Packet Structure and Receiver Design for Low Latency Wireless Communications with Ultra-Short Packets Byungju Lee ,Member, IEEE , Sunho Park ,Member, IEEE , David J

796 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 66, NO. 2, FEBRUARY 2018 Packet Structure and Receiver Design for Low Latency Wireless Communications With 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 much and low latency communication (uRLLC) as one of key use lower latency than what current wireless systems can guaran- cases for 5G wireless communications. 1 One direct way to tee. The main challenge in fulfilling these requirements is the meet the stringent low latency requirements is to use a short- development of short packet transmission, in contrast to most of the current standards, which use a long data packet structure. sized packet. This is in contrast to most current wireless Since the available training resources are limited by the packet systems whose sole purpose is to transmit long data packets size, reliable channel and interference covariance estimation with efficiently. Indeed, most current physical layer design relies reduced training overhead are crucial to any system using short heavily on long codes to approach Shannon capacity. Sensors data packets. In this paper, we propose an efficient receiver that and devices in an IoT networks transmit a very small amount exploits useful information available in the data transmission period to enhance the reliability of the short packet transmission. of information such as environmental data (e.g., temperature, In the proposed method, the receive filter (i.e., the sample humidity, and pollution density), locations, and emergency covariance matrix) is estimated using the received samples from alarm, and thus asymptotic capac ity-achieving principles are the data transmission without using an interference training not relevant to the transmission of short packets. In view period. A channel estimation algorithm to use the most reliable of this, 5G physical layer design (e.g., pilot transmission data symbols as virtual pilots is employed to improve quality of the channel estimate. Simulation results verify that the proposed strategy, coding scheme, hybrid automatic repeat request) receiver algorithms enhance the reception quality of the short needs to be reevaluated and potentially redesigned as a whole. packet transmission. Many papers have been dedicated to analyze performance Index Terms — 5G wireless communications, short data metrics that are relevant to short packet communication, packets, low latency, Internet of Things, energy harvesting, including the maximal achievabl e rate at finite packet length virtual pilots. and finite packet error probability instead of using two classic I. I NTRODUCTION information-theoretic metrics, the ergodic capacity and the IFTH generation (5G) communication networks will be outage capacity [8]–[11]. Finite block-length analysis has been Fa key enabler in realizing the Internet of Things (IoT) extended to spectrum sharing networks using rate adapta- era and hyper-connected society [2]–[4]. To support real- tion [12] and wireless energy and information transmission time applications with stringent delay requirements and mas- using feedback [13]. sive machine-type devices, communication systems supporting In this paper, we consider practical constraints that are ultra low latency are needed [5]–[7]. For this reason, Interna- encountered when implementing a short packet transmission tional telecommunication union (ITU) defined ultra reliable framework. First, massive and simultaneous communications among autonomous devices will induce inter-device interfer- Manuscript received December 3, 2016; revised May 5, 2017 and ence at the receiver in an IoT network. In order to control the August 4, 2017; accepted September 11, 2017. Date of publication September 21, 2017; date of current version February 14, 2018. This inter-device interference, a technique to use multiple receive work was supported in part by the National Science Foundation (NSF) antennas has been proposed by utilizing the spatial degrees grant CNS1642982 and the National Res earch Foundation of Korea (NRF) of freedom (DoF) provided by multiple receive antennas to grant funded by the Korean government (MSIP) (2014R1A5A1011478 and 2016K1A3A1A20006019). This paper was p resented at the GLOBECOM, balance interference suppression and desired signal power Washington, USA, December 4–8, 2016 [1]. The associate editor coordinating improvement [14]. To implement this approach, the receiver the review of this paper and approving it for publication was A. Tajer. needs to acquire the desired CSI and the interference plus (Corresponding author: Byonghyo Shim.) B. Lee and D. J. Love are with the School of Electrical and noise covariance. While the desired CSI can be estimated Computer Engineering, Purdue Univ ersity, West Lafayette, IN 47907 USA using pilot signals, direct estimation of the interfering CSI (e-mail: [email protected] du; [email protected]). is difficult due to the large number of interfering devices in S. Park, H. Ji, and B. Shim are with the Institute of New Media and Communications and the School of Electrical and Computer Engi- the IoT network. One way to tackle this problem is to use an 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 available 1Three key use cases include enhanc e mobile broadband (eMBB), massive online at http://ieeexplore.ieee.org. machine-type communications (mMTC), and ultra reliable and low latency Digital Object Identifier 10.1109/TCOMM.2017.2755012 communication (uRLLC) [6]. 0090-6778 © 2017 I EEE. Personal u se is perm itted, but republication/redistri bution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. LEE et al. : PACKET STRUCTURE AND RECEIVER DESIGN FOR LOW LATENCY WIRELESS COMMUNICATIONS 797 interference training period in which the interference (plus noise) covariance matrix can be estimated by listening to interference-only transmissions [15]. The main drawback of this approach is that it incurs a severe transmission rate loss since the target transmit device should remain silent during the interference training period. Also, the interference training period would not be large enough in obtaining the reliable estimate of the interference covariance for this short-sized packets, resulting in severe degradation in performance. Moreover, since current systems are designed to carry long data packets, the pilot transmission period can be made relatively small even though the actual period of pilot signals is large. However, the portion of time used for pilot signals is unduly large in a short-sized packet framework if the Fig. 1. A paired AP receives the desired signal from a target device and is training period is not reduced. On the other hand, if the pilot subject to interference (dashed lines) from neighboring devices. length is shortened, there would be a significant degradation in performance. Since there is a trade-off between the duration of the pilot training period and the data transmission period, technique suited to the short packet transmission. the main challenge is to perform a reliable channel estimation In Section IV, we describe the proposed virtual pilot while affecting the minimal impact on the duration of data based channel estimation technique. In Section V, we present transmission period. simulation results to verify the performance of the proposed An aim of this paper is to propose an efficient receiver scheme. We conclude the paper in Section VI. technique that exploits information obtained during the data We briefly summarize notation used in this paper. We employ uppercase boldface letters for matrices and lower- transmission period to improve the reception quality of the H T system in the short packet transmission. Intuitively, when time case boldface letters for vectors. The superscripts (·) and (·) resources are limited, we need to use all received data to denote the conjugate transpose and transpose, respectively. optimize the receiver performance. With this goal in mind, C denotes the field of complex numbers. · p indicates we propose a receive filtering algorithm that estimates the the p-norm. IN is the N× N identity matrix. E[·] is the interference covariance matrix using the received signal from expectation operator. ⊗ is the Kronecker product operator. CN (m,σ 2)denotes a complex Gaussian random variable with the normal data transmission period in the IoT network. In 2 doing so, the interference training period becomes unnecessary mean m and variance σ. and the transmission rate loss caused by the interference II. S YSTEM DESCRIPTION training period can be avoided. We show from analysis and numerical experiments that the proposed method achieves a A. System Model and Packet Structure linear scaling of SINR in the number of receive antennas. We consider uplink communication in an IoT networks Next, we propose a low latency frame structure adequate such as wireless sensor networks, ad hoc network, and energy for the one-shot random access where pilot and data are harvesting network, with an example setup shown in Fig. 1. transmitted simultaneously. We propose a strategy to exploit We assume that the target transmit device has a single antenna the data symbols received from the target transmit device to and the paired access point (AP) receiver has N antennas. improve the channel estimation quality at the receiver. There Since there are a large number of devices in the radio have been previous studies exploiting data signals for channel transmission range, the receive d signal contains interference estimation including the non-OFDM system with frequency- from adjacent devices as well as the desired information. 2 selective channel [16], wireless LAN (IEEE 802.11n) [17], and We assume a block-fading channel model, and each block LTE systems with long packet [18] In this paper, we choose consists of Nb channel uses, among which Np uses are for the most reliable received data symbols, referred to as virtual the pilot training and Nd uses are for the data transmission pilots , among all possible soft decision data symbols and then (see Fig. 2(a)). use them to re-estimate the channel. Our proposed method In this setup, the received signal for the -th channel use in is distinct from previous efforts in the sense that select a the i-th fading block is given by virtual pilot group making a dominant contribution to the J channel estimation quality. Towards this end, we design a yi[]= β0h0,is0,i[]+ βjhj,isj,i[]+ ni[] (1) mean square error (MSE) based virtual pilot selection strategy. j=1 We show from numerical simulations that the proposed method outperforms the conventional receiver technique in the short 2In this work, we assume that the AP receiver experiences interference from devices in neighboring cells for both channel estimation phase and data packet transmission (e.g., packet size is set to tens of bytes). transmission phase. In short packet transmission, the packet length would be The remainder of the paper is organized as follows. far shorter than the channel coherent time and thus the channel can be fairly In Section II, we describe the structure of a packet and review static and at least slowly varying within a packet. Therefore, in the short packet regime, impact of mis-aligned coherenc e block would not be significant. For conventional receiver techniques. In Section III, we present the sake of simplicity, we assume that the coherence times of the desired the proposed interference covariance matrix estimation channel and interfering channels are equal. 798 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 66, NO. 2, FEBRUARY 2018

