Related Work

In [4], Ikuno et al. analyze the problem of link adaptationin systems with HARQ. The authors use a model where eachround of retransmission provides both incremental redundancy(additional parity bits) and improved signal-to noise ratio(SNR) (systematic bits). Using this model, they derive a linkerror prediction model which computes for each retransmis-sion round a separate error prediction curve depending on aneffective SNR. This mapping curve allows for efficient linkadaptation based on a given effective SNR. A detailed overviewof centralized RAN and possible functional splits on PHY andMAC layer has been provided by Dötsch et al. in [5]. Amongothers, they elaborate on the impact of performing HARQcentrally under nonideal backhaul. The proposed solution is tosuspend the HARQ process and to increase the retransmissioninterval by 8 ms. However, it also reduces the achievablepeak data rate by 50% and its applicability is limited by themaximum number of HARQ processes. Finally, Wu et al. [6]provide an overview of HARQ under Rayleigh fading with aframework for analyzing the throughput performance.

C. Contributions

This paper introduces an opportunistic HARQ approachwhere the RRH estimates the probability of decoding successbased on the received SNR. Using this estimate, the RRHsends HARQ feedback to the mobile terminal, and forwards thereceived packets as well as information on the HARQ feedbackto the central processor.

If this approach is applied, the central processor could thencombine the received packets, taking into account the HARQfeedback provided by the RRH. The RRH needs not decodeany packet, and only deploys one mapping curve using aneffective SNR based on the channel state information from alltransmissions. Due to the fact that only one mapping curve isused, the approach is independent of the number of number ofHARQ retransmissions.

In this paper, we focus on the introduction, performanceanalysis, and discussion of the opportunistic HARQ approach.

II. SYSTEM MODEL AND NOTATION

Throughout this paper, italic letters indicate scalars, vectorsare indicated with x, x

n∼ CN (0, σ2x) denotes a circularly sym-

metric Gaussian random variable (r.v.) with zero mean andvariance σ2

x. We further use Ex{f(x)} to denote the expectationof f(x) with respect to r.v. x.

We consider a single-link uplink scenario with one mobileterminal and one RRH, where the mobile terminal transmitscodewords with N consecutive channel input letters. Eachcodeword is selected from a set of 2L different codewords,i.e., the effective code-rate for one transmitted block is given

by R = (L/N) bpcu (bit per channel use). Furthermore, weconsider block Rayleigh fading such that the received signalis given by

yt(n) = htxt(n) + wt(n), (1)

where t ∈ [0;T − 1] denotes the (t+ 1)-th transmission roundof the same (but independently encoded) codeword, n ∈[0;N − 1] denotes the letter within each codeword, xt(n)

n∼CN (0, σ2

x) denotes the channel input, htn∼ CN (0, 1) is the

i.i.d. random channel fading process constant over onecodeword duration, and wt(n)

n∼ CN (0, 1) is additive whiteGaussian noise (AWGN) of unit power. We use h(t) =[ht . . . h0] to denote the vector of channel events of the firstt+ 1 transmissions. The SNR for transmission index t is givenby γt = σ2

x|ht|2. Similar to h(t), we define γ(t) = [γ0 . . . γt].In the following, we will further use k to denote the codewordindex.

III. HYBRID ARQ

A. HARQ With Incremental Redundancy

Assume an initial transmission x0 = [x0(0), . . . x0(N − 1)]with rate Rinit = L/N . After receiving the codeword, thereceiver attempts to decode x0 and provides feedback to thetransmitter accordingly. If the receiver was unable to decode x0,the message is reencoded and re-transmitted in x1. This processis continued until the receiver either successfully decoded x0 ora maximum number of transmissions T has been reached. Thefunction Pre(Rinit, h(t)) denotes the probability of decodingerror under a given vector of channel events h(t).

A system based on HARQ needs to be optimized suchthat an outage probability Prtarget is not exceeded, i.e.,Eh{Pre(Rinit, h(T − 1))} ≤ Prtarget. The effective rate afterblock t is given by Reff(t) = (1/t+ 1)Rinit. Let tk denote thenumber of transmissions for the k-th codeword, the expectednumber of transmissions is given by

E{tk} = 1 +

T−2∑t=0

Eh {Pre (Rinit, h(t))} . (2)

Using this expression, the expected effective rate can be de-fined by Eh,t{Reff(t)} = Reff = 1/E{tk}Rinit. We are nowinterested in maximizing Reff under the maximum outageprobability constraint Prtarget and a maximum number of Ttransmissions for each codeword.

