Physical Layer Abstraction for Ultra-Reliable Communications in 5G Multi-Connectivity Networks

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1 Physical Layer Abstraction for Ultra-Reliable Communications in 5G Multi-Connectivity Networks Waqar Anwar, Kedar Kulkarni, Norman Franchi and Gerhard Fettweis Vodafone Chair Mobile Communications Systems, Technische Universität Dresden, Germany {waqar.anwar, kedar.kulkarni, norman.franchi, Abstract The fifth generation 5G) of mobile communication will enable new use-cases such as self driving cars, smart automation and mission critical applications, which require ultra-reliable communications. Multi-Connectivity MC) is a promising approach to achieve high reliability in wireless networks. In order to enable MC and efficiently utilize radio resources, dynamic link adaptation is required for choosing appropriate modulation schemes and number of links. This can be achieved by using an effective link quality metric such as effective signal-to-noise ratio SNR) and mapping it to the packet error rate, a process referred to as physical layer abstraction PLA). In this paper, we investigate and compare the performance of existing PLA methods especially exponential effective SNR mapping ) and received bit information rate ), for OFDM-based MC systems. Furthermore, we propose a new robust PLA method, called enhanced e). The e minimizes the efforts of optimizing tuning parameter by fitting the variations in tuning parameter to known curves as a function of channel and diversity order. Simulation results show that e outperforms the state of the art PLAs for different channel conditions, modulation and diversity orders. Index Terms Physical Layer Abstraction, Multi- Connectivity, Diversity Combining, Dynamic Link Adaption, URLLC, 5G I. INTRODUCTION Emerging applications in the context of ultra-reliable and low latency communications URLLC) pose a massive challenge to the physical layer of 5G cellular networks. To achieve reliability in 4G, Hybridautomatic-repeat-request HARQ) procedure is used, which retransmits incorrectly received packets. However, in most URLLC applications, the timing constraints do not permit multiple retransmissions. Therefore, multiconnectivity MC) is considered as a promising approach to enable URLLC in 5G by establishing multiple parallel links in the frequency domain []. In MC, a user equipment UE) is simultaneously connected to multiple base stations BSs) via more than one physical link using single or multiple carrier frequencies. Currently, MC is exclusively used to increase data rates, such as dualconnectivity in LTE [2]. But MC can also significantly reduce outage probability, and hence improve the reliability, by exploiting diversity in space and frequency [], [3]. Different diversity combining methods are known to take advantage of the multiple diversity branches, such as selection combining SC), maximum ratio combining MRC) and joint decoding JD). Wolf et. al. [] has shown the reliability gain of MC with SC, MRC and JD. To enable MC and efficiently utilize radio resources in varying channel conditions, link adaptation capabilities are required. This includes adaptive modulation and coding where a transmitter chooses a modulation and coding scheme MCS) from a set of MCSs depending on channel conditions and target packet-error-rate PER). It is an integral part of current and next generation wireless systems such as LTE, 5G New Radio NR) and IEEE 802.ax. In case of MC both MCS and the number of parallel links are required to be adopted. PLA enables link adaptation by generating a link quality metric, which is then fed back to the BS. In orthogonal-frequencydivision-multiplexing OFDM) systems, each subcarrier experiences different fading conditions. Therefore, to evaluate overall performance of the system, it is necessary to map instantaneous SNRs of different sub-carriers to a single effective SNR ESNR). Moreover, in case of MC, a single link quality metric is required to represent all connected links to adapt the MCS and the number of parallel links. In literature, most commonly used methods for PLA are exponential effective SNR mapping ) and received bit mutual information rate ) [4], [5]. These are used for following purposes: first, they can be used in the implementation of a UE to compute the feedback and second, they can be used in large-scale system level simulations to speed up simulation time. Wu et. al. [5] proposed based PLA for heterogeneous networks of IEEE 802. and LTE. Study provides comparison and analysis of and in ITU International Telecommunication Union) defined channel model. The given results are specific to a channel model and cannot be generalized to other scenarios. In [6], based model is considered to generate link quality metric for OFDM based systems. Kaltenberger et. al. [7] highlighted applications of PLA in system-level evaluations. Several other studies compared the performance of these algorithms and verified their accuracy [4], [8], [9]. However, the above mentioned work only consider communication over a single link with a fixed channel model. Multi-link diversity and varying channel conditions are not taken into account. Moreover, traditional PLA methods require optimization of a fitting parameter