receiver [19]–[27]. 3Denoting the covariance of the interfer- 2 H ence plus noise as =σI+ρ βjhjhj, the receive filter j of the conventional MMSE receiver is [28] H H −1 ∗ v h0h0v h0 v =argmax H = −1 . (3) v v v h0 2 Plugging (3) into (2), we obtain the best achievable SINR as H −1 2 ρ( h h0) SINR ∗= 0 J H −1 2 H −1 h0 (σ I+ρ βjhjhj) h0 j=1 H −1 =ρh0 h0. (4) Note that the conventional MMSE receiver usually requires an interference training period to estimate . Recall that the covariance matrix is a statistic of the noise and interfer- Fig. 2. Packet structure of (a) the conventional MMSE receiver for long ence. Since orthogonality among the large number of pilot data packets, (b) the conventional MMSE receiver for short data packets, and sequences cannot be guaranteed, it is not easy to estimate the (c) the proposed linear receiver for short data packets. interfering channels hj(j=1,··· ,J)individually. To handle this issue, an approach to es timate the sample covariance ˆ −α/ 2 using a specially designed interference training period was where β0 = d0 is the attenuation factor for the target proposed [15]. In order to observe the covariance associated transmit device ( β0>0), αis the path-loss exponent ( α> 2), N×1 with the interference and noise, the target transmit device h0,i∈C is the channel vector between the target transmit should remain silent in this period. The sample covariance device and AP receiver, s0,i[]is the symbol transmitted by ˆ 2 obtained in the interference training period is the target transmit device ( E[| s0,i[]| ]= ρ), Jis the number −α/ 2 K of interfering devices from neighboring cells, βj = d 1 j ˆ= r[i]r[i]H (5) is the attenuation factor for the j-th interferer (β j > 0), K N×1 i=1 hj,i∈C is the channel vector between the j-th interferer and AP receiver, sj,i[]is the symbol transmitted by the where K is the duration of the training period and r[i] 2 N×1 J j-th interferer (E[| sj,i[]| ] = ρ) ,and ni[] ∈ C is 2 is the i-th received sample ( r[i] = βjhjsj[i]+ n[i]). the complex Gaussian noise vector (ni[] ∼ CN (0,σ I)) . j=1 ˆ−1 Also, without loss of generality, we assume that the distances ˆ h0 By replacing with in (3), i.e., using vˆ= ˆ−1 instead d,d,..., d are sorted in ascending order. In this work, h0 2 0 1 J of v∗, we obtain the SINR estimate we assume that the channel remains unchanged within a H −1 2 block and changes independently from block-to-block. In the ρ( h ˆ h0) SINR = 0 . (6) sequel, we skip the fading block index ifor notational H −H −1 h ˆ ˆ h0 convenience. 0 Using a Gaussian approximation for the interference, 4the expected SINR 5of (6) becomes [29] B. Conventional Receiver Technique H −1 2 ρ( h ˆ h0) If a unit norm receive filter vis applied to the received E [SINR ]= E 0 ˆ ˆ H ˆ−H ˆ−1 signal vector y[], an estimate of the desired symbol is sˆ0[]= h0 h0 vHy[]and the resulting SINR is N−1 = 1− SINR ∗. (7) H H K+1 ρv h0h v SINR (v)= 0 . (2) J Note that the expected SINR in (7) contains an additional H 2 H N−1 v (σ I+ρ βjhjhj)v scaling factor 1 −K+1. Since the interference training period K j=1 3The conventional performance measures such as ergodic capacity may not Under the condition that the target rate of the transmit device is be suitable for short-packet communication systems because these metrics R=log 2(1+τ) , we say a communication is successful if the pertain to the asymptotic regime of long data packets [10], [11]. Nonetheless, received SINR is larger than τ. Hence, the outage probability this quantity is still simple and useful tool to analyze the behavior of the at SINR threshold τis expressed as P = P[SINR (v)≤τ]. proposed scheme. out 4Gaussian approximation of interferences becomes more accurate when the Note that the receive filter vcan be designed to remove density of machine-type devices becomes higher. the interference or to boost the power of the desired signal. 5Since the average analysis is relevant only if there are sufficiently many In order to minimize the outage probability, a receive filter packets, the expected SINR might not be an ideal metric for the short packet based communication systems. Nevertheless, unless the packet length weight should be designed to maximize the SINR of the is extremely short, hundreds of samples might be used in the computation of receiver. This receiver is commonly dubbed as an MMSE the expected SINR and thus average SINR is still meaningful. LEE et al. : PACKET STRUCTURE AND RECEIVER DESIGN FOR LOW LATENCY WIRELESS COMMUNICATIONS 799 for the short packet framework would be very small, E[SINR ] From (9) and (10), we have would be much smaller than SINR ∗, the best achievable SINR −1 2 in (4). Further, when the number of antennas N increases, H H h0 +ρh0h0 h0 there would also be a loss in the SINR and achievable rate, H −1 2 2 which makes this approach unsuitable for the small packet (h h0) = hH −1h − 0 transmission. 0 0 H −1 ρ+h0 h0 2 H −1 ∗ 2 ρh h0 ρSINR III. R ECEIVER DESIGN = 0 = (11) ρ+hH −1h ρ2+SINR ∗ Recall that two main ingredients of the receive filter in (3) 0 0 are the channel vector h0and the covariance matrix of the ∗ H −1 where SINR =ρh0 h0(see (4)). Now, by plugging (10) interference and noise. In this section, we present a strategy to into the denominator of (9), we have estimate the covariance matrix using measurements in the −1 −1 data transmission period and show that the achievable SINR H H H h0 +ρh0h0 +ρh0h0 h0 of this strategy equals SINR ∗. By estimating the covariance −1 H −1 −1 H −1 matrix in the normal data transmission period instead of the h0h h0h =hH −1− 0 −1− 0 h interference training period, we can avoid the transmission rate 0 H −1 H −1 0 ρ+h h0 ρ+h h0 loss caused by the interference training period. 0 0 H −1 H −1 H −1 Note that the received signal y[] = h0 s0[] + h h0h h0h h0 J = hH − 0 0 −1h − 0 0 H −1 0 H −1 βjhjsj[] + n[]contains interference from adjacent ρ+h0 h0 ρ+h0 h0 j=1 devices and noise as well as the desired signal. Using the ρ2hH −1h ρ3SINR ∗ −1 0 0 0 h0 = 2= 2 ∗2. (12) receive filter v= −1 , the estimate of the desired symbol ρ+hH −1h (ρ +SINR ) 0 h0 2 0 0 becomes Plugging (11) and (12) into (9), we have H sˆ0[]= v y[] ∗ 2 ρ ρSINR H H J H 2 −1 ρ2+SINR ∗ ρh0(ρ h0h0 +ρ j=1βjhjhj+σI) SINR = =SINR ∗, (13) = y[] prop ρ3SINR ∗ H H J H 2 −1 ∗ ρh0(ρ h0h0 +ρ j=1βjhjhj+σI) 2 (ρ 2+SINR )2 hH −1 which is the desired result. = 0 0 y[] (8) H −1 It is worth noting that the main goal of Theorem 1 is h 2 0 0 to validate the method of estimating the covariance matrix H where 0= +ρh0h0. In the following theorem, we show in using only normal data transmission. By achieving the that the best possible SINR in (4) can be achieved even with maximum SINR and avoiding the interference training period, the inclusion of the desired signal in the covariance matrix. 6 the proposed method can exploit an additional Kchannel uses Theorem 1: When the covariance matrix 0 is employed for the data transmission period compared to the conventional −1 0 h0 MMSE receiver. in the receive filter v= −1 , the SINR of the proposed 0 h0 2 By slightly modifying this result and using a Gaussian ∗ H −1 strategy is SINR =ρh0 h0. approximation for the interference, we can obtain the SINR Proof: Let SINR prop be the SINR of the proposed strategy. expression for a realistic scen ario where the sample covari- Then, using (2), we have ance matrix is employed . In this scenario, we use ˆ0 = ˆ ˆˆH −1 2 + ρh0h0 instead of 0, and thus the modified receive H H 8 ρ h0 +ρh0h0 h0 filter is SINR prop = . (9) H H −1 H −1 −1 h +ρhh +ρhh h ˆ h0 0 0 0 0 0 0 vˆ= 0 . (14) ˆ−1 We first consider the numerator. Using the matrix inversion 0 h0 2 lemma, 7we have Theorem 2: When the sample covariance in (14) is employed, the expected SINR of the proposed linear MMSE −1 −1 H −1 H −1 h0h0 +ρh0h = − . (10) receiver is 0 ρ+hH −1h 0 0 H ˆ−1 2 ρ( h0 0 h0) Eˆ SINR prop = Eˆ 6 0 0 H ˆ−1 ˆ−1 In this section, we focus on the effect of covariance matrix 0and the h0 0 0 h0 sample covariance matrix ˆ0 on SINR under the assumption that h0 is perfectly known at the receiver. We discuss the effect of estimated channel N−1 ∗ ˆ = 1− SINR . (15) h0in the next section. Nd+1 7 H Note that (10) can be obtained by letting A= ,B = h0,C = h0 −1 and D = ρIin the matrix inversion lemma A−BD −1C = A−1+ 8 ˆ ˆ ˆ −1 Here we use h0instead of h0in 0in order to observe the effect of 0 A−1B D−CA −1B CA −1. on SINR. 800 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 66, NO. 2, FEBRUARY 2018

