packet structure and receiver design for low latency

796 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 66, NO. 2, FEBRUARY 2018

Packet Structure and Receiver Design for LowLatency Wireless CommunicationsWith Ultra-Short Packets

Byungju Lee ,Member, IEEE, Sunho Park,Member, IEEE, David J. Love,Fellow, IEEE,

Hyoungju Ji,Member, IEEE, and Byonghyo Shim,Senior Member, IEEE

Abstract— Fifth generation wireless standards require muchlower latency than what current wireless systems can guaran-tee. The main challenge in fulfilling these requirements is thedevelopment of short packet transmission, in contrast to most ofthe current standards, which use a long data packet structure.Since the available training resources are limited by the packetsize, reliable channel and interference covariance estimation withreduced training overhead are crucial to any system using shortdata packets. In this paper, we propose an efficient receiver thatexploits useful information available in the data transmissionperiod to enhance the reliability of the short packet transmission.In the proposed method, the receive filter (i.e., the samplecovariance matrix) is estimated using the received samples fromthe data transmission without using an interference trainingperiod. A channel estimation algorithm to use the most reliabledata symbols as virtual pilots is employed to improve quality ofthe channel estimate. Simulationresults verify that the proposedreceiver algorithms enhance the reception quality of the shortpacket transmission.

Index Terms— 5G wireless communications, short datapackets, low latency, Internet of Things, energy harvesting,virtual pilots.

I. INTRODUCTION

FIFTH generation (5G) communication networks will bea key enabler in realizing the Internet of Things (IoT)era and hyper-connected society [2]–[4]. To support real-time applications with stringentdelay requirements and mas-sive machine-type devices, communication systems supportingultra low latency are needed [5]–[7]. For this reason, Interna-tional telecommunication union (ITU) defined ultra reliable

Manuscript received December 3, 2016; revised May 5, 2017 andAugust 4, 2017; accepted September 11, 2017. Date of publicationSeptember 21, 2017; date of current version February 14, 2018. Thiswork was supported in part by the National Science Foundation (NSF)grant CNS1642982 and the National Research Foundation of Korea (NRF)grant funded by the Korean government (MSIP) (2014R1A5A1011478 and2016K1A3A1A20006019). This paper was presented at the GLOBECOM,Washington, USA, December 4–8, 2016 [1]. The associate editor coordinatingthe review of this paper and approving it for publication was A. Tajer.(Corresponding author: Byonghyo Shim.)B. Lee and D. J. Love are with the School of Electrical andComputer Engineering, Purdue University, West Lafayette, IN 47907 USA(e-mail: [email protected]; [email protected]).S. Park, H. Ji, and B. Shim are with the Institute of New Mediaand Communications and the School of Electrical and Computer Engi-neering, Seoul National University, Seoul 08826, South Korea (e-mail:[email protected]; [email protected]; [email protected]).Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TCOMM.2017.2755012

and low latency communication (uRLLC) as one of key usecases for 5G wireless communications.1One direct way tomeet the stringent low latency requirements is to use a short-sized packet. This is in contrast to most current wirelesssystems whose sole purpose is to transmit long data packetsefficiently. Indeed, most current physical layer design reliesheavily on long codes to approach Shannon capacity. Sensorsand devices in an IoT networks transmit a very small amountof information such as environmental data (e.g., temperature,humidity, and pollution density), locations, and emergencyalarm, and thus asymptotic capacity-achieving principles arenot relevant to the transmission of short packets. In viewof this, 5G physical layer design (e.g., pilot transmissionstrategy, coding scheme, hybrid automatic repeat request)needs to be reevaluated and potentially redesigned as a whole.Many papers have been dedicated to analyze performancemetrics that are relevant to short packet communication,including the maximal achievable rate at finite packet lengthand finite packet error probability instead of using two classicinformation-theoretic metrics, the ergodic capacity and theoutage capacity [8]–[11]. Finite block-length analysis has beenextended to spectrum sharing networks using rate adapta-tion [12] and wireless energy and information transmissionusing feedback [13].In this paper, we consider practical constraints that areencountered when implementing a short packet transmissionframework. First, massive and simultaneous communicationsamong autonomous devices will induce inter-device interfer-ence at the receiver in an IoT network. In order to control theinter-device interference, a technique to use multiple receiveantennas has been proposed by utilizing the spatial degreesof freedom (DoF) provided by multiple receive antennas tobalance interference suppression and desired signal powerimprovement [14]. To implement this approach, the receiverneeds to acquire the desired CSI and the interference plusnoise covariance. While the desired CSI can be estimatedusing pilot signals, direct estimation of the interfering CSIis difficult due to the large number of interfering devices inthe IoT network. One way to tackle this problem is to use an

1Three key use cases include enhance mobile broadband (eMBB), massivemachine-type communications (mMTC), and ultra reliable and low latencycommunication (uRLLC) [6].

0090-6778 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

https://orcid.org/0000-0002-1710-2324

https://orcid.org/0000-0003-3384-5010

https://orcid.org/0000-0001-5051-1763

https://orcid.org/0000-0002-2606-8623

LEEet al.: PACKET STRUCTURE AND RECEIVER DESIGN FOR LOW LATENCY WIRELESS COMMUNICATIONS 797

interference training periodin which the interference (plusnoise) covariance matrix can be estimated by listening tointerference-only transmissions [15]. The main drawback ofthis approach is that it incurs a severe transmission rate losssince the target transmit device should remain silent duringthe interference training period. Also, the interference trainingperiod would not be large enough in obtaining the reliableestimate of the interference covariance for this short-sizedpackets, resulting in severe degradation in performance.Moreover, since current systems are designed to carry

long data packets, the pilot transmission period can be maderelatively small even though the actual period of pilot signalsis large. However, the portion of time used for pilot signalsis unduly large in a short-sized packet framework if thetraining period is not reduced. On the other hand, if the pilotlength is shortened, there would be a significant degradationin performance. Since there is a trade-off between the durationof the pilot training period and the data transmission period,the main challenge is to perform a reliable channel estimationwhile affecting the minimal impact on the duration of datatransmission period.An aim of this paper is to propose an efficient receiver

