Time-variance of 60 GHz vehicular infrastructure-to-infrastructure (I2I) channel
Introduction
Smart cities are cities on the move; having a mission of delivering people and goods with zero congestion, zero fatality and zero energy wastage. For realizing this mission, a smart city needs an intelligent transport system (ITS) [1]. As far as the communication aspect of ITS is concerned, historically, the urban ITS planners were more concerned about vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) modes of communication [2]. This is because the V2V and V2I channels are essentially wireless and establishing reliable low-latency link over these channels is challenging. Infrastructure-to-infrastructure (I2I) communication is also an integral part of the ITS initiative [3], and due to their rapid, dynamic and non-invasive nature of installation, wireless I2I links are preferred over wired links in several smart-road based ITS applications. In order to implement wireless I2I communication, transceivers may be fitted with different kind of roadside units (RSUs) [4], e.g., short height traffic sign posts, overhead gantries, and cantilever sign supports. The traditional role of these RSUs is to support the basic ITS goals, i.e. driver assistance or traffic management. As the vehicular networks scale up, ITS computations are being shifted to the edge, and the RSUs are going to play bigger roles in the form of edge computing devices [5]. For example, RSUs can form the cloudlet layer of a vehicular fog computing (VFC) architecture [6] for internet of vehicles (IoV) [7], [8].
Vehicular wireless I2I channels realize fixed-to-fixed (F2F) radio communication between two RSUs. For any F2F radio channel with stationary transmitter (TX) and receiver (RX), the time-variance is caused by mobility of the scatterers. These mobile scatterers, say passersby for an indoor scenario, or passing vehicles for an outdoor scenario, cause changes in path lengths in a fading multipath channel. When viewed in frequency-domain, this yields a change in carrier frequency termed as Doppler shift which is proportional to the velocity of the scatterer, and the spectral broadening caused by the time rate of change of the channel is measured with the Doppler spread. Information about Doppler spread is critical for V2V applications such as platooning [9]. In the context of V2I applications, accurate estimation of the Doppler spread is required for designing adaptive transceivers, smart antennas and for determining cellular handoffs [10]. Doppler spread information can also be used for I2I applications like speed estimation. The radar-based solution has a lower latency compared to camera-based solution, owing to the video acquisition and processing time of the later [11]. As the Doppler shift is a linear function of the carrier frequency, it is of greater concern while moving up in the frequency ladder to the millimeter wave (mmWave) regime. The Doppler spread in the unlicensed 60 GHz mmWave band would be 10-30 times of that in the current sub-6 GHz band [12], with a range spanning from 10 Hz to 20 kHz [13] depending on the velocity of the scatterers. Moreover, compared to V2V links, the effect of moving scatterers is much more pronounced in F2F links; walking pedestrians with a velocity order of ∼1 m/s [14] or even the tree leaves fluttering in the wind [15] are important for F2F channel modelling. For highways, the moving vehicles have a velocity an order higher (>10 m/s), and contribute significantly to the time-variance of the roadside wireless I2I links.
Time-variance of the F2F channel due to moving scatterers is described in Fig. 1 and has been discussed in several literature [16], [15], [17], [18], [19], [20], [14], [21], [22] both from the experimental [16], [15], [17] and the theoretical [18], [19], [20], [14], [21], [22] point of views. Early measurements date back to the 90's [16] dealing with human-induced motion in an indoor environment. Later on, experiments were carried out for more specific use cases, like effect of foliage movement in short-range outdoor links [15] or the effect of building sways in rooftop to rooftop links [17]. On the theoretical side, analytical expressions for the auto-correlation function (ACF) and the expression of the Doppler spectra, through a Foutier Transform (FT) of the ACF, is found in [18], [20]. There is another group of research papers [19], [14], [22] which developed the corresponding theory from the ring-of-scatterers geometric model, where each multipath component reaches a static RX from a static TX after being bounced by a moving scatterer. While the angle of arrival (AoA) and the angle of departure (AoD) are uniformly distributed, a series of different distributions, namely, exponential, Gaussian, uniform, triangular and Laplacian, were used to model the scatterer velocity. In [21], an elliptical scattering model is proposed instead of the popular circular ring model. With reference to these published results, contributions of this present text are as follows:
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We present measurement data of a 60 GHz mmWave roadside I2I channel sounding campaign to investigate the Doppler characteristics of the channel. To the best of our knowledge, no related text is available in the open literature. Further, an interpolation method is introduced to calculate accurate value of Doppler spread from the discrete ACF attainable from the measured data set.