ˆ ˆ ˆˆH Proof: By the direct substitution of 0 = +ρh0h0 into (6), we have 2 H ˆ−1 h0 0 h0 SINR = . (16) H ˆ−1 ˆ−1 h0 0 0 h0 ˆ ˆˆH H ˆ H Let = +ρ( h0h0 −h0h0),then 0= +ρh0h0 and −1 H −1 ˆ−1 −1 h0h0 0 = − H −1 by the matrix inversion lemma. ρ+h0 h0 Therefore,

−1 H −1 2 H −1 h0h0 ρ h − H −1 h0 0 ρ+h h0 SINR = 0 −1 H −1 −1 H −1 H −1 h0h0 −1 h0h0 h0 − H −1 − H −1 h0 ρ+h0 h0 ρ+h0 h0

H −1 2 ρh0 h0 ρ H −1 H −1 2 ρ+h0 h0 ρ h h0 = = 0 . (17) 2 H −1 −1 H −1 −1 ρh0 h0 h0 h0 H −1 2 (ρ +h0 h0)

∗ 1 1 SINR SINR −2 −2 Further, by denoting κ= SINR ∗, = ( ρ ) h0, −1 −1 and ˆ1= 2 2,wehave 2 H ˜−1 1 ρ h0 h0 κ= SINR ∗ H ˜−1 ˜−1 h0 h0 2 H ˆ−1 1 = . (18) H ˆ−2 1 Note that the joint distribution of the elements of ˆfollows the central complex Wishart distribution CW (M,N; )[30]. −1 −1 −1 −1 Hence, E[ˆ1] = 2E[ ] 2 = 2 2 = I,and ˆ1 is a complex Wishart distribution CW (Nd,N;I). The probability density function of κis given by [29] (N +1) d (Nd+2−N)−1 P(κ) = κ Fig. 3. The received SINR of the proposed method and conventional MMSE (N−1)(Nd+2−N) receiver for Nb=100 and 1000. We set J=30, SNR =0dB, Np=0.1Nb, (N−1)−1 (1−κ) (19) K=0.1Nb,Nd=0.8Nb,Nd=0.9Nb. where κfollows the regularized incomplete beta distribution. Since the interference training period is unnecessary, Since (i)= (i− 1)!for an integer i, the expectation the data transmission period is improved from Nd to of κis Nd=Nd+K and at the same time the covariance matrix 1 is estimated using samples in the data transmission period E[κ]= κP(κ) dκ 0 (see Fig. 2). Therefore, we obtain a more accurate estimation 1 of the interference covariance in the short packet framework. Nd! = κNd+2−N(1−κ) N−2dκ The effect of the sample covariance matrix on the received (N −2)!(N +1−N)! d d 0 SINR shows the efficacy of the proposed receiver by obtaining N−1 =1− . (20) a larger scaling factor 1− N−1 .InFig.3,weplotthe Nd+1 Nd+1 2 received SINR as a function of the number of receive antennas ρ hH ˆ−1h 1 0 0 0 N. When the packet size N is large (e.g., N =1000 ),which Recalling that κ= ∗ , we further have b b SINR hH ˆ−1 ˆ−1h 0 0 0 0 corresponds to the packet length of current wireless systems, H ˆ−1 2 K = 0.1Nb is also sufficiently larger than the number of ρ( h0 0 h0) Eˆ SINR prop = Eˆ antennas N so that scaling factor of the proposed scheme 0 0 H ˆ−1 ˆ−1 h0 0 0 h0 N−1 N−1 1− N +1 and the conventional MMSE receiver 1− K+1 N−1 d = 1− SINR ∗. are not much different. This behavior, however, does not Nd+1 hold true for short-sized packet regime. In fact, as shown in Fig. 3(a), we see that the performance of the proposed LEE et al. : PACKET STRUCTURE AND RECEIVER DESIGN FOR LOW LATENCY WIRELESS COMMUNICATIONS 801 scheme improves linearly with N. Since the interference train- where (23) is due to Cov (a,b)= E[ab H] − E[a]E[bH] 9 ing is needed for the conventional MMSE receiver, we observe and ηp is the variance of the interference plus noise. The that when Nbis small (e.g., Nb=100) the performance of the corresponding MMSE-based channel estimate hˆ0is conventional MMSE SINR receiver with sample covariance −1 ˆ H H matrix does not scale with N. h0=Chh P0 P0Chh P0 +ηpIN P0h0+zp −1 H =(NpChh +ηpIN) Chh P0(P0h0+zp) IV. J OINT PILOT AND DATA SYMBOL −1 ηp 1 H BASED CHANNEL ESTIMATION = IN +Chh Chh h0+ P0zp . (25) Np Np In the previous sections, we assumed that the desired chan- ˆ nel h0is perfectly known. As mentioned, when we consider We observe from (25) that the estimated channel vector h0 the short packet transmission, the training period should also converges to the original channel vector h0 as the training be reduced to avoid an excessive amount of training overhead. period Np increases. This clearly de monstrates that there In this section, we propose a channel estimation technique would be a degradation in the channel estimation quality for that jointly uses the pilot signals and data symbols to improve the short packet regime. To enhance the channel estimation channel estimation quality. In a nutshell, the proposed channel quality without increasing the pilot overhead, we exploit the estimation technique picks a small number of reliable data virtual pilots in the re-estimation of channels. Using the delib- symbols among all available data symbols. erately chosen virtual pilots together with the conventional Using the chosen data symbols (which we call virtual pilots ) pilots, the channel is re-estimated, and the newly generated together with the pilot signals in the re-estimation of the channel estimate will be used for the symbol detection. When channel vector, we achieve great improvement of the channel Nv data symbols are selected for the virtual pilot purpose, estimation performance in the short packet regime. the received signals are J (1) (1) (1) (1) A. The Joint Pilot and Data Symbol Based y =h0s0 + βjhjsj +n Channel Estimation j=1 . Before we proceed, we briefly review conventional MMSE- . based channel estimation. The received pilot signals in the J (Nv) (Nv) (Nv) (Nv) training period are expressed as y =h0s0 + βjhjsj +n (26) J j=1 (1) (1) (1) (1) (i) y =h0p0 + βjhjsj +n (i) (i) where y is the i-th observation, n is the i-th noise, s0 is j=1 the data symbol of the target transmit device, and s(i)is the . j . data symbol of the j-th interferer. The NvN×1 vectorized J virtual pilot observations can be expressed as (Np) (Np) (Np) (Np) y =h0p + βjhjs +n (21) 0 j y =Sh +z (27) j=1 v 0 0 v