technique that exploits information obtained during thedatatransmission periodto improve the reception quality of thesystem in the short packet transmission. Intuitively, when timeresources are limited, we need to useallreceived data tooptimize the receiver performance. With this goal in mind,we propose a receive filtering algorithm that estimates theinterference covariance matrix using the received signal fromthe normal data transmission period in the IoT network. Indoing so, the interference training period becomes unnecessaryand the transmission rate loss caused by the interferencetraining period can be avoided. We show from analysis andnumerical experiments that the proposed method achieves alinear scaling of SINR in the number of receive antennas.Next, we propose a low latency frame structure adequatefor the one-shot random access where pilot and data aretransmitted simultaneously. We propose a strategy to exploitthe data symbols received from the target transmit device toimprove the channel estimation quality at the receiver. Therehave been previous studies exploiting data signals for channelestimation including the non-OFDM system with frequency-selective channel [16], wireless LAN (IEEE 802.11n) [17], andLTE systems with long packet [18] In this paper, we choosethe most reliable received data symbols, referred to asvirtualpilots, among all possible soft decision data symbols and thenuse them to re-estimate the channel. Our proposed methodis distinct from previous efforts in the sense that select avirtual pilot group making a dominant contribution to thechannel estimation quality. Towards this end, we design amean square error (MSE) based virtual pilot selection strategy.We show from numerical simulations that the proposed methodoutperforms the conventional receiver technique in the shortpacket transmission (e.g., packet size is set to tens of bytes).The remainder of the paper is organized as follows.In Section II, we describe the structure of a packet and reviewconventional receiver techniques. In Section III, we presentthe proposed interference covariance matrix estimation

Fig. 1. A paired AP receives the desired signal from a target device and issubject to interference (dashed lines) from neighboring devices.

technique suited to the short packet transmission.In Section IV, we describe the proposed virtual pilotbased channel estimation technique. In Section V, we presentsimulation results to verify the performance of the proposedscheme. We conclude the paper in Section VI.We briefly summarize notation used in this paper.We employ uppercase boldface letters for matrices and lower-case boldface letters for vectors. The superscripts(·)Hand(·)T

denote the conjugate transpose and transpose, respectively.Cdenotes the field of complex numbers. · pindicatesthep-norm.IN is theN×Nidentity matrix.E[·]is theexpectation operator.⊗ is the Kronecker product operator.CN(m,σ2)denotes a complex Gaussian random variable withmeanmand varianceσ2.

II. SYSTEMDESCRIPTION

A. System Model and Packet Structure

We consider uplink communication in an IoT networkssuch as wireless sensor networks, ad hoc network, and energyharvesting network, with an example setup shown in Fig. 1.We assume that the target transmit device has a single antennaand the paired access point (AP) receiver hasNantennas.Since there are a large number of devices in the radiotransmission range, the received signal contains interferencefrom adjacent devices as well asthe desired information.2

We assume a block-fading channel model, and each blockconsists ofNbchannel uses, among whichNpuses are forthe pilot training andNduses are for the data transmission(see Fig. 2(a)).In this setup, the received signal for the-th channel use inthei-th fading block is given by

yi[]=β0h0,is0,i[]+

J

j=1

βjhj,isj,i[]+ni[] (1)

2In this work, we assume that the AP receiver experiences interferencefrom devices in neighboring cells for both channel estimation phase and datatransmission phase. In short packet transmission, the packet length would befar shorter than the channel coherenttime and thus the channel can be fairlystatic and at least slowly varying within a packet. Therefore, in the short packetregime, impact of mis-aligned coherence block would not be significant. Forthe sake of simplicity, we assume that the coherence times of the desiredchannel and interfering channels are equal.


Fig. 2. Packet structure of (a) the conventional MMSE receiver for longdata packets, (b) the conventional MMSE receiver for short data packets, and(c) the proposed linear receiver for short data packets.

whereβ0= d−α/20 is the attenuation factor for the target

transmit device (β0>0),αis the path-loss exponent (α>2),h0,i∈C

N×1is the channel vector between the target transmitdevice and AP receiver,s0,i[]is the symbol transmitted bythe target transmit device (E[|s0,i[]|

2]=ρ),Jis the number

of interfering devices from neighboring cells,βj= d−α/2j

is the attenuation factor for thej-th interferer(βj> 0),hj,i∈C

N×1is the channel vector between thej-th interfererand AP receiver,sj,i[]is the symbol transmitted by thej-th interferer(E[|sj,i[]|

2] =ρ),andni[]∈CN×1is

the complex Gaussian noise vector(ni[] ∼CN(0,σ2I)).

Also, without loss of generality, we assume that the distancesd0,d1,...,dJare sorted in ascending order. In this work,we assume that the channel remains unchanged within ablock and changes independentlyfrom block-to-block. In thesequel, we skip the fading block indexifor notationalconvenience.

B. Conventional Receiver Technique

If a unit norm receive filtervis applied to the receivedsignal vectory[], an estimate of the desired symbol iss0[]=vHy[]and the resulting SINR is

SINR(v)=ρvHh0h

H0v

vH(σ2I+ρJ

j=1βjhjh

Hj)v

. (2)

Under the condition that the target rate of the transmit device isR=log2(1+τ), we say a communication is successful if thereceived SINR is larger thanτ. Hence, the outage probabilityat SINR thresholdτis expressed asPout=P[SINR(v)≤τ].Note that the receive filtervcan be designed to removethe interference or to boost the power of the desired signal.In order to minimize the outage probability, a receive filterweight should be designed to maximize the SINR of thereceiver. This receiver is commonly dubbed as anMMSE

receiver[19]–[27].3Denoting the covariance of the interfer-ence plus noise as =σ2I+ρ

jβjhjh

Hj, the receive filter

of the conventional MMSE receiver is [28]

v∗=argmaxv

vHh0hH0v

vH v=

−1h0−1h02

. (3)

Plugging (3) into (2), we obtain the best achievable SINR as

SINR∗=ρ(hH0

−1h0)2

hH0−1(σ2I+ρ

J

j=1βjhjh

Hj)

−1h0

=ρhH0−1h0. (4)

Note that the conventional MMSE receiver usually requiresan interference training period to estimate . Recall that thecovariance matrix is a statistic of the noise and interfer-ence. Since orthogonality among the large number of pilotsequences cannot be guaranteed, it is not easy to estimate theinterfering channelshj(j=1,···,J)individually. To handle

this issue, an approach to estimate the sample covarianceˆ

using a specially designed interference training period wasproposed [15]. In order to observe the covariance associatedwith the interference and noise, the target transmit deviceshould remain silent in this period. The sample covarianceˆobtained in the interference training period is

=1

K

K

i=1

r[i]r[i]H (5)

where K is the duration of the training period andr[i]

is thei-th received sample (r[i] =J

j=1βjhjsj[i]+n[i]).