B. Opportunistic HARQ

In the case of opportunistic HARQ, we do not send feedbackbased on the actual decoding result but based on the esti-mated error probability. Let us define random variable π(t, h) =Pre(Rinit, h(t)) and the set

P =

{(h, t) : Pre (Rinit, h(t)) ≤ Pr

th∨ t = T

}. (3)

In the case of perfect HARQ, the feedback is chosen basedon the actual decoding success, i.e., a NACK is sent withprobability Pre(Rinit, h(t)). In order to fulfill the target errorprobability, the initial rate is chosen such that E{π(t, h)} =

ROST AND PRASAD: OPPORTUNISTIC HYBRID ARQ—ENABLER OF CENTRALIZED-RAN OVER NONIDEAL BACKHAUL 483

Prtarget. In our system, we have an additional ambiguity be-cause we cannot guarantee that after sending an ACK, thecodeword can be decoded. Therefore, the error probability isdecomposed into two parts: the probability that the channelconditions do not satisfy (3), and that (3) is satisfied but stilla decoding error occurs. Therefore, the threshold probabilitymust be chosen such that

Pr(P) +

∫(h,t)∈P

π(t,h)ph|t(h|t)dπt,h ≤ Prtarget . (4)

Hence, we need to determine Prth and Rinit under a givenchannel probability density function ph|t for channel vector h(t)at transmission t and maximum delay T . If Prth = Prtarget /2,the previous condition is fulfilled because from (3) follows thatPr(P) ≤ Prth, and the second part can be upper bounded byE{π(t,h)} = Prth. The previous constraint needs to be trans-formed into an effective SNR constraint such that a minimumrequired effective SNR is determined through mapping curvesand compared to an actual effective SNR γeff .

IV. ERROR PROBABILITY ANALYSIS

In this section, we derive an upper bound on the error prob-ability for finite length codewords and multiple transmissions.We show how an effective SNR can be determined which isthen used to decide upon HARQ retransmissions.

A. Error Probability Upper Bound for OneTransmission Block

In order to determine an error probability upper bound fora given code-rate R and one transmission block (T = 1), weuse the upper bound derived by [7, Eq. (7.4.35-36)] for energy-constraint Gaussian input signals and AWGN with SNR γ:

Pre(R, γ) = c1e−NEr(R,γ) (5)

Er(R, γ) =R0(γ)−R (6)

R0(γ) =

[1 +

γ

2−√

1 +γ2

4

]log2 e

+ log2

[1

2

(1 +

√1 +

γ2

4

)](7)

where we set ρ = 1 in [7, Eq. (7.4.35-36)], and we use binaryinformation measure. Function R0(γ) in (7) is referred to ascut-off rate which depends upon the actual SNR γ. The constantc1 is not further detailed here as it has only minor impact andscales slower than the exponential term.

B. Error Probability Upper Bound for T Transmission Blocks

If the message is re-encoded and re-transmitted, independentinformation will be provided for the decoding process. Hence,the actual blocklength increases to NT , while the effective SNRis more difficult to determine. This implies that the error expo-nent increases linearly in T and therefore the error probabilitydecreases exponentially.

The case of T independent transmission blocks can be mod-elled using the parallel Gaussian channel [8]. Each transmission

is modeled as an independent Gaussian channel with channelgain ht. In order to extend (7) accordingly, we use the deriva-tions in [7, Section 7.5], which derives the cut-off rate in thecase of parallel Gaussian channels. We apply the followinglower bound on the error probability [7, Eq. (7.5.33)]:

Pre(Rinit, γ(t)

)= cte

−NTEr(Rinit,γ(t)) (8)

Er

(Rinit, γ(t)

)=

1

T

T−1∑t=0

R0(γt)−Reff(T ). (9)

The main problem with (9) is the first term on the right handside which represents an average of cut-off rates. In the case ofa practical deployment, it would be difficult to compute this av-erage and use it in a mapping curve which links SNR and blockerror rate. Therefore, we need an expression which determinesan effective SNR γeff to obtain a close approximation of (9).

C. Approximation Utilizing Combined SNR

In order to approximate (9), we use a low SNR and a highSNR approximation. From the concavity of R0 follows

Pre(Rinit, γ(t)

)≤ cte

−NEr(Rinit,γ(t)), (10)

Er

(Rinit, γ(t)

)=R0(γeff,low)−Reff , (11)

γeff,low =T−1∑t=0

γt. (12)

From Er(Rinit, γ(t)) ≤ TEr(Rinit, γ(t)) follows that (10)constitutes an upper bound. The approximation based onγeff,low is only tight at low SNR while at high SNR, the approx-imation in (11) becomes very loose. At high SNR, R0(γeff,low)strongly underestimates the actual cut-off rate.