(i) (i) (i) where S0 = s0 ⊗ IN (of size NvN × N) is the vir- where y is the i-th observation, n is the i-th noise, p0 is (1) (Nv)T tual pilot matrix where s0 =[ s0 ,..., s0 ] is the data the i-th pilot signal in the target transmit device, and Npis the J (1) (1)T symbol sequence and zv = ( βjhjs + n ) ··· total number of pilot observations. The NpN×1 vectorized j=1 j received pilot signals are T J (Nv) (Nv)T ( j=1βjhjsj +n ) is the interference plus noise y =Ph +z (22) p 0 0 p signal vector in the virtual pilot transmission period. By where P0 = p0⊗ IN is NpN × N-dimensional training stacking the pilot observation vector yp and virtual pilot (N ) (1) p T observation vector yv, we obtain the composite observation matrix with p0 = [ p0 ,..., p0 ], and zp = (N ) T vector ycfor the channel re-estimation as J (1) (1)T J p (Np)T ( j=1βjhjsj +n ) ··· ( j=1βjhjsj +n ) yp P0 zp is the interference plus noise vector over the training yc= = h0+ . (28) yv S0 zv period. We assume that h0 follows a circular symmetric complex normal distribution, i.e., h0 ∼ CN (0,Chh )where The MMSE estimate of the proposed scheme is expressed as −1 Chh = Cov (h0,h0). The MMSE weight matrix minimizing hˆ0= Cov (h0,yc)Cov (yc,yc) yc −1 the mean square error between the original channel vector h0 = yc (29) and the estimate hˆ0=Wy pis [31] −1 9Since it is hard to obtain exact variance J β2Nρ+σ2, we instead W =Cov h0,yp Cov yp,yp j=1 j ¯2 2 ¯ ¯α/ 2 H H use ηp = Jβ Nρ+σ where β = d is obtained by using the cell- = E[h0yp]E[ypyp] (23) radius d¯under the assumption that the interferers are closer to the receiver H H H (i.e., β¯ >β ). Thus, the channel estimation might be slightly pessimistic. = E[h0h0P0 +h0zp] j H H H H H H Also, the reason to treat interference as noise in (24) is because it is difﬁcult ×E[P0h0h0P0 +P0h0zp +zph0P0 +zpzp] to acquire the covariance of the interference. Note that the MSE formula −1 in (37) is obtained under the assumption that h as well as the interfering H H 0 =Chh P0 P0Chh P0 +ηpIN (24) channels are spatially uncorrelated. 802 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 66, NO. 2, FEBRUARY 2018

Fig. 4. Block diagram of the receiver using virtual pilot and pilot signal in t he re-estimation of the channel. Among all the data symbols, symbols with small MSE are chosen as virtual pilots. Note t hat symbols with small MSE are green colored. where While the conventional MMSE estimate in (25) uses only the received pilot sequence for the channel estimation, the pro- =Cov (h,y) 0 c posed channel estimator in (29) utilizes the most reliable = E[hyH] E[hyH]= C PH C S¯H (30) 0 p 0 v hh 0 hh 0 data symbols, i.e., the soft symbol estimate S¯0 and second and order moments 0, as virtual pilots. Clearly, reliability of the soft symbols directly affects the quality of the proposed = Cov (yc,yc) H H channel estimation so that we need to choose virtual pilots E[ypy ] E[ypy ] = p v with caution. H H E[yvy ] E[yvy ] p v B. Virtual Pilot Selection H ¯H P0Chh P0 +ηpI P 0Chh S0 Since the virtual pilots can improve the channel estimation = ¯ H .(31) S0Chh P0 0⊗diag (Chh )+ηvI quality of the proposed method, the best way to select virtual ¯ (1) (Nv)T Note that S0= E[S0]=¯s0⊗IN where s¯0=[¯ s0 ,..., s¯0 ] pilots would be to compare the performance metric (e.g., MSE (i) of the estimated channel) of all possible Nd data symbol is obtained from the ﬁrst order moment of s0 [32]. That is, Nv Q combinations and then choose the combination achieving 1 1 s¯(i)=E[s(i)]= θ 1+c(i)tanh L(c(i)) the minimum MSE. Since this procedure is computationally 0 0 2 0,k 2 0,k demanding and hence not pragmatic, we use a simple subopti- θ∈ k=1 (32) mal approach to compute the MSE when single data symbol is (i) used for the virtual pilot. Among all data symbols, we choose where is a constellation set, c0,k is the k-th coded bit, Q is the number of (coded) bits mapped to a data symbol the Nv-best data symbols generating the smallest MSE as (i) Q virtual pilots (see Fig. 4). Although this approach does not s0 in 2 -ary quadrature amplitude modulation (QAM) con- (i) consider the correlation among virtual pilot symbols and hence stellations, and L(c0,k)is the log-likelihood ratio (LLR) of (i) is not optimal, computational complexity is much smaller than the k-th coded bit mapped from a data symbol s0 . 0 = the approach using all possible symbol combinations. Also, ¯(1) ¯(Nv)T [λ0 ,..., λ0 ] is the vector of the second order moments this approach is effective in improving the quality of channel (i) of s0 given by re-estimation. (n) ¯(i) (i)2 Let hˆ be the estimated channel vector when the n-th data λ0 = E[| s0 |] 0 Q symbol is used as a virtual pilot, then the MSE metric εn 1 1 = |θ|2 1+c(i)tanh L(c(i)) .(33) for the hypothetical selection of the n-th data symbol is 2 0,k 2 0,k expressed as θ∈ k=1 Plugging (29) and (30) into (28), we obtain the channel ˆ(n)2 ˜˜−1 zp εn= E h0−h0 2 =tr Cov h0− (n) estimate hˆ0as yv ˆ H ¯H −1 yp h0= Chh P0 Chh S0 =tr Cov (h0)−Cov ˜˜ (n) −1 y PC PH +ηI P C S¯H y v × 0 hh 0 p 0 hh 0 p . −1 H ¯ H =tr Cov (h0)− ˜˜ ˜ (34) S0Chh P0 0⊗diag (Chh )+ηvI yv LEE et al. : PACKET STRUCTURE AND RECEIVER DESIGN FOR LOW LATENCY WIRELESS COMMUNICATIONS 803 where