By replacing withˆin (3), i.e., usingv=−1h0−1h02

instead

ofv∗, we obtain the SINR estimate

SINR=ρ(hH0

−1h0)2

hH0−H −1h0

. (6)

Using a Gaussian approximation for the interference,4theexpected SINR5of (6) becomes [29]

E [SINR]=Eρ(hH0

−1h0)2

hH0−H −1h0

= 1−N−1

K+1SINR∗. (7)

Note that the expected SINR in(7) contains an additionalscaling factor 1−N−1K+1. Since the interference training periodK

3The conventional performance measures such as ergodic capacity may notbe suitable for short-packet communication systems because these metricspertain to the asymptotic regime of long data packets [10], [11]. Nonetheless,this quantity is still simple and useful tool to analyze the behavior of theproposed scheme.4Gaussian approximation of interferences becomes more accurate when thedensity of machine-type devices becomes higher.5Since the average analysis is relevant only if there are sufficiently manypackets, the expected SINR might not be an ideal metric for the shortpacket based communication systems. Nevertheless, unless the packet lengthis extremely short, hundreds of samples might be used in the computation ofthe expected SINR and thus average SINR is still meaningful.


for the short packet framework would be very small,E[SINR]would be much smaller than SINR∗, the best achievable SINRin (4). Further, when the number of antennasNincreases,there would also be a loss in the SINR and achievable rate,which makes this approach unsuitable for the small packettransmission.

III. RECEIVERDESIGN

Recall that two main ingredients of the receive filter in (3)are the channel vectorh0and the covariance matrix of theinterference and noise. In this section, we present a strategy toestimate the covariance matrix using measurements in thedata transmission period and show that the achievable SINRof this strategy equals SINR∗. By estimating the covariancematrix in the normal data transmission period instead of theinterference training period, we can avoid the transmission rateloss caused by the interference training period.Note that the received signal y[] = h0 s0[] +J

j=1βjhjsj[]+n[]contains interference from adjacent

devices and noise as well as the desired signal. Using the

receive filterv=−10 h0−10 h02

, the estimate of the desired symbol

becomes

s0[]=vHy[]

=ρhH0(ρh0h

H0+ρ

Jj=1βjhjh

Hj+σ

2I)−1

ρhH0(ρh0hH0+ρ

Jj=1βjhjh

Hj+σ

2I)−12y[]

=hH0

−10

hH0−10 2

y[] (8)

where 0= +ρh0hH0. In the following theorem, we show

that the best possible SINR in (4) can be achieved even withthe inclusion of the desired signal in the covariance matrix.6

Theorem 1: When the covariance matrix 0is employed

in the receive filterv=−10 h0−10 h02

, the SINR of the proposed

strategy isSINR∗=ρhH0−1h0.

Proof:Let SINRpropbe the SINR of the proposed strategy.Then, using (2), we have

SINRprop=ρ hH0 +ρh0h

H0−1h0

2

hH0 +ρh0hH0−1

+ρh0hH0−1h0.(9)

We first consider the numerator. Using the matrix inversionlemma,7we have

+ρh0hH0

−1= −1−

−1h0hH0

−1

ρ+hH0−1h0

. (10)

6In this section, we focus on the effect of covariance matrix 0and thesample covariance matrix 0on SINR under the assumption thath0isperfectly known at the receiver. We discuss the effect of estimated channelh0in the next section.7Note that (10) can be obtained by letting A= ,B=h0,C=h

H0

andD=ρIin the matrix inversion lemma A−BD−1C−1= A−1+

A−1B D−CA−1B−1CA−1.

From (9) and (10), we have

hH0 +ρh0hH0

−1h0

2

= hH0−1h0−

(hH0−1h0)

2

ρ+hH0−1h0

2

=ρhH0

−1h0

ρ+hH0−1h0

2

=ρSINR∗

ρ2+SINR∗

2

(11)

where SINR∗=ρhH0−1h0(see (4)). Now, by plugging (10)

into the denominator of (9), we have

hH0 +ρh0hH0

−1+ρh0h

H0

−1h0

=hH0−1−

−1h0hH0−1

ρ+hH0−1h0

−1−−1h0h

H0

−1

ρ+hH0−1h0

h0

= hH0−hH0

−1h0hH0

ρ+hH0−1h0

−1h0−−1h0h

H0

−1h0

ρ+hH0−1h0

=ρ2hH0

−1h0

ρ+hH0−1h0

2=

ρ3SINR∗

(ρ2+SINR∗)2. (12)

Plugging (11) and (12) into (9), we have

SINRprop=ρ ρSINR∗

ρ2+SINR∗

2

ρ3SINR∗

(ρ2+SINR∗)2

=SINR∗, (13)

which is the desired result.It is worth noting that the main goal of Theorem 1 isto validate the method of estimating the covariance matrixin using only normal data transmission. By achieving themaximum SINR and avoiding the interference training period,the proposed method canexploit an additionalKchannel usesfor the data transmission period compared to the conventionalMMSE receiver.By slightly modifying this result and using a Gaussian

approximation for the interference, we can obtain the SINRexpression for a realistic scenario where the sample covari-ance matrix is employed. In this scenario, we use 0 =ˆ+ρh0h

H0 instead of 0, and thus the modified receive

filter is8

v=−10 h0−10 h02

. (14)

Theorem 2: When the sample covariance in (14) isemployed, the expected SINR of the proposed linear MMSEreceiver is

E0SINRprop =E

0

ρ(hH0−10 h0)

2

hH0−10

−10 h0

= 1−N−1

Nd+1SINR∗. (15)

8Here we useh0instead ofh0in 0in order to observe the effect of 0on SINR.


