Static Skew Compensation in Multi Core Radio Over Fiber Systems for 5G Mmwave Beamforming

Static Skew Compensation in Multi Core Radio over Fiber systems for 5G Mmwave Beamforming

Thomas Nikas (1), Evangelos Pikasis(2), Dimitris Syvridis(1) (1): Dept. of Informatics and Telecommunications National and Kapodistrian University of Athens, [email protected] (2): Eulambia Advanced technologies Ltd, [email protected]

Abstract—Multicore fibers can be used for Radio over Fiber to some kilometers. A tolerant to environmental variations transmission of mmwave signals for phased array antennas in 5G solution is using multi-core fibers (MCFs) for RoF networks. The inter-core skew of these fibers distort the transmission instead of an SMF bundle. MCFs are less prone radiation pattern. We propose an efficient method to compensate the differential delays, without full equalization of the to effective length variations due to temperature and transmission path lengths, reducing the power loss and mechanical stress perturbations. Nevertheless, homogenous complexity. MCFs are reported to exhibit inter-core maximum static skew in the order of 0.5 ns/km, while the temperature imposed Keywords—Radio over fiber, Phased arrays, Beam steering. maximum dynamic skew is 0.06 ps/km/°C [3]. It is obvious from these figures that the major factor affecting the antenna I. INTRODUCTION radiation pattern is the value of the static inter-core skew. The he centralization of the Baseband Units (BBUs) and compensation of the static skew can be performed either in the Tsimplification of the remote radio heads (RRHs) are key optical or the electrical domain. Switchable optical delay lines elements for the forthcoming 5G networks. The bandwidth can be inserted at the output of the OBFN introducing requirements push the operating frequencies to mmwave and additional power loss. benefits from using dense networks of pico and fempto-cells In this paper, we perform theoretical analysis and [1]. Radio over Fiber (RoF) becomes a promising technique to simulations quantifying the MCF static skew effects on the serve network densification and flexible resource allocation, antenna array factor (AF) and RF channel frequency response greatly simplifying the RRHs. The Radio Frequency (RF) and introduce an efficient compensation process, without full chain at RRH amplifies and feeds the antenna, surpassing the equalization of the transmission path lengths. electrical LO and frequency mixing stages. Antenna beam-forming (BF) is utilized to alleviate the free II. ANALYTICAL MODEL space path loss and through wall attenuation, important factors for efficient radio coverage at mmwave frequencies. The In order to evaluate the MCF skew effects on the antenna ( extended bandwidth and narrow beams required for AF we consider N /2 spaced isotropic radiating elements in a throughput maximization imposes the use of true time delay uniform linear array (ULA). Each element exhibits flat (TTD) elements for phase shifting of the currents feeding the frequency response within the signal bandwidth. The antenna to avoid beam squint. Efficient TTD optical beam modulation format proposed for 5G is the orthogonal forming networks (OBFNs) have been proposed which frequency division modulation (OFDM), so the baseband data ¨và©² provide multiple squint-free RF beams [2]. Since the OBFNs ʚ ʛ ? v Ë± signal s(t) is expressed as 1 2 Ɣ Ι# where Xk is ΙͰͯ require thermal stabilization and multiple control signals, it is v more beneficial to locate them at the CU. The modulated the complex symbol modulating the k-th subcarrier, Ts is the optical carriers undergo the required time delays per antenna OFDM symbol duration without the cyclic prefix and NF is the element and then transmitted to the RRHs. The detected IFFT length. The baseband signal is up-converted to mmwave. mmwave signals are amplified and feed the antenna elements. After optical modulation and passing through the OBFN, the In order to preserve the RF phase relations, equal optical and optical signal outputs are launched to N cores of an MCF, electrical path lengths are required after the OBFN. The each core corresponding to an antenna element. After electrical path length equality can be easily achieved since the transmission, the inter-core skew imposes differential time RF circuitry at RRH consists of photodiodes, transimpedance delays i, i=1,..,N between each core and the core with and mmwave amplifiers. Most challenging is the optical path minimum effective path length, which is considered as length equality, taking into account that the distance between reference (zero delay). At RRH, the N photocurrents are read Θͦϐ!Ė/ the CU and the RRHs can range from several hundred meters as ̓ʚ͝Qͨʛ Ɣ̓ͤQ$ *ͧʚͨƎ$ʛ *# , i = 1,.., N where ̓ͤQ$ is the