yp ˜=Cov h0, (n) yv H (n)H = E[h0yp]E[h0yv ] H (n)∗ = Chh P0 (s¯0 )Chh (35) and

yp ˜=Cov (n) yv H (n)H E[ypyp] E[ypyv ] = (n) H (n)(n)H E[yv yp]E[yv yv ] PC PH +ηI(s¯(n))∗PC = 0 hh 0 p 0 0 hh (36) (n)∗ H ¯(n) (s¯0 )Chh P0 λ0 Chh +ηvI (n) (n) (n) using yv =s h0+zv is the virtual pilot observation vector 0 Fig. 5. PER performance of receiver techniques as a function of SNR. We set for the n-th data symbol. From (34), (35), and (36), εn is r=1/2, N=6, J=6, Np=10, K=10, Nd=40, Nd=50, Nb=60, expressed as (see Appendix) Nv=20. ¯(n) 2 λ0 (n)2 εn= N(1−γ(1+γp) (λ¯ ) p ¯(n) 0 2) Proposed method with estimated CSI: we set the inter- λ0 +ηv ference training period as Nd=Nb−Np. 2ηλ¯(n)+η2 (λ¯(n))3 2 v 0 v ¯(n) 0 3) Proposed method with virtual pilot signals (VPS): we −γp λ +γp ¯(n) 0 ¯(n) 3 λ0 +ηv (λ0 +ηv) choose Nv-best virtual pilots with the smallest MSE for (λ¯(n))2 N2 λ¯(n) the channel re-estimation. + 0 p+ 0 (2γ +N2−1)−γ) (n) (n) p p p 4) Proposed method with accurate VPS: we use (λ¯ +η)2γp λ¯ +η 0 v 0 v Nv-accurate data symbols as virtual p ilots in the (37) re-estimation of the channel vector. where γ = Np . Note that ε depends on the reliability of In Fig. 5, we plot the PER performance of all techniques p Np+ηp n soft decisions (i.e., the second order statistic of data symbol under consideration. In this simulations, we use the half (n) 1 ¯ rate ( r= 2) convolutional code with feedback polynomial λ0 in (33)). Hence, in order to achieve the minimum MSE, ¯(n) 1+ D+ D2 and feedforward polynomial 1 + D2.11 In the the desired data symbol maximizing λ0 should be chosen as proposed method, 20 data symbols are used as VPS ( Nv=20). the virtual pilot. Once εnfor all nare computed, we choose We set J= 6 as dominant neighboring interfering devices. Nvdata symbols minimizing εn(see Fig. 7). Observations of We observe that the proposed method with VPS achieves more virtual pilots and normal pilots are used for the re-estimation −3 of the channel vector. than 2 dB gain over the conventional MMSE receiver at 10 PER point. We also observe that the addition of VPS achieves more than 1 dB gain over the proposed method without VPS. V. S IMULATION RESULTS AND DISCUSSIONS 3 In Fig. 6, we plot the PER performance with code rate r= 4 In this section, we evaluate the performance of the proposed convolutional code with feedback polynomial 1 +D2+D3and algorithm. In our setup, we assu me that adjacent interfering feedforward polynomial 1 + D+ D3. We observe from the 2 devices are randomly located on a square (of area 100 m ). figure that the performance gain of the proposed method with The target receiver is located at center and the target transmit VPS is 2 dB over the conventional MMSE receiver and more device is located 1 meter away from the receiver. The packet than 0.8 dB over the proposed method without VPS at 10 −3 10 size is set to 100 bits. As a performance measure, we con- PER point. sider a packet error rate (PER). We assume that elements of In Fig. 8, we plot the PER performance result of the channel vector for each device are i.i.d. zero mean complex schemes we considered with polar code and convolutional Gaussian random variables with unit variance. codes. We set the block length Nbas 64 since the block length In our simulations, we study the performance of the follow- of the polar code should be always a power of 2. We observe ing receiver techniques: from the figure that the proposed method with polar code is 1) MMSE receiver with estimated CSI (conventional superior to the convolutional code based schemes. Specifically, MMSE receiver) [15]: we set the interference training we observe that use of polar code will bring one dB over the period as K. convolutional code at 10 −3PER point.

10 In order to meet the stringent delay requirements, packet size of the 11 In IoT systems, convolutional code s are preferred over turbo or LDPC uRLLC use case is set to 100 ∼200 bits [35], [36]. codes [5]. 804 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 66, NO. 2, FEBRUARY 2018

Fig. 6. PER performance of receiver techniques as a function of SNR. We set Fig. 8. PER performance of receiver techniques as a function of SNR with r=3/4, N=6, J=6, Np=10, K=10, Nd=40, Nd=50, Nb=60, polar code and convolutional codes. We set r=1/2, N=6, J=6, Np=10, Nv=20. Nd=54, Nb=64, Nv=20.

Fig. 7. PER performance of receiver techniques as a function of SNR over the Rician fading channel. We set r=1/2, N=6, J=6, Np=10, K=10, Nd=40, Nd=50, Nb=60, Nv=20. Fig. 9. Throughput of receiver techniques as a function of number of receive antennas N for temporally-correlated block fading channel. We set 1 SNR =0dB, r= 2,J= 6, Np = 10, K = 10, Nd = 40, Nd = 50, We next consider the performance of the proposed method Nb=60, Nv=20. over the Rician fading channel. Note that Rician fading includes the line-of-sight (LOS) signal propagation, which can be more general and realistic than Rayleigh fading [33]. We consider temporally correlated channels that are modeled In this simulations, we use the Rician K-factor K = 6dB. by a ﬁrst order Gauss-Markov process [34] as h[k] = ξh Due to the LOS components of the interference channels, [k−1]+ 1−ξ2g[k]where g[k]is the innovation process, we observe from Fig. 7 that the performance of all receivers which is modeled as having i.i.d entries distributed with under consideration is worse than the case using the Rayleigh CN (0,1)and 0 ≤ ξ ≤ 1 is the temporal correlation fading channel. From numerical results, the proposed method coefﬁcient. In this simulations, we use ξ= 0.9881 for the with VPS is still effective and achieving more than 1.5 dB moderate mobile speed. To evaluate the throughput, we present gain over the conventional MMSE receiver at 10 −3PER point. Monte-Carlo simulation results with 10000 iterations. Since We also observe that the addition of VPS achieves around each iteration consists of 10 fading blocks, the maximum 0.8 dB gain over the proposed method without VPS. throughput is about 5 Mbps. As observed in (7) and (15), In Fig. 9, we plot the throughput as a function of the number when the number of receive antennas Nincreases, the training of receive antennas N for temporally correlated channels. period used for the sample covariance matrix computation LEE et al. : PACKET STRUCTURE AND RECEIVER DESIGN FOR LOW LATENCY WIRELESS COMMUNICATIONS 805

the proposed method using VPS performs close to the MMSE receiver using the perfect CSI (5 ∼7% throughput loss) and also provides 21% gain over the conventional MMSE receiver when J≤30. Finally, in Fig. 11, we show the throughput as a function of packet size Nb. We observe that the rate loss of the proposed method over the MMSE receiver with perfect CSI is around 6% ∼ 13%, which is far better than the rate loss of the conventional MMSE receiver (12% ∼ 32%). These results demonstrate that the proposed method has clear beneﬁt over the conventional MMSE receiver in the short packet transmission.