Proof: By the direct substitution of 0= ˆ+ρh0hH0

into (6), we have

SINR=hH0

−10 h0

2

hH0−10

−10 h0

. (16)

Let = +ρ(h0hH0−h0h

H0),then 0= +ρh0h

H0 and

−10 = −1−

−1h0hH0

−1

ρ+hH0−1h0

by the matrix inversion lemma.

Therefore,

SINR=

ρ hH0−1−

−1h0hH0−1

ρ+hH0−1h0

h0

2

hH0−1−

−1h0hH0−1

ρ+hH0−1h0

−1−−1h0h

H0−1

ρ+hH0−1h0

h0

=

ρρhH0

−1h0

ρ+hH0−1h0

2

ρ2hH0−1 −1h0

(ρ+hH0−1h0)2

=ρhH0

−1h02

hH0−1 −1h0

. (17)

Further, by denotingκ= SINRSINR∗, =(SINR

∗

ρ )−12 −12h0,

and 1=−12 −12,wehave

κ=1

SINR∗

ρ hH0−1h0

2

hH0−1 −1h0

=

H −11

2

H −21

. (18)

Note that the joint distribution of the elements ofˆfollowsthe central complex Wishart distributionCW(M,N; )[30].

Hence,E[1] =−12E[]−

12 = −12 −12 = I,and

1is a complex Wishart distributionCW(Nd,N;I).Theprobability density function ofκis given by [29]

P(κ)=(Nd+1)

(N−1)(Nd+2−N)κ(Nd+2−N)−1

(1−κ)(N−1)−1 (19)

whereκfollows the regularized incomplete beta distribution.Since (i)= (i−1)!for an integeri, the expectationofκis

E[κ]=1

0κP(κ)dκ

=Nd!

(Nd−2)!(Nd+1−N)!

1

0κNd+2−N(1−κ)N−2dκ

=1−N−1

Nd+1. (20)

Recalling thatκ= 1SINR∗

ρhH0−10 h0

2

hH0−10

−10 h0, we further have

E0SINRprop =E

0

ρ(hH0−10 h0)

2

hH0−10

−10 h0

= 1−N−1

Nd+1SINR∗.

Fig. 3. The received SINR of the proposed method and conventional MMSEreceiver forNb=100 and 1000. We setJ=30, SNR=0dB,Np=0.1Nb,K=0.1Nb,Nd=0.8Nb,Nd=0.9Nb.

Since the interference training period is unnecessary,the data transmission period is improved fromNd toNd=Nd+K and at the same time the covariance matrixis estimated using samples in the data transmission period(see Fig. 2). Therefore, we obtain a more accurate estimationof the interference covariance in the short packet framework.The effect of the sample covariance matrix on the receivedSINR shows the efficacy of the proposed receiver by obtaining

a larger scaling factor 1− N−1Nd+1

.InFig.3,weplotthe

received SINR as a function of the number of receive antennasN. When the packet sizeNbis large (e.g.,Nb=1000),whichcorresponds to the packet length of current wireless systems,K = 0.1Nbis also sufficiently larger than the number ofantennasNso that scaling factor of the proposed scheme

1− N−1Nd+1

and the conventional MMSE receiver1−N−1K+1

are not much different. This behavior, however, does nothold true for short-sized packet regime. In fact, as shownin Fig. 3(a), we see that the performance of the proposed


scheme improves linearly withN. Since the interference train-ing is needed for the conventional MMSE receiver, we observethat whenNbis small (e.g.,Nb=100) the performance of theconventional MMSE SINR receiver with sample covariancematrix does not scale withN.

IV. JOINTPILOT ANDDATASYMBOLBASEDCHANNELESTIMATION

In the previous sections, we assumed that the desired chan-nelh0is perfectly known. As mentioned, when we considerthe short packet transmission, the training period should alsobe reduced to avoid an excessive amount of training overhead.In this section, we propose a channel estimation techniquethat jointly uses the pilot signals and data symbols to improvechannel estimation quality. In a nutshell, the proposed channelestimation technique picks a small number of reliable datasymbols among all available data symbols.Using the chosen data symbols (which we callvirtual pilots)together with the pilot signals in the re-estimation of thechannel vector, we achieve great improvement of the channelestimation performance in the short packet regime.

A. The Joint Pilot and Data Symbol BasedChannel Estimation

Before we proceed, we briefly review conventional MMSE-based channel estimation. The received pilot signals in thetraining period are expressed as

y(1)=h0p(1)0 +

J

j=1

βjhjs(1)j +n

(1)

...

y(Np)=h0p(Np)0 +

J

j=1

βjhjs(Np)j +n(Np) (21)

wherey(i)is thei-th observation,n(i)is thei-th noise,p(i)0 isthei-th pilot signal in the target transmit device, andNpis thetotal number of pilot observations. TheNpN×1 vectorizedreceived pilot signals are

yp=P0h0+zp (22)

whereP0 = p0⊗IN isNpN×N-dimensional training

matrix with p0 = [p(1)0,...,p(Np)0 ]T, andzp =

( Jj=1βjhjs

(1)j +n

(1))T···( Jj=1βjhjs

(Np)j +n(Np))T

T

is the interference plus noise vector over the trainingperiod. We assume thath0 follows a circular symmetriccomplex normal distribution, i.e.,h0∼ CN(0,Chh)whereChh=Cov(h0,h0). The MMSE weight matrix minimizingthe mean square error between the original channel vectorh0and the estimateh0=Wypis [31]

W =Covh0,ypCovyp,yp−1

=E[h0yHp]E[ypy

Hp] (23)

=E[h0hH0PH0+h0z

Hp]

×E[P0h0hH0PH0+P0h0z

Hp+zph

H0PH0+zpz

Hp]

=ChhPH0 P0ChhP

H0+ηpIN

−1(24)

where (23) is due to Cov(a,b)= E[abH]−E[a]E[bH]andηpis the variance of the interference plus noise.