Therefore, we need an approximation of R0 for large valuesof γ. Consider (7) and its high SNR approximation given by

limγ→∞

R0(γ) = log2 e+ log2(γ/4) (13)

which is tight for high SNR but only loose for low SNR, whereit strongly underestimates the actual cut-off rate. We can usethis approximation now to derive a high SNR approximationfor the sum of individual cut-off rates:

limγ→∞

T−1∑t=0

R0(γt) =

T−1∑t=0

[log2 e+ log2(γt/4)] (14)

=T log2 e/4 +

T−1∑t=0

log2(γt) (15)

= log2(e/4)T + log2

(T−1∏t=0

γt

)(16)

= log2

[(e/4)T

T−1∏t=0

γt

]. (17)

Define

γeff,high = (e/4)TT−1∏t=0

γt, (18)

484 IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 3, NO. 5, OCTOBER 2014

Fig. 3. Achievable outage rate for block Rayleigh fading, ε = 10−4, codingover five 3GPP LTE PRBs, and Pth = ε/2.

then Pre(Rinit, γ(t)) ≤ Pre(Rinit, γeff,high).Both expressions, (12) and (18), are used to approximate the

combined SNR by using the maximum of both expressions:

γeff = max

(T−1∑t=0

γt, (e/4)T

T−1∏t=0

γt

), (19)

which is used in (7) to approximate the error probability. Ina practical application, a lookup table could be used instead,which maps the effective SNR to an expected error probability.

V. NUMERICAL RESULTS

In this section, we assess the previously introduced oppor-tunistic HARQ approach based on (9) and based on the effec-tive SNR approximation in (19). We compare both to a fixednumber of transmissions, i.e., each codeword is transmitted andencoded independently T times. Furthermore, we compare theperformance with optimal HARQ where the feedback is sentbased on the actual decoding result. All four approaches mustnot exceed an outage probability of ε = 10−4.

Fig. 3 shows the achievable outage rate for independentand identical block Rayleigh fading, N = 360 (five 3GPP LTEPRBs), Pth = ε/2, and T = [1, 2, 3, 4]. For T = 1, Reff of allfour approaches coincides below 0.1 bpcu and is therefore onlyrecognizable at the bottom of the figure. The results show thatopportunistic HARQ is able to maintain the benefits of HARQand offers the same diversity gain. The benefits compared to afixed number of transmissions would increase with decreasingoutage probability ε. We can further observe that the effec-tive SNR in (19) implies only a minor performance loss forT = 3 and T = 4 compared to optimal HARQ and opportunis-tic HARQ based on (9).

VI. CONCLUSION AND OUTLOOK

In this paper, we introduced an opportunistic HARQ ap-proach which does not provide HARQ feedback based on the

actual decoding but based on the channel state information.In currently deployed centralized RAN, a very high capacityand very low latency connection between RRH and centralprocessor is required in order to provide HARQ feedbackwithin the required time, i.e., 3 ms in the case of 3GPP LTEFDD. Our approach divides the HARQ process into a time-critical part and computationally intense part. The time-criticalpart, i.e., determining HARQ feedback, is implemented at theRRH based on available channel state information and withoutthe need to decode the received codeword. The computationallyintense part, i.e., decoding the received codeword, is movedtowards the central processor where advanced and computa-tionally intense algorithms may be implemented.

Since the time-critical part has been removed from the centralprocessor (at least the part of particular relevance to PHY andMAC), it is possible to relax realtime constraints and deploynonrealtime general purpose processors which may imply com-putational jitter. It further allows for using nonideal backhaulin a centralized RAN architecture which is critical in areasof high deployment costs, e.g., small-cell deployments wheretrenching optical fiber would constitute a major part of thecapital expenditures.

From the presented results, we can conclude that the pro-posed opportunistic HARQ using Pth = ε/2 provides the sameperformance benefits as HARQ based on the actual decodingresult, and using the derived effective SNR achieves the sameperformance within about 0.1 bpcu. The derived effective SNRis an appropriate approximation which is applicable for anindependent number of re-transmissions. It further allows fora performance prediction based on a single mapping curve, i.e.,in a practical application, only one mapping curve is necessaryto derive the expected block error probability. In our futurework, we will apply opportunistic HARQ as well as the derivedeffective SNR to actual 3GPP LTE modulation and codingschemes in order to prove its applicability to practically relevantscenarios.

ACKNOWLEDGMENT

The authors would like to thank their colleagues from iJOINfor their contributions. The views expressed are those of theauthors and do not necessarily represent the project.

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