VI. C ONCLUSION Short packet transmission systems are critical to fulfilling the stringent low latency requirements of the fifth generation (5G) wireless standards. We proposed a receiver technique suited to short packet transmission. Our work was motivated by the observation that the insufficient training period resulting Fig. 10. Throughput of receiver techniques a s a function of interfering devices 1 from a small packet structure causes severe degradation in the for temporally-correlated block fading channel. We set SNR =10 dB, r= 2, N=6, Np=10, K=10, Nd=40, Nd=50, Nb=60, Nv=20. desired channel and interference covariance matrix estimation. By exploiting reliable symbols in the data transmission period, the proposed receiver algorithm achieves improved estimation and eventual throughput gain. Although our study in this work focused on the low latency communication, the main concept can be readily extended t o massive machine-type communications scenario (mMTC use case) and high throughput massive MIMO scenario (eMBB use case) of 5G wireless communications. In both scenarios, the channel estimation quality would be crucial to achieve the desired goal. Also a noncoherent approach that does not rely on the pilot signal might be alternative option for uRLLC communication.

APPENDIX DERIVATION OF (37)

Recall from (34) that εnis given by −1 H εn=tr Cov (h0)− ˜˜ ˜ (38) where yp ˜=Cov h, = C PH (s¯(n))∗C (39) 0 y(n) hh 0 0 hh Fig. 11. Throughput of receiver techniques as a function of Nb for v temporally-correlated block fading channel. We set J= 6, SNR = 0dB, and N=8, Np=0.1Nb,K=0.1Nb,Nd=0.8Nb,Nd=0.9Nb,Nv=0.2Nd. yp yp ˜=Cov (n) , (n) yv yv should also be increased to attain the target SINR. Thus, when H (n)∗ P0Chh P0 +ηpI P 0Chh (s¯0 ) the interfering training period K is ﬁxed, the scaling factor = (n) H (n) . (40) s¯ Chh P λ¯ Chh +ηvI 1− N−1 decreases with the number of receiver antennas N. 0 0 0 K+1 For convenience, we let As a result, we observe the throughput degradation on the conventional MMSE receiver when number of receive antennas is H (n)∗ 1 2 = Chh P0 (s¯0 )Chh , (41) large ( N≥7). Whereas, the throughput of the proposed VPS PC PH +ηI P C (s¯(n))∗ scheme increases with the number of receive antennas N. 11 12 = 0 hh 0 p 0 hh 0 , (42) (n) H ¯(n) In Fig. 10, we plot the throughput as a function of the 21 22 s¯0 Chh P0 λ0 Chh +ηvI number of adjacent int erfering devices J. Since the accuracy and of the covariance matrix estimation deteriorates as the number −1 of interfering devices Jgrows large, we see that the throughput 11 12 = 11 12 , (43) decreases with Jfor all methods simulated. We observe that 21 22 21 22 806 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 66, NO. 2, FEBRUARY 2018

¯(n) ¯(n) 2 then 2 λ0 (n)2 2 2ηvλ0 +ηv = N(1−γ(1+γp) (λ¯ )−γ( ) p ¯(n) 0 p ¯(n) 11 12 H λ0 +ηv λ0 +ηv εn=tr Chh − 1 2 1 2 21 22 ¯(n)3 ¯(n)2 2 (n) (λ0 ) (λ0 ) Np H H ×λ¯ +γp + =tr (Chh − 1 11 − 2 21 0 (n) 3 (n) 2 1 1 (λ¯ +ηv) (λ¯ +ηv) γp H H 0 0 − 1 12 2 − 2 22 2). (44) ¯(n) λ0 2 + (2γp+N −1)−γp) (50) Using the inversion formula of partitioned matrices [20], ¯(n) p λ0 +ηv we have where γ = Np . −1 −1 p Np+ηp 11 =( 11 − 12 22 21 ) −1 −1 −1 12 =− 12 ( 22 − 21 21 ) 11 11 REFERENCES −1 −1 −1 21 =− 22 21 ( 11 − 12 22 21 ) −1 −1 [1] B. Lee, S. Park, D. J. Love, H. Ji, and B. Shim, “Packet structure and 22 =( 22 − 21 11 12 ) . (45) receiver design for low-latency communications with ultra-small packets,” in Proc. IEEE Global Commun. (GLOBECOM) Conf. , Dec. 2016, Using (45), we further have pp. 1–6. [2] L. Atzori, A. Iera, and G. Morabito , “The Internet of Things: A survey,” H H 1 11 1 =Chh P0 11 P0Chh Comput. Netw. , vol. 54, no. 15, pp. 2787–2805, Oct. 2010. H (n)∗ [3] E. 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[21] H. Gao, P. J. Smith, and M. V. Clark, “Theoretical reliability of MMSE David J. Love (S’98–M’05–SM’09–F’15) received linear diversity combining in Rayleigh-fading additive interference chan- the B.S. (Hons.), M.S.E., and Ph.D. degrees in nels,” IEEE Trans. Commun. , vol. 46, no. 5, pp. 666–672, May 1998. electrical engineering from The University of Texas [22] D. Tse and P. Viswanath, Fundamentals of Wireless Communications . at Austin in 2000, 2002, and 2004, respectively. Cambridge, U.K.: Cambridge Univ. Press, 2005. From 2000 to 2002, he was with Texas Instruments, [23] P. Li, D. Paul, R. Narasimhan, and J. Cioffi, “On the distribution of Dallas, TX, USA. Since 2004, he has been with SINR for the MMSE MIMO receiver and performance analysis,” IEEE the School of Electrical and Computer Engineering, Trans. Inf. Theory , vol. 52, no. 1, pp. 271–286, Jan. 