normalized complex amplitude of the i-th photocurrent, ͌& ͂ Ɣ Ɣ͕͖ȕ ̓ ͙ͯ%ͦ_ʚ!Ėͮ& ĦʛcĜ ͙ͯ%ͦ_!Ė-Ĝ ʚVʛ ͯΘʚ$ͯͥʛϐΡΗΜWt & ͤQ$ ̓ͤQ$ Ɣɳ̓ͤQ$ɳ# and ɳ̓ͤQ$ɳ is the same for all i, if no ͒& $Ͱͥ side-lobe suppression measures are considered. The term In (4), the transmitted QAM symbols ͒& are perfectly Z1',ͤis the phase delay step imposed by the OBFN to steer demodulated at the receiver in the absence of noise. Since ͦ$ is the beam to QͤT The photocurrents feed the isotropic antenna a function of the angle %, the quantity ̿ ʚ͝Qͨʛ ÿ ͦ elements and since the electrical far field of the ͦ ͂ ͊ʚʛ Ɣȕ & ʚWʛ transmitted wave is proportional to ̓ʚ͝Qͨʛ, the received at &Ͱͯ ÿ ͈ ʚ ʛ ͦ 0 distance ri field from the i-th antenna element is ̿ ͝Q ͨ Ɣ is the total received power at %, normalized to the number of ͕̓ʚ͝Q ͨʛ#ͯΘͦ_!Ė-Ĝ , where a symbolizes the linear electrical the used subcarriers N , with N 0 N . Using (4) and (5) we field – antenna current relation and line of sight path loss. The Fu Fu F can calculate the frequency response and the normalized total factor a is assumed time invariant and frequency independent received power at any % and consequently the array within the signal bandwidth, in order to analyze solely the factor͊ʚʛ. effects of inter-core skew on the AF. Since the analytical model does not encounter the effects of noise, the parameters ͕Q ͖ are only scaling factors and can be set to ͕͖ Ɣ S. In all cases, the total transmitted electrical power is normalized to ͦ ȕɳ̓ͤQ$ɳ Ɣ SʚXʛ $Ͱͥ

III. STATIC SKEW PARADIGM AND COMPENSATION ͦ At first, we calculate the transfer function fΙ and the AF ͊ʚʛ for a ULA of N=4 elements, at a carrier frequency of ͚ Ɣ TXGHz. The IFFT length is set to 4096 and the OFDM

signal is composed of 3332 subcarriers with 240 kHz spacing, Fig. 1: The ray tracing model for N=4, ͗ Ɣ !Ė ͎ͧ Ɣ S ʚTVR)f8ʛ, resulting in a signal bandwidth of 800 The receiver antenna is located at distance ͦͤ from the MHz. It should be noted that our analytic model is more transmitter and considered isotropic (fig.1). The distance ͦͤis general in terms of modulation formats and not specifically set to several thousands of free space wavelengths , based on OFDM. On the other hand, OFDM is straightforward ensuring that the receiver is located at the transmitter far field. in acquiring the channel transfer function in frequency The distance of each transmitter antenna element to the domain. The antenna elements are fed with uniform current receiver is distribution and ɳ̓ͤQ$ɳƔS :͈ following the total power ͦ ͦ ϐ ϐ ϐ constraint in (6). The beam steering angle was set to % =0° and ͦ$ Ɣǯͦͤ ƍͭ$ ƎT*ͦͤ *ͭ$ *!-1ʚ ƎʛQ Ǝ ƙƙ ʚS ʛ 0 ͦ ͦ ͦ the inter-core differential delays set to zero. The ZĖ ͂ ͦ % ͊ʚʛ ͭ$ ƔʠTʠ͝Ǝ ʡƎSʡ , ͝ ƔSQUQ͈ (1b) corresponding & at 0 and values are depicted in ͦ ͨ ͦ fig.2 and fig.3 (blue lines). ͂& is flat over the signal The total field ̿ʚͨʛat the receiver antenna is the vector sum of all the fields generated from each transmitter antenna bandwidth and the AF corresponds to a typical ULA of four ( element /2 spaced elements. ͦ ʚ ʛ Next, we calculate ͂& at %0 and ͊ imposing delays %ͦ_!Ė/ ͯ%ͦ_!Ė-Ĝ ̿ʚͨʛ Ɣȕ ͕̓ͤQ$ͧʚͨƎXʛ͙ ͙ ʚTʛ with values of 0.00, 0.44, 0.50, 0.10 ns which correspond to 1 $Ͱͥ ʚͨʛ km of RoF transmission through cores 2, 3, 6, and 7 of the The receiver antenna current can be read as ͖*̿ . The ͦ MCF studied in [3]. Core 2 is considered as reference. ͂& factor ͖ symbolizes the electrical field – antenna current ͊ʚʛ relation, assumed to have the same time invariability and and are depicted in fig.2 and fig.3 with red lines. As ͂ ͦ frequency independence properties of a. After down- expected, & resembles to the transfer function of a frequency selective channel. This is attributed to the vector conversion from fc, analog to digital conversion and applying FFT, the complex baseband received signal ͌ʚͨʛ is summing of fields produced from different antenna elements transformed to the discrete frequency domain: with variable delays, as in the case of multipath propagation. Moreover, the antenna radiation pattern is severely distorted ͯ%ͦ_ʚ!Ėͮ& ĦʛcĜ ͯ%ͦ_!Ė-Ĝ ͌& Ɣ͕͖ȕ ̓ͤQ$͒&͙ ͙ ʚUʛ due to the phase misalignment of the RF signals feeding the $Ͱͥ antenna elements, originated from the differential delays The inter-core skew delays impose phase delays i introduced through the RoF transmission. proportional to the subcarrier frequency. If we consider the The obvious compensation method of the inter-core skew transmitted OFDM symbols as pilot symbols for channel effects is to add optical or electrical delay lines in order to estimation, then a zero forcing frequency domain equalizer perfectly equalize the end to end delays, as stated in the will output the transfer function:

introduction. Nevertheless, the severe radiation pattern uniform current distribution of the antenna elements. distortion can be partially compensated, if we apply phase In order to evaluate the inter-core skew effects on the leads $ to the antenna elements equal to the residuals modulo wireless channel, we calculated the coherence bandwidth ̼. 24 of the differential phase lags introduced by the static inter- The definition of ̼ is based on the complex autocorrelation ͚ Ɣ0#+ʚTZ͚ QTZʛ ͮϦ Ȳ ȳǳ Ȳ core skew at the carrier frequency , $ $ . function ͌, Ɣ ?&ͰͯϦ ϝY ϝ&ͯ, of the frequency response ϝY Ȳ , The compensated transfer function ϝY is: ͤTͭ ͤTͩ [4]. ̼ , ̼ are the values of where ɳ͌,ɳ has decreased to Ħ Ȳ ͯ%ͦ_ʚ!Ėͮ& ĦʛcĜ ͯ%ͦ_!Ė-Ĝ %eĜ ϝY Ɣȕ ̓ͤQ$͙ ͙ ͙ ʚYʛ 0.9 or 0.5 of its maximum value respectively. Setting the $Ͱͥ ͦ summing limits of k to Ə͈0 T and after algebraic ɳϝȲɳ % ͊ʚʛ The calculated Y at 0 and using (7) are depicted in manipulation and approximations we get: fig.2 and fig.3 (black lines). In fig. 3, the array factor shape is Sƍʚ͈ƎSʛʚ͈ ƍSʛ , 0 ͯ%ͦ_ʠ ʡcĜ ͌ Ɣ ȕ͙ Ħ ʚSRʛ restored, with slightly stronger side-lobes and shallower nulls. , ͈ ͦ $Ͱͥ In fig.2, ͂& shows a frequency selective behavior as Next we calculate ɳ͌,ɳ using (10), normalize the results to expected. ɳ͌,Q)ɳƔɳ͌,ɳ ͌ͤ and depict them in fig.4:

Fig. 2: Calculated frequency response. Blue: w/o skew, red: w/ skew, black: w/ compensation Fig. 4: The autocorrelation function ɳ͌,Q)ɳ using eq. 10. Coherence ͤTͭ ͤTͩ bandwidth estimation: ̼ Ȟ UUZ͇͂ͮ , ̼ Ȟ YZ[͇͂ͮ. ͤTͩ The Α value is fairly equal to the signal bandwidth in this particular case, by only compensating the residual $ and

most of the static skew can be left uncompensated. In any case, if the uncompensated static skew limits ̼ to values lower than the signal bandwidth, a partial compensation using electrical or optical means can be applied to restore the coherence bandwidth. ACKNOWLEDGMENT Fig. 3: Calculated array factor. Blue: w/o skew, red: w/ skew, This work was supported in part by the EU project black: w/ compensation blueSPACE (H2020-ICT2016-2, 762055).

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