9The

corresponding MMSE-based channel estimateh0is

h0=ChhPH0 P0ChhP

H0+ηpIN

−1P0h0+zp

=(NpChh+ηpIN)−1ChhP

H0(P0h0+zp)

=ηp

NpIN+Chh

−1

Chh h0+1

NpPH0zp . (25)

We observe from (25) that the estimated channel vector h0converges to the original channel vectorh0as the trainingperiodNp increases. This clearly demonstrates that therewould be a degradation in the channel estimation quality forthe short packet regime. To enhance the channel estimationquality without increasing the pilot overhead, we exploit thevirtual pilots in the re-estimation of channels. Using the delib-erately chosen virtual pilots together with the conventionalpilots, the channel is re-estimated, and the newly generatedchannel estimate will be used for the symbol detection. WhenNvdata symbols are selected for the virtual pilot purpose,the received signals are

y(1)=h0s(1)0 +

J

j=1

βjhjs(1)j +n

(1)

...

y(Nv)=h0s(Nv)0 +

J

j=1

βjhjs(Nv)j +n(Nv) (26)

wherey(i)is thei-th observation,n(i)is thei-th noise,s(i)0 is

the data symbol of the target transmit device, ands(i)j is thedata symbol of thej-th interferer. TheNvN×1 vectorizedvirtual pilot observations can be expressed as

yv=S0h0+zv (27)

where S0 = s0⊗IN (of sizeNvN× N) is the vir-tual pilot matrix wheres0=[s

(1)0 ,...,s

(Nv)0 ]T is the data

symbol sequence andzv = ( Jj=1βjhjs

(1)j +n

(1))T···

( Jj=1βjhjs

(Nv)j +n(Nv))T

Tis the interference plus noise

signal vector in the virtual pilot transmission period. Bystacking the pilot observation vectorypand virtual pilotobservation vectoryv, we obtain the composite observationvectorycfor the channel re-estimation as

yc=ypyv=P0S0h0+

zpzv. (28)

The MMSE estimate of the proposed scheme is expressed as

h0=Cov(h0,yc)Cov(yc,yc)−1yc

= −1yc (29)

9Since it is hard to obtain exact variance Jj=1β

2jNρ+σ

2, we instead

useηp= Jβ2Nρ+σ2where β= dα/2is obtained by using the cell-

radiusdunder the assumption that the interferers are closer to the receiver(i.e.,β >βj). Thus, the channel estimation might be slightly pessimistic.Also, the reason to treat interference as noise in (24) is because it is difficultto acquire the covariance of the interference. Note that the MSE formulain (37) is obtained under the assumption thath0as well as the interferingchannels are spatially uncorrelated.


Fig. 4. Block diagram of the receiver using virtual pilot and pilot signal in the re-estimation of the channel. Among all the data symbols, symbols withsmall MSE are chosen as virtual pilots. Note that symbols with small MSE are green colored.

where

=Cov(h0,yc)

= E[h0yHp] E[h0y

Hv]= ChhP

H0 ChhS

H0 (30)

and

=Cov(yc,yc)

=E[ypy

Hp] E[ypy

Hv]

E[yvyHp] E[yvy

Hv]

=P0ChhP

H0+ηpI P0ChhS

H0

S0ChhPH0 0⊗diag(Chh)+ηvI

.(31)

Note thatS0=E[S0]=s0⊗INwheres0=[s(1)0 ,...,s

(Nv)0 ]T

is obtained from the first order moment ofs(i)0 [32]. That is,

s(i)0 =E[s(i)0]=

θ∈

θ

Q

k=1

1

21+c(i)0,ktanh

1

2L(c(i)0,k)

(32)

where is a constellation set,c(i)0,kis the k-th coded bit,

Q is the number of (coded) bits mapped to a data symbol

s(i)0 in 2Q-ary quadrature amplitude modulation (QAM) con-

stellations, andL(c(i)0,k)is the log-likelihood ratio (LLR) of

thek-th coded bit mapped from a data symbols(i)0. 0=

[λ(1)0,...,λ

(Nv)0 ]Tis the vector of the second order moments

ofs(i)0 given by

λ(i)0 =E[|s(i)0|2]

=θ∈

|θ|2Q

k=1

1

21+c(i)0,ktanh

1

2L(c(i)0,k) .(33)

Plugging (29) and (30) into (28), we obtain the channelestimateh0as

h0= ChhPH0 ChhS

H0

×P0ChhP

H0+ηpI P0ChhS

H0

S0ChhPH0 0⊗diag(Chh)+ηvI

−1ypyv.

While the conventional MMSE estimate in (25) uses only thereceived pilot sequence for the channel estimation, the pro-posed channel estimator in (29) utilizes the most reliabledata symbols, i.e., the soft symbol estimateS0and secondorder moments 0, as virtual pilots. Clearly, reliability ofthe soft symbols directly affects the quality of the proposedchannel estimation so that we need to choose virtual pilotswith caution.

B. Virtual Pilot Selection

Since the virtual pilots can improve the channel estimationquality of the proposed method, the best way to select virtualpilots would be to compare the performance metric (e.g., MSEof the estimated channel) of all possible Nd

Nvdata symbol

combinations and then choose the combination achievingthe minimum MSE. Since this procedure is computationallydemanding and hence not pragmatic, we use a simple subopti-mal approach to compute the MSE when single data symbol isused for the virtual pilot. Among all data symbols, we choosetheNv-best data symbols generating the smallest MSE asvirtual pilots (see Fig. 4). Although this approach does notconsider the correlation among virtual pilot symbols and henceis not optimal, computational complexity is much smaller thanthe approach using all possible symbol combinations. Also,this approach is effective in improving the quality of channelre-estimation.