2 Fig.. Multi-Connectivity Communications scenario to achieve optimal SNR mapping. The fitting parameter is dependent on channel conditions, modulation and diversity orders and diversity combining schemes. Extension of these methods to MC will require maintaining a lookup table that lists optimal fitting parameters for given modulation, channel conditions and MC parameters which is infeasible. Therefore, it is of interest to find a generalized model that captures variation in the fitting parameter with given system parameters. In this paper, we consider an OFDM system with MC where the source transmits same data on multiple links. Received OFDM symbols from multiple links are combined using diversity combining techniques such as SC and MRC. The subcarrier SNRs are then mapped to an ESNR using PLA algorithms. We abstract the physical layer performance of a MC system using existing PLA algorithms. Moreover, we derived an enhanced e) method which is more accurate than existing PLAs and suitable for ultra-reliable communications. To achieve optimum performance, these PLAs require optimization of fitting parameter depending on channel type, diversity order and modulation scheme. In order to reduce optimization efforts, we propose curve fitting approach to model optimization parameter as a function of channel type, diversity order and modulation scheme. We evaluate and compare the performance of traditional PLAs i.e. and ) with e under varying channel conditions, changing diversity order and modulation schemes. Extensive results based on full PHY simulations are provided for validation. II. MULTI-CONNECTIVITY SYSTEM MODEL We consider a MC cellular network, as shown in Fig., consisting of a link management entity LME), B accessible base stations BS i, i B = {, 2,..., B}) serving to a user equipment UE i, i U = {, 2,..., U}). The LME assigns required number of links to UE depending on quality of service QoS) requirement. We consider that all BSs and UEs have a single TX/RX antenna per RF front-end and all are operating at different frequency bands. We focus on downlink communication where BSs transmit same data to UE over multiple links. UE combines the received data using MRC, then computes the ESNR and fed back to LME. We denote the number of OFDM subcarriers by N, the number of BSs simultaneously connected with UE by L and the channel coefficient on the lth link and at the nth subcarrier by h l,n. It is assumed that the channel coefficients on all links are independent, identically distributed iid). This is particularly true when BSs are spaced sufficiently apart and are operating at different frequency bands in a rich scattering environment. The link between BS and a UE is modeled either with Rayleigh or Rician fading. The Rician channel models are characterized by Rician factor κ, which is defined as the ratio of signal power in dominant line-of-sight LOS) component to power on scattered paths [0]. The considered channel parameters are specifically chosen to model the typical urban outdoor environment. We assume block fading channel, where channel coefficients remain unchanged in one packet duration. Long term fading effects such as shadowing and path loss are not considered in this paper due to their negligible effects on frequency selectivity of the channel. In case of MC, we assume that average received SNR per link is equal and fading on all connected links is uncorrelated. In a frequency selective channel, each OFDM subcarrier undergoes independent fading. Instantaneous SNR on nth subcarrier in lth link is given by γ l,n = γ tx h l,n 2, where γ tx is the transmit SNR of BSs. In case of MC, the signals received by a UE from L RF frontends are combined subcarrier-wise using MRC or SC. After combining, the received SNR on nth subcarrier is L given by γ n = { γ tx l= h l,n 2 in case of MRC and γ n = γ tx max h,n 2,..., h N,n 2} in case of SC []. In order to generate a combined link quality metric, PLA is used to map the vector of SNRs of all subcarriers γ = [γ, γ 2,..., γ N ] to an ESNR, as explained in Fig. 2. III. PHYSICAL LAYER ABSTRACTION PLA) PHY abstraction is used to model the performance of physical layer in terms of symbol error rate SER)) as a function of the received SNR. In an OFDM based system, each subcarrier can has different probability of symbol error due to frequency selective fading. The overall SER can be expressed as SER eff = N SER n, ) N where N is the number of OFDM subcarriers and SER n is the symbol error probability at the nth subcarrier. For BPSK, SER can be written as ) Q 2γeff = N N ) Q 2γn, 2)