2006. Purdue University, West Lafayette, IN, USA, where [24] N. Kim, Y. Lee, and H. Park, “Performance analysis of MIMO system he is currently a Professor and recognized as a with linear MMSE receiver,” IEEE Trans. Wireless Commun. ,vol.7, University Faculty Scholar. He leads the College of no. 11, pp. 4474–4478, Nov. 2008. Engineering Preeminent Team on Efficient Spectrum [25] J. Park, B. Lee, and B. Shim, “A MMSE vector precoding with block Usage. He has been very involved in commercialization of his research with diagonalization for multiuser MIMO downlink,” IEEE Trans. Commun. , around 30 U.S. patent filings, 27 of w hich have issued. He is a frequent vol. 60, no. 2, pp. 569–577, Feb. 2012. consultant on cellular and WiFi systems, including patent licensing and liti- [26] S. A. M. Ghanem. (Nov. 2014). “Multiple access Gaussian channels with gation. His research interests are in the design and analysis of communication arbitrary inputs: Optimal precoding and power allocation.” [Online]. systems and MIMO array processing. He has served as an Editor of the IEEE Available: https://arxiv.org/abs/1411.0446 TRANSACTIONS ON COMMUNICATIONS , an Associate Editor of the IEEE [27] S. T. Veetil, K. Kuchi, and R. K. Ganti, “Performance of PZF and TRANSACTIONS ON SIGNAL PROCESSING , and a Guest Editor for special MMSE receivers in cellular networks with multi-user spatial multiplex- issues of the IEEE J OURNAL ON SELECTED AREAS IN COMMUNICATIONS ing,” IEEE Trans. Wireless Commun. , vol. 14, no. 9, pp. 4867–4878, and the EURASIP Journal on Wireless Communications and Networking . Sep. 2015. Dr. Love has been recognized as the Thomson Reuters Highly Cited [28] H. Cox, R. Zeskind, and M. Owen, “Robust adaptive beamforming,” Researcher. He is a fellow of the Royal Statistical Society, and he has been IEEE Trans. Acoust., Speech, Signal Process. , vol. ASSP-35, no. 10, inducted into Tau Beta Pi and Eta Ka ppa Nu. Along with his co-authors, pp. 1365–1375, Oct. 1987. he received best paper awards from the IEEE Communications Soci- [29] I. Reed, J. Mallet, and L. Brennan, “Rapid convergence rate in adaptive ety (2016 IEEE Communications Societ y Stephen O. Rice Prize), the IEEE arrays,” IEEE Trans. Aerosp. Electron. Syst. , vol. AES-10, no. 6, Signal Processing Society (2015 IEEE Si gnal Processing Society Best Paper pp. 853–863, Nov. 1974. Award), and the IEEE Vehicular Technol ogy Society (2009 IEEE Transactions [30] N. Goodman, “Statistical analysis based on a certain multivariate com- on Vehicular Technology Jack Neubauer Memorial Award). He has received plex gaussian distribution,” Ann. Math. Stat. , vol. 34, no. 1, pp. 152–177, multiple IEEE Global Communications Conference (Globecom) best paper Mar. 1963. awards. He was a recipient of the Fall 2010 Purdue HKN Outstanding [31] G. Fordor, P. D. Marco, and M. Telek, “On the impact of antenna Teacher Award, the Fall 2013 Purdue ECE Graduate Student Association correlation on the pilot-data balance in multiple antenna systems,” in Outstanding Faculty Award, and the Spring 2015 Purdue HKN Outstanding Proc. IEEE Int. Conf. Commun. (ICC) , Jun. 2015, pp. 2590–2596. Professor Award. He was an invited participant to the 2011 NAE Frontiers of [32] B. M. Hochwald and S. ten Brink, “Achieving near-capacity on Engineering Education Symposium and the 2016 EU-US NAE Frontiers of a multiple-antenna channel,” IEEE Trans. Commun. , vol. 51, no. 3, Engineering Symposium. In 2003, he received the IEEE Vehicular Technology pp. 389–399, Mar. 2003. Society Daniel Noble Fellowship. [33] J. Zhang, L. Dai, Z. He, S. Jin, and X. Li. (Mar. 2017). “Performance analysis of mixed-ADC massive MIMO systems over Rician fading Hyoungju Ji (M’17) is currently pursuing the channels.” [Online]. Available: https://arxiv.org/abs/1703.03642 Ph.D. degree with the School of Electrical and [34] W. C. Jakes, Microwave Mobile Communications . New York, NY, USA: Computer Engineering, Seoul National University, Wiley, 1975. Seoul, South Korea. He joined Samsung Elec- [35] F. Fettweis and S. Alamouti, “5G: Personal mobile Internet beyond tronics in 2007, and has been involved in 3GPP what cellular did to telephony,” IEEE Commun. Mag. , vol. 52, no. 2, RAN1 LTE, LTE-Adv, and LTE-A Pro technol- pp. 140–145, Feb. 2014. ogy developments and standardization. His cur- [36] C. Bockelmann et al. , “Massive machine-type communications in 5G: rent interests include ultra-reliable low-latency Physical and MAC-layer solutions,” IEEE Commun. Mag. , vol. 54, no. 9, transmission, multi-antenna techniques (FD-MIMO), pp. 59–65, Sep. 2016. massive machine type communications, and IoT communications.