Leth(n)0 be the estimated channel vector when then-th data

symbol is used as a virtual pilot, then the MSE metricεnfor the hypothetical selection of then-th data symbol isexpressed as

εn=E h0−h(n)0

22 =trCov h0− ˜

−1 zpy(n)v

=trCov(h0)−Cov ˜ −1 ypy(n)v

=trCov(h0)−˜−1˜H (34)


where

˜=Cov h0,ypy(n)v

= E[h0yHp]E[h0y

(n)Hv ]

= ChhPH0 (s

(n)0 )∗Chh (35)

and

˜=Covypy(n)v

=E[ypy

Hp]E[ypy

(n)Hv ]

E[y(n)v y

Hp]E[y

(n)vy

(n)Hv ]

=P0ChhP

H0+ηpI(s

(n)0 )∗P0Chh

(s(n)0 )∗ChhP

H0 λ

(n)0 Chh+ηvI

(36)

usingy(n)v =s(n)0 h0+z

(n)v is the virtual pilot observation vector

for then-th data symbol. From (34), (35), and (36),εnisexpressed as (see Appendix)

εn=N(1−γ2p(1+γp)

λ(n)0

λ(n)0 +ηv(λ(n)0 )2

−γ2p2ηvλ

(n)0 +η

2v

λ(n)0 +ηvλ(n)0 +γp

(λ(n)0 )3

(λ(n)0 +ηv)3

+(λ(n)0 )2

(λ(n)0 +ηv)

2

N2p

γp+

λ(n)0

λ(n)0 +ηv

(2γp+N2p−1)−γp)

(37)

whereγp=NpNp+ηp

. Note thatεndepends on the reliability of

soft decisions (i.e., the second order statistic of data symbolλ(n)0 in (33)). Hence, in order to achieve the minimum MSE,

the desired data symbol maximizingλ(n)0 should be chosen as

the virtual pilot. Onceεnfor allnare computed, we chooseNvdata symbols minimizingεn(see Fig. 7). Observations ofvirtual pilots and normal pilots are used for the re-estimationof the channel vector.

V. SIMULATIONRESULTS ANDDISCUSSIONS

In this section, we evaluate the performance of the proposedalgorithm. In our setup, we assume that adjacent interferingdevices are randomly located on a square (of area 100m2).The target receiver is located at center and the target transmitdevice is located 1 meter away from the receiver. The packetsize is set to 100 bits.10As a performance measure, we con-sider a packet error rate (PER). We assume that elements ofchannel vector for each device are i.i.d. zero mean complexGaussian random variables with unit variance.In our simulations, we study the performance of the follow-

ing receiver techniques:

1) MMSE receiver with estimated CSI (conventionalMMSE receiver) [15]: we set the interference trainingperiod asK.

10In order to meet the stringent delay requirements, packet size of theuRLLC use case is set to 100∼200 bits [35], [36].

Fig. 5. PER performance of receiver techniques as a function of SNR. We setr=1/2,N=6,J=6,Np=10,K=10,Nd=40,Nd=50,Nb=60,Nv=20.

2) Proposed method with estimated CSI: we set the inter-ference training period asNd=Nb−Np.

3) Proposed method with virtual pilot signals (VPS): wechooseNv-best virtual pilots with the smallest MSE forthe channel re-estimation.

4) Proposed method with accurate VPS: we useNv-accurate data symbols as virtual pilots in there-estimation of the channel vector.

In Fig. 5, we plot the PER performance of all techniquesunder consideration. In this simulations, we use the halfrate (r= 1

2) convolutional code with feedback polynomial

1+D+D2and feedforward polynomial 1+D2.11In theproposed method, 20 data symbols are used as VPS (Nv=20).We set J=6 as dominant neighboring interfering devices.We observe that the proposed method with VPS achieves morethan 2 dB gain over the conventional MMSE receiver at 10−3

PER point. We also observe that the addition of VPS achievesmore than 1 dB gain over the proposed method without VPS.In Fig. 6, we plot the PER performance with code rater=34convolutional code with feedback polynomial 1+D2+D3andfeedforward polynomial 1+D+D3. We observe from thefigure that the performance gain of the proposed method withVPS is 2 dB over the conventional MMSE receiver and morethan 0.8 dB over the proposed method without VPS at 10−3

PER point.In Fig. 8, we plot the PER performance result of theschemes we considered with polar code and convolutionalcodes. We set the block lengthNbas 64 since the block lengthof the polar code should be always a power of 2. We observefrom the figure that the proposed method with polar code issuperior to the convolutional code based schemes. Specifically,we observe that use of polar code will bring one dB over theconvolutional code at 10−3PER point.

11In IoT systems, convolutional codes are preferred over turbo or LDPCcodes [5].


Fig. 6. PER performance of receiver techniques as a function of SNR. We setr=3/4,N=6,J=6,Np=10,K=10,Nd=40,Nd=50,Nb=60,Nv=20.

Fig. 7. PER performance of receiver techniques as a function of SNR overthe Rician fading channel. We setr=1/2,N=6,J=6,Np=10,K=10,Nd=40,Nd=50,Nb=60,Nv=20.

We next consider the performance of the proposed methodover the Rician fading channel. Note that Rician fadingincludes the line-of-sight (LOS) signal propagation, whichcan be more general and realistic than Rayleigh fading [33].In this simulations, we use the Rician K-factorK=6dB.Due to the LOS components of the interference channels,we observe from Fig. 7 that the performance of all receiversunder consideration is worse than the case using the Rayleighfading channel. From numerical results, the proposed methodwith VPS is still effective and achieving more than 1.5 dBgain over the conventional MMSE receiver at 10−3PER point.We also observe that the addition of VPS achieves around0.8 dB gain over the proposed method without VPS.In Fig. 9, we plot the throughput as a function of the number

of receive antennasN for temporally correlated channels.

Fig. 8. PER performance of receiver techniques as a function of SNR withpolar code and convolutional codes. We setr=1/2,N=6,J=6,Np=10,Nd=54,Nb=64,Nv=20.

Fig. 9. Throughput of receiver techniques as a function of number ofreceive antennas N for temporally-correlated block fading channel. We setSNR=0dB,r= 1

2,J=6,Np=10,K=10,Nd=40,Nd=50,Nb=60,Nv=20.