3 Exact Chernoff bound Improved approximation Qx) Fig. 2. PHY abstraction modeling concept for multi-link diversity where γ eff is the ESNR of a wideband system having the same SER as the average SER over all OFDM subcarriers and γ n is the post processing SNR at nth subcarrier. The ESNR is a suitable quality metric to predict SER in a multi-state channel. Traditionally, and have been the popular methods to map the received SNRs γ) to an ESNR. In case of MC with diversity combining a single ESNR is computed over all combined links. This is achieved by subcarrier-wise combining the links using diversity combining techniques and then mapping the resultant SNR vector γ) to an ESNR. In Fig. 2 concept of PHY abstraction for multi-link diversity is shown. A. Exponential Effective SNR Mapping ) is derived by upper bounding SER in Eq. ) 2 using Chernoff bound, written as Q x) 2 exp x2 2 [2]. In general, we can write as [8] N γ eff = β ln exp γ ) ) n, 3) N β where β is a modulation and channel dependent fitting parameter. Optimum value of β is found by the leastsquare fit that minimizes mean square error MSE) between ESNR γ eff ) obtained from and AWGN SNR γ AWGN ) at the same value of SER, that is β = arg min β γ AWGN γ eff β) 2. 4) B. Received Bit Information Rate ) ESNR γ eff ) using is computed as [4] { γ eff = βφ N ) } γn Φ, 5) N β where Φ is a mapping function defined as { Φ γ, M) = log 2 M) M M E X log M 2 m= k= exp X 2 ) )} γ s k s m )+X 2, 6) where X is a zero-mean complex Gaussian random variable with variance, i.e., X CN0,) and M is the modulation order. In 5), β is the fitting parameter that needs to be optimized as done in 4) x Fig. 3. Comparison between chernoff bound and used approximation C. Enhanced e) To calculate a robust link-quality metric for ultrareliable communication, we use a tighter ) bound on SER, given by Q x) 2πx exp x2 2 [2, eq.)]. In Fig. 3, chernoff bound and the bound in [2, eq.)] is plotted. The new bound is tighter for x >. Most practical communication systems operate in environments where received SNR is higher than. Thus, this is a good approximation. Using this bound, SER in 2) is upper bounded as P s 4πγ exp γ). 7) For an OFDM system with N subcarriers, we can write P s exp γ n ). 8) N 4πγn Then, in terms of ESNR, we have γeff exp γ eff ) = N exp γ n ). 9) γn After taking log and rearranging 9), we get ) log γ eff )+2γ eff = 2 log exp γ n ). 0) N γn By doing exponential operation on both sides and multiplying with 2, we get 2γ eff exp 2γ eff ) = 2 N 2 exp γ n )). ) γn From ), we can write the ESNR expression for enhanced as ) 2 γ eff = 2 W 2 e γn/β, 2) N γn

4 where W ) is Lambert-W function, defined as z = W ze z ) [3]. The expression in 2) can be generalized to other modulation schemes as ) 2 γ eff = β 2 W 2 e γn/β, 3) β N γn where β is the fitting parameter that needs to be optimized as defined in 4). IV. APPROXIMATION OF β The β parameter in 3), 5) and 3) is a fitting parameter for optimal SNR mapping. It needs to be optimized for each modulation scheme and channel profile. Moreover, in case of MC, β also depends on diversity order and diversity combining methods. In an environment where channel changes over time and different combinations of κ and L are possible, optimizing β for each possible combination and for all modulation schemes is challenging. Therefore, we propose a curve fitting technique to capture the variations in optimal value of β with respect to κ and L. This technique requires β to be optimized for only a few combinations of κ and L to capture the pattern in its variation. Once the pattern is approximated with known mathematical curves e.g. linear, exponential), it can be used to approximate β for other combination. This considerably reduces complexity of optimization and need to maintain huge look up tables. Fig. 4 plots optimal value of β versus κ for varying diversity orders. The solid lines show values of β optimized through exhaustive search. It is observed that the value of β changes faster for lower values of L and κ and becomes stable for higher values. This is due to the fact that LOS component becomes dominant with increasing κ, which reduces the effect of deep fades due to multipath component. On the other hand, with increasing L, the variance of received SNR vector γ) decreases. Therefore, the optimal value of β changes with varying κ and L. However, for higher values of L, further improvement in diversity gain with each additional link decreases [3] and therefore change in β also become marginal. To capture the variation in β with respect to κ, we use two models as follows. ) Linear curve fitting model β = aκ + b, 4) where a and b are the fitting coefficients. 