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We put forward a novel mathematical model for the ACF which fits well with the measured data and obeys the general trend of theoretical ACFs derived for static TX/RX and moving scatterers. The corresponding Doppler spectra also matches nicely with measurement and is in line with the Doppler spectra trends for F2F channels.
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We explain a framework for simulating time-variant channel impulse response (CIR) for mmWave I2I channels with moving scatterers using Doppler spread information.
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The proposed model is further tested in scenarios other than the measurement scenario (having different scatterer velocity) where too the trend is found to match.
The rest of the paper is organized as follows. Section 2 contains a brief description of the measurement campaign. In Section 3, we present our ACF model, compare it with analytical results from literature and further plot the resultant Doppler spectrum. In Section 4, the CIR simulation framework is developed. Section 5 describes the detailed analytical model for ACF and its comparison with existing analytical models. Finally, section 6 concludes the paper.
Section snippets
Measurement
The I2I measurement campaign was conducted in an urban-highway in Brno, Czech Republic. As shown in the illustration in Fig. 2, the TX antenna is mounted at an elevation of 5 m above the road mimicking an installation on an overhead gantry. It is an open waveguide antenna having a 6 dBi gain on the main lobe which is directed towards the RX. The RX antenna, on the other hand, is a directional horn antenna with 24 dBi gain mounted 1.6 m above the ground level. The height resembles the typical
Discrete auto-correlation function
Under the wide sense stationary uncorrelated scattering (WSSUS) assumption, the auto-correlation function (ACF) is defined as, where denotes the expectation operator.
In order to analyze the time-variance of the I2I channel from the measured CIR, we define a discrete ACF, , which varies with t with respect to the CIR at measurement time , where, is the discrete correlation between
Time variant CIR simulation
In order to simulate time-varying CIR, highlighting only the moving scatterers and suppressing the effect of static scatterers, we relate the correlation of CIR with its delayed version to the correlation of CIRs recorded after the same amount of delay.
Scatterers appear as streaks in the time-variant CIR plot, where each streak is uniquely associated with a scatterer, stationary or non-stationary. We begin our analysis with a situation as shown in Fig. 6, where only one dominant moving
Proposed ACF model and corresponding Doppler spectrum
Analytical models of ACF for situations with static scatterers and moving TX/RX follow the classical Jakes' model. The ACF expressions in these cases involve a Bessel function of first kind which causes ripples and negative values [19, Fig. 2–Fig. 5]. The undulations are also observable irrespective of the mobility distribution of the scatterer for V2V scenarios [14, Fig. 2–Fig. 3]. However, for F2F channels with moving scatterers having various velocity distribution, the ACFs show a common
Conclusion
From measurement based data set, we have developed a simple analytical model of the ACF to characterize the time-variance of an I2I channel operating in the 60 GHz frequency band for an urban highway scenario. To overcome the limitation in the measurement time resolution a linear piece-wise interpolation technique is used to model the ACF and estimate the Doppler spread. The Doppler spread estimated from the ACF can be used to simulate time-variant CIRs and for vehicular speed estimation. The
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the Czech Science Foundation, Project No. 17-27068S Mobile channel analysis and modelling in millimeter wave band, and by the National Sustainability Program under grant LO1401 Interdisciplinary Research of Wireless Technologies. For the research, the infrastructure of the SIX Center was used. The work of A. Chandra is supported by Core Research Grant (CRG), Science and Engineering Research Board, Department of Science and Technology, Government of India, Grant No.
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