We consider temporally correlated channels that are modeledby a first order Gauss-Markov process [34] ash[k] =ξh[k−1]+ 1−ξ2g[k]whereg[k]is the innovation process,which is modeled as having i.i.d entries distributed withCN(0,1)and 0≤ ξ ≤ 1 is the temporal correlationcoefficient. In this simulations, we useξ=0.9881 for themoderate mobile speed. To evaluate the throughput, we presentMonte-Carlo simulation results with 10000 iterations. Sinceeach iteration consists of 10 fading blocks, the maximumthroughput is about 5 Mbps. As observed in (7) and (15),when the number of receive antennasNincreases, the trainingperiod used for the sample covariance matrix computation


Fig. 10. Throughput of receiver techniques as a function of interfering devicesfor temporally-correlated block fading channel. We setSNR=10 dB,r=12,N=6,Np=10,K=10,Nd=40,Nd=50,Nb=60,Nv=20.

Fig. 11. Throughput of receiver techniques as a function ofNbfortemporally-correlated block fading channel. We setJ=6, SNR=0dB,N=8,Np=0.1Nb,K=0.1Nb,Nd=0.8Nb,Nd=0.9Nb,Nv=0.2Nd.

should also be increased to attain the target SINR. Thus, whenthe interfering training periodKis fixed, the scaling factor

1−N−1K+1 decreases with the number of receiver antennasN.

As a result, we observe the throughput degradation on the con-ventional MMSE receiver when number of receive antennas islarge (N≥7). Whereas, the throughput of the proposed VPSscheme increases with the number of receive antennasN.In Fig. 10, we plot the throughput as a function of the

number of adjacent interfering devicesJ. Since the accuracyof the covariance matrix estimation deteriorates as the numberof interfering devicesJgrows large, we see that the throughputdecreases withJfor all methods simulated. We observe that

the proposed method using VPS performs close to the MMSEreceiver using the perfect CSI (5∼7% throughput loss) andalso provides 21% gain over the conventional MMSE receiverwhenJ≤30.Finally, in Fig. 11, we show the throughput as a functionof packet sizeNb. We observe that the rate loss of theproposed method over the MMSE receiver with perfect CSIis around 6%∼13%, which is far better than the rate lossof the conventional MMSE receiver (12%∼ 32%). Theseresults demonstrate that the proposed method has clear benefitover the conventional MMSE receiver in the short packettransmission.

VI. CONCLUSION

Short packet transmission systems are critical to fulfillingthe stringent low latency requirements of the fifth genera-tion (5G) wireless standards. We proposed a receiver techniquesuited to short packet transmission. Our work was motivatedby the observation that the insufficient training period resultingfrom a small packet structure causes severe degradation in thedesired channel and interference covariance matrix estimation.By exploiting reliable symbols in the data transmission period,the proposed receiver algorithmachieves improved estimationand eventual throughput gain. Although our study in thiswork focused on the low latency communication, the mainconcept can be readily extended to massive machine-type com-munications scenario (mMTC use case) and high throughputmassive MIMO scenario (eMBB use case) of 5G wirelesscommunications. In both scenarios, the channel estimationquality would be crucial to achieve the desired goal. Also anoncoherent approach that does not rely on the pilot signalmight be alternative option for uRLLC communication.

APPENDIXDERIVATION OF(37)

Recall from (34) thatεnis given by

εn=trCov(h0)− ˜−1˜H (38)

where

=Cov h0,ypy(n)v

= ChhPH0 (s(n)0 )

∗Chh (39)

and

˜=Covypy(n)v,ypy(n)v

=P0ChhP

H0+ηpI P0Chh(s

(n)0 )∗

s(n)0 ChhPH0 λ(n)0 Chh+ηvI

. (40)

For convenience, we let

1 2 = ChhPH0 (s

(n)0 )∗Chh , (41)

11 12

21 22=P0ChhP

H0+ηpI P0Chh(s

(n)0 )∗

s(n)0 ChhP

H0 λ

(n)0 Chh+ηvI

, (42)

and

11 12

21 22= 11 12

21 22

−1

, (43)


then

εn=trChh− 1 211 12

21 221 2

H

=tr(Chh− 1 11H1− 2 21

H1

− 1 12H2− 2 22

H2). (44)

Using the inversion formula of partitioned matrices [20],we have

11=(11− 12−122 21)

−1

12=−−111 12(22− 21

−111 21)

−1

21=−−122 21(11− 12

−122 21)

−1

22=(22− 21−111 12)

−1. (45)

Using (45), we further have

1 11H1 =ChhP

H0 11P0Chh

2 21H1 =(s

(n)0 )∗Chh 21P0Chh

1 12H2 =s

(n)0 ChhP

H0 12Chh

2 22H2 =λ

(n)0 Chh 22Chh. (46)

Using the matrix inversion lemma ((A−BD−1C)−1=A−1+A−1B(D−CA−1B)CA−1) and noting that

=PH0 11P0

=PH0−111P0

=λ(n)0 22

=λ(n)0

−122, (47)

we further have

1 11H1 =Chh (I+Chh Chh −(λ(n)0 )

2Chh

× ChhChh )Chh

2 21H1 =−Chh Chh(I+ Chh Chh−(λ

(n)0 )2 Chh

×Chh ChhChh) Chh

1 12H2 =−Chh Chh(I+ Chh Chh−

×C2hh C2hh) Chh

2 22H2 =Chh (I+Chh Chh −C2hh C2hh )Chh.

(48)

Under the assumption that there is no correlation amongreceive antennas,Chh=I, and hence (47) becomes

=PH0(P0PH0+ηpI)P0=Np(Np+ηp)I

=PH0(P0PH0+ηpI)

−1P0=Np

Np+ηpI

=(s(n)0 )∗I(λ

(n)0 I+ηvI)s

(n)0 I=λ

(n)0 (λ

(n)0 +ηv)I

=(s(n)0 )∗I(λ

(n)0 I+ηvI)

−1s(n)0 I=

λ(n)0

λ(n)0 +ηvI. (49)

Plugging (48) and (49) into (44) and after some manipulations,we have

εn=tr(I− ( )2 +( )2 −(λ(n)0 )

2(( )3 +( )2)

+ I− ( )3+ ( )2−I− −2 − )

=N(1−γ2p(1+γp)λ(n)0

λ(n)0 +ηv

(λ(n)0 )2−γ2p(

2ηvλ(n)0 +η

2v

λ(n)0 +ηv

)

×λ(n)0 +γp(λ(n)0 )3

(λ(n)0 +ηv)

3+(λ(n)0 )2

(λ(n)0 +ηv)

2

N2p

γp

+λ(n)0

λ(n)0 +ηv(2γp+N

2p−1)−γp) (50)

whereγp=NpNp+ηp

.