2) Exponential curve fitting model β = a + b exp cκ)), 5) where a, b, and c are the fitting coefficients. The fitting coefficients are found using least-squares fit and require that at least two observation points for 4) and three observation points for 5) are available L =,2,3 Optimized 0.0 Linear fit Exponential fit Fig QAM: Optimized value of β with MRC TABLE I FITTING COEFFICIENTS FOR USED MODULATION SCHEMES Mod. BPSK QPSK 6QAM 64QAM L Linear Exponential a b a b c In Fig. 4, we also plot linear and exponential approximation of β as function of κ using markers. The exponential model is a better fit compared to the linear model due to inverse exponential growth of β with increasing κ. But, it requires optimization of three coefficients as compared to two in case of the linear model. In Table I coefficients of linear and exponential model are provided for various modulations and diversity order. Only a few parameters need to be stored for each modulation. From Table I, values of β can be approximated for almost every combination of κ and L. In Section V, the performance of e with linear and exponential approximation of β is compared. V. SIMULATION RESULTS To evaluate the performance of proposed and traditional PLA methods, we use full PHY simulation of an OFDM system. The simulation parameters are given in Table II. We consider Rician fading channel with unit average gain. Note that Rayleigh fading is a special case of Rician fading with κ = 0 and single link communication is a special case of MC with L =. In case of L 2, links are modeled with same channel characteristics but uncorrelated fading. The parameters used to model the channels are also provided in Table II. Values of these parameters are chosen to create a realistic 20

5 PER TABLE II SIMULATION PARAMETERS Parameter Value Modulation schemes BPSK, QPSK, 6-QAM, 64-QAM Bandwidth BW) 0 MHz no. of OFDM subcarriers 28 Subcarrier spacing KHz Carrier frequency 2500 MHz Small scale fading Rician κ = 0 20) Maximum user speed 30 km/h RMS delay spread 200 ns Coherence bandwidth 50%) MHz no. of multi-path components 4 Packet Size 00 bytes Maximum no. of links 5 Diversity combining method MRC AWGN e BPSK QPSK 6-QAM 64-QAM ESNR db) Fig. 5. PER versus ESNR for L = and κ = 0 channel profile for a typical urban outdoor environment. Different fading effects such as fast fading and frequency selective fading are taken into account. We investigate the effect of changing κ and diversity order on PER prediction using, and e based effective SNR mapping. PER can be described in terms of SER as PER = SER) PL, where P L is number of symbols per packet. We consider a fixed packet length of 00 bytes. However, the results can be extended to other packet-lengths using the transformation given in [4]. In order to evaluate the performance of PLA, root-mean-square error ) is used as performance metric. We consider 5 equidistant samples in the range of 0 0 < PER < 0 3 to calculate the. is written as = T γ AWGNi γ effi ) 2, 6) T i= where γ AWGNi is the AWGN SNR in db at the ith sample, γ effi is the ESNR in db at the ith sample and T is the total number of samples used to compute. Fig. 5 plots PER versus ESNR for different modulation orders under Rayleigh fading κ = 0) and L =. The reference curves for AWGN channel are obtained from theoretical expressions [] and represented by solid lines. It is observed that at lower values of PER < 0 2 ), all given methods are considerably accurate except in case of 64-QAM) in PER prediction. However, e is the most accurate for all modulation schemes, while performs the worst. Furthermore, inaccuracy of and increases with modulation order. A look-up table can be generated from Fig. 5 to perform link adaptation against a certain quality of service QoS). It can also be used for system level evaluation without running time consuming link-level simulations. For example, if the desired objective is to achieve maximum throughput with PER < 0 3, choice of modulation is BPSK if db < γ eff 4 db, QPSK if 4 db < γ eff 2 db, 6-QAM if 2 db < γ eff 27 db and 64-QAM for γ eff > 27 db. In case of γ eff < db, LME should assign more links or replace a weak link with a better one. Fig. 6 compares the performance of PLAs in varying channel conditions κ) and diversity order L) for 6- QAM. In Fig. 6a) vs κ is plotted for L =. It can be seen that decreases with increasing κ. This is because LOS component becomes dominant with increasing κ. Thus, channel behavior is closer to AWGN channel resulting in lower mapping error. Furthermore, it is observed that e with optimized β performs the best. The difference in e with optimized β and its exponential fitting is negligible but linear fitting performs slightly worse. It is due to the better approximation of β with exponential model compared to linear as shown in Section IV. Nevertheless, e along its both approximations outperforms the and. The performance of traditional is the worst for κ 5 and slightly better than for higher values of κ. The comparison of vs L using MRC) for κ = 0 is shown in Fig. 6b). It is observed that also decreases with increasing L for all considered algorithms. It is due to the fact that by increasing diversity order variance of the received SNR vector γ is reduced, which results in lower mapping error. Furthermore, it can be seen that e with all its variants outperforms and. However, perform slightly better than for L 4 and worse otherwise. The effect of increasing both κ and L on is shown in Fig. 6c) & 6d). It is apparent that increasing both κ and L improves the performance of PLAs. Moreover, difference among, e and its variants becomes negligible. For higher values of κ and L such as κ 20 and L 5, reaches to a steady state and further improvement is very marginal.