Byungju Lee (M’15) received the B.S. and Ph.D. Byonghyo Shim (S’95–M’97–SM’09) received the degrees from the School of Information and Com- B.S. and M.S. degrees in control and instrumentation munication, Korea University, Seoul, South Korea, engineering from Seoul National University, South in 2008 and 2014, respectively. From 2014 to Korea, in 1995 and 1997, respectively, and the M.S. 2015, he was a Post-Doctoral Fellow with the degree in mathematics and the Ph.D. degree in elec- Department of Electrical and Computer Engineering, trical and computer engineering from the University Seoul National University. He was a Post-Doctoral of Illinois at Urbana–Champaign, USA, in 2004 and Scholar with the School of Electrical and Computer 2005, respectively. From 1997 and 2000, he was with Engineering, Purdue University, West Lafayette, IN, the Department of Electronics Engineering, Korean USA, from 2015 to 2017. He joined Samsung Elec- Air Force Academy, as an Ofﬁcer (First Lieutenant) tronics in 2017, has been involved in research and and an Academic Full-time Instructor. From 2005 to standardization for 3GPP 5G NR. His res earch interests include physical layer 2007, he was with Qualcomm Inc., San Diego, CA, USA, as a Staff Engineer. system design for 5G wireless communications. From 2007 to 2014, he was with the School of Information and Communica- tion, Korea University, Seoul, as an A ssociate Professor. Since 2014, he has been with the Seoul National University, where he is currently a Professor with the Department of Electrical and Computer Engineering. His research interests include wireless communications, statistical signal processing, estimation and Sunho Park (M’16) received the B.S., M.S., detection, compressed sensing, and information theory. and Ph.D. degrees from the School of Informa- Dr. Shim is an elected member of the S ignal Processing for Communications tion and Communication, Korea University, Seoul, and Networking Technical Committee of the IEEE Signal Processing Society. in 2008, 2010, and 2015, respectively. Since 2015, He was a recipient of the M. E. Van Valkenburg Research Award from the ECE he has been with the Institute of New Media and Department of the University of Illinois in 2005, the Hadong Young Engineer Communications, Seoul Nati onal University, Seoul, Award from IEIE in 2010, and the Irwin Jacobs Award from Qualcomm and South Korea, as a Research Assistant Professor. His KICS in 2016. He has been an Associate Editor of the IEEE T RANSAC - research interests incl ude wireless communications TIONS ON SIGNAL PROCESSING , the IEEE W IRELESS COMMUNICATIONS and signal processing. LETTERS ,and Journal of Communications and Networks , and a Guest Editor of the IEEE J OURNAL ON SELECTED AREAS IN COMMUNICATIONS .