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Byungju Lee(M’15) received the B.S. and Ph.D.degrees from the School of Information and Com-munication, Korea University, Seoul, South Korea,in 2008 and 2014, respectively. From 2014 to2015, he was a Post-Doctoral Fellow with theDepartment of Electrical and Computer Engineering,Seoul National University. He was a Post-DoctoralScholar with the School of Electrical and ComputerEngineering, Purdue University, West Lafayette, IN,USA, from 2015 to 2017. He joined Samsung Elec-tronics in 2017, has been involved in research and

standardization for 3GPP 5G NR. His research interests include physical layersystem design for 5G wireless communications.

Sunho Park (M’16) received the B.S., M.S.,and Ph.D. degrees from the School of Informa-tion and Communication, Korea University, Seoul,in 2008, 2010, and 2015, respectively. Since 2015,he has been with the Institute of New Media andCommunications, Seoul National University, Seoul,South Korea, as a Research Assistant Professor. Hisresearch interests include wireless communicationsand signal processing.

David J. Love(S’98–M’05–SM’09–F’15) receivedthe B.S. (Hons.), M.S.E., and Ph.D. degrees inelectrical engineering from The University of Texasat Austin in 2000, 2002, and 2004, respectively.From 2000 to 2002, he was with Texas Instruments,Dallas, TX, USA. Since 2004, he has been withthe School of Electrical and Computer Engineering,Purdue University, West Lafayette, IN, USA, wherehe is currently a Professor and recognized as aUniversity Faculty Scholar. He leads the College ofEngineering Preeminent Team on Efficient Spectrum

Usage. He has been very involved in commercialization of his research witharound 30 U.S. patent filings, 27 of which have issued. He is a frequentconsultant on cellular and WiFi systems, including patent licensing and liti-gation. His research interests are in the design and analysis of communicationsystems and MIMO array processing. He has served as an Editor of the IEEETRANSACTIONS ONCOMMUNICATIONS, an Associate Editor of the IEEETRANSACTIONS ONSIGNALPROCESSING, and a Guest Editor for specialissues of the IEEE JOURNAL ONSELECTEDAREAS INCOMMUNICATIONSand theEURASIP Journal on Wireless Communications and Networking.Dr. Love has been recognized as the Thomson Reuters Highly CitedResearcher. He is a fellow of the Royal Statistical Society, and he has beeninducted into Tau Beta Pi and Eta Kappa Nu. Along with his co-authors,he received best paper awards from the IEEE Communications Soci-ety (2016 IEEE Communications Society Stephen O. Rice Prize), the IEEESignal Processing Society (2015 IEEE Signal Processing Society Best PaperAward), and the IEEE Vehicular Technology Society (2009 IEEE Transactionson Vehicular Technology Jack Neubauer Memorial Award). He has receivedmultiple IEEE Global Communications Conference (Globecom) best paperawards. He was a recipient of the Fall 2010 Purdue HKN OutstandingTeacher Award, the Fall 2013 Purdue ECE Graduate Student AssociationOutstanding Faculty Award, and the Spring 2015 Purdue HKN OutstandingProfessor Award. He was an invited participant to the 2011 NAE Frontiers ofEngineering Education Symposium and the 2016 EU-US NAE Frontiers ofEngineering Symposium. In 2003, he received the IEEE Vehicular TechnologySociety Daniel Noble Fellowship.

Hyoungju Ji (M’17) is currently pursuing thePh.D. degree with the School of Electrical andComputer Engineering, Seoul National University,Seoul, South Korea. He joined Samsung Elec-tronics in 2007, and has been involved in 3GPPRAN1 LTE, LTE-Adv, and LTE-A Pro technol-ogy developments and standardization. His cur-rent interests include ultra-reliable low-latencytransmission, multi-antenna techniques (FD-MIMO),massive machine type communications, and IoTcommunications.

Byonghyo Shim(S’95–M’97–SM’09) received theB.S. and M.S. degrees in control and instrumentationengineering from Seoul National University, SouthKorea, in 1995 and 1997, respectively, and the M.S.degree in mathematics and the Ph.D. degree in elec-trical and computer engineering from the Universityof Illinois at Urbana–Champaign, USA, in 2004 and2005, respectively. From 1997 and 2000, he was withthe Department of Electronics Engineering, KoreanAir Force Academy, as an Officer (First Lieutenant)and an Academic Full-time Instructor. From 2005 to

2007, he was with Qualcomm Inc., San Diego, CA, USA, as a Staff Engineer.From 2007 to 2014, he was with the School of Information and Communica-tion, Korea University, Seoul, as an Associate Professor. Since 2014, he hasbeen with the Seoul National University, where he is currently a Professor withthe Department of Electrical and Computer Engineering. His research interestsinclude wireless communications, statistical signal processing, estimation anddetection, compressed sensing, and information theory.Dr. Shim is an elected member of the Signal Processing for Communicationsand Networking Technical Committee of the IEEE Signal Processing Society.He was a recipient of the M. E. Van Valkenburg Research Award from the ECEDepartment of the University of Illinois in 2005, the Hadong Young EngineerAward from IEIE in 2010, and the Irwin Jacobs Award from Qualcomm andKICS in 2016. He has been an Associate Editor of the IEEE TRANSAC-TIONS ONSIGNALPROCESSING, the IEEE WIRELESSCOMMUNICATIONSLETTERS,andJournal of Communications and Networks, and a Guest Editorof the IEEE JOURNAL ONSELECTEDAREAS INCOMMUNICATIONS.

packet structure and receiver design for low latency

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