6 e e 0.20 e Linear 0.20 e Linear 0.8 e Exponential 0.8 e Exponential a) vs κ for L = Single link) L Number of links) 4 5 0,05 b) vs L for κ = 0 Rayleigh fading) 0.00 e 0.00 e e Linear e Exponential e Linear e Exponential , L Number of links) 4 5 c) vs L for κ = L Number of links) 4 5 d) vs L for κ = 20 Fig QAM: of various combinations of κ & L VI. CONCLUSION We investigated and compared the performance of traditional PLA methods i.e., ) for a multiconnectivity based OFDM system in terms of. A new robust abstraction method called enhanced exponential effective SNR mapping e) is presented. In order to achieve optimum performance, PLAs require calibration of tuning parameter which depends on channel type, modulation and diversity order. By linear and exponential fitting of the tuning parameter, we proposed extensions of e i.e. e-linear and eexponential. Through simulation results, it is shown that e and its extensions outperform traditional PLAs. Moreover, we evaluated the performance of PLAs in changing diversity order and line of sight conditions κ). It is observed that increasing diversity order or κ improves the mapping performance of PLAs. Future work will focus on evaluating the performance of e in coded modulation and imperfect channel estimation. ACKNOWLEDGMENT This work has been supported in part by the Federal Ministry of Education and Research of the Federal Republic of Germany BMBF) in the framework of the project 5G NetMobil with funding number 6KIS0688. The authors alone are responsible for the content of the paper. REFERENCES [] A. Wolf, P. Schulz, D. Oehmann, M. Doerpinghaus, and G. Fettweis, On the gain of joint decoding for multi-connectivity, in IEEE Global Communications Conference, 207. [2] C. Rosa, K. Pedersen, H. Wang, P. H. Michaelsen, S. Barbera, E. Malkamaki, T. Henttonen, and B. Sebire, Dual connectivity for lte small cell evolution: functionality and performance aspects, IEEE Communications Magazine, vol. 54, no. 6, 206. [3] M. Ehrig, M. Petri, V. Sark, A. G. Tesfay, S. Melnyk, H. Schotten, W. Anwar, N. Franchi, G. Fettweis, and N. Marchenko, Reliable wireless communication and positioning enabling mobile control and safety applications in industrial environments, in 207 IEEE International Conference on Industrial Technology ICIT), 207. [4] R. Hoefel and O. Bejarano, On application of PHY layer abstraction techniques for system level simulation and adaptive modulation in IEEE 802.ac/ax systems, vol. 3, [5] J. Wu, Z. Yin, J. Zhang, and W. Heng, Physical layer abstraction algorithms research for 802.n and LTE downlink, in 200 International Symposium on Signals, Systems and Electronics, vol., Sept 200, pp. 4. [6] J. Francis and N. B. Mehta, -based link adaptation in point-to-point and multi-cell OFDM systems: Modeling and analysis, IEEE Transactions on Wireless Communications, vol. 3, 204. [7] F. Kaltenberger, I. Latif, and R. Knopp, On scalability, robustness and accuracy of physical layer abstraction for large-scale system-level evaluations of LTE networks, in 203 Asilomar Conference on Signals, Systems and Computers, 203. [8] Z. Hanzaz and H. D. Schotten, Analysis of effective SINR mapping models for MIMO OFDM in LTE system, in 9th International Wireless Communications and Mobile Computing Conference IWCMC), 203. [9] X. He, K. Niu, Z. He, and J. Lin, Link layer abstraction in MIMO-OFDM system, in 2007 International Workshop on Cross Layer Design, Sept 2007, pp [0] A. Goldsmith, Wireless Communications. Cambridge University Press, [] J. R. Barry, D. G. Messerschmitt, and E. A. Lee, Digital Communication: Third Edition. Norwell, MA, USA: Kluwer Academic Publishers, [2] S. A. Dyer and J. S. Dyer, Approximations to error functions, IEEE Instrumentation Measurement Magazine, vol. 0, [3] R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, On the LambertW function, Advances in Computational Mathematics, vol. 5, no., Dec 996.