**1. Introduction**

As a result of population growth and the consequent expansion of transportation systems, including highways, railways, and airways, environmental noise pollution has been increasing. Noise pollution continues to constitute a major environmental health problem in Europe [1,2]. Among the health effects, annoyance is one of the principal environmental noise [3] issues; however, it is not merely an annoyance, as several works have detected health problems, such as sleep disorders [4], learning impairment [5], and heart diseases [6]. Thus, noise impact is one of the main environmental health concerns [7], and the harmful effects it causes on social and economic aspects have been proved [8].

The European Union reacted to this alarming increase of environmental noise pollution, especially in densely populated cities, with the Environmental Noise Directive 2002/49/EC (END) [9]. In accordance with the END, the CNOSSOS-EU methodological framework aims to improve the

consistency and comparability of noise assessment results across the EU Member States [10] for its application. The main pillars of the END are the following: (i) Determining the noise exposure; (ii) updating information related to the noise available to citizens; and (iii) preventing and reducing environmental noise, where necessary.

Recent studies have showed that the effects of noise on people do not only depend on the level of noise, but also on the type of sound. In fact, in 2018, the WHO incorporated noises, such as leisure noise and wind turbine noise [11]. To accomplish the goal of measuring each type of noise source, the Anomalous Noise Event Detector (ANED) [12] was designed by this team to rule out non-road traffic noise (RTN) events from road traffic noise measurements. The ANED is an algorithm based on the spectral distribution of the different types of RTN and anomalous noise events (ANE) in order to properly identify them and, in this study, it is proven that the sound propagation and its impact on spectral behavior may change its performance [13]. Furthermore, by changing the temporal and spectral distribution of the signal, human perception may also change with respect to a reference noise measured in outdoor environmental conditions [14]. Our team has begun work on the evaluation of the perception of certain types of sound in outdoor conditions [15,16], with promising results that are still under study in the urban environment of Rome.

In an urban environment, a detailed study and simulated reproduction of the propagation of a sound—as it will be perceived by people—is a key factor in the evaluation and prediction of how people will react to the noise [3]; this approximation is called auralization [17]; virtual reality has even been used to reproduce the audio-visual environment [18]. Propagation modelling, with the final goal of auralization, has been proposed in the literature from two points of view: (i) Geometrical acoustics, and (ii) wave-based methods [19]. The analysis detailed in this work is based on the wide-band channel sounding principles which are widely used in communications [20], which demonstrate the usefulness of studying channel fading [21,22]. The techniques of channel estimation, taking into account multi-path propagation and its subsequent coherence bandwidth, have been found to be useful in acoustic propagation environments, mainly in underwater channels [23,24]. Several studies have been conducted in this area, with analysis of the scattering function, multi-path intensity profile, the coherence of an underwater acoustic channel [25], and analysing the impact of the coherence bandwidth on the transmission of pressure waves in image transmission [26].

The authors have made the assumption that the acoustic recordings are wide-band, given that the influence of the channel is in-band frequency selective [19]. The final goal of this preliminary study is to accurately determine whether the frequency selectivity of the channel changes the spectral distribution of several recorded acoustic raw signals [27]. The impulse response of the outdoor urban environment corresponds to the simulation of three different multi-path acoustic channels. We accurately describe each impulse response of the channel and its effects on the spectral distribution of real-life acoustic data collected in the framework of the DYNAMAP pilot project carried out in Milan, focusing on the coherence bandwidth. This work intends to be a first step in the analysis of the frequency selectivity applied to non-traffic-related noise, in order to evaluate the effect of the channel [28] on the spectrum-temporal vision of several real-operation raw signals collected in the Milan pilot of project DYNAMAP [29,30], with the final goal of its impact on auralization.

This paper is structured as follows. Section 2 details the methodology used to conduct this analysis. Section 3 details the conditions under which the acoustic raw data were collected in a real-operation environment. Section 4 details the mathematical models used to simulate the propagation impairments by means of pseudo-noise sequences. Section 5 details the results of the propagation of the simulated channels using real-life data and, finally, Section 6 details the conclusions and future work.

### **2. Overview of Methodology**

The study we present in this paper uses the basis of the application of propagation modelling methods in an outdoor environment with the concept of wide-band sounding using pseudo-noise (PN) sequences, mostly used in channel soundings in communications. The acoustic communication systems are considered to be wide-band, since the channel coherence bandwidth is similar, or even narrower, than the acoustic signal bandwidth.

### *2.1. Outdoor Acoustic Propagation Modelling Basics*

Propagation modelling with auralization purposes can be done both with geometrical acoustics and wave-based methods [19]. Urban sound propagation modelling should take into account the reflections coming from facades and other reflection surfaces, which might be specular or diffuse [31–33]. Each element has its own frequency-dependent reflection properties, which modifies the phase and the amplitude of the acoustic wave, accordingly.

Furthermore, modelling of the diffraction corresponding to the acoustic wave should also be included; in an urban environment, they often occur with multiple building edges, roofs, and corners [34]. Additionally, meteorological conditions will affect at least the long-range sound propagation; wind and turbulence also play a role in this [35]. This brief review of the most relevant elements for modelling the acoustic channel in a city demonstrates its complexity.

This work does not intend to deal with this in depth but, rather, the influence of the most basic parameters of acoustic propagation (e.g., attenuation, reflection, and influence of the medium of propagation) from a real network.

### *2.2. Wide-Band Channel Sounding with PN-Sequences*

Any wide-band sounding focuses on the analysis of time-frequency dispersive features of the channel under study. Time dispersion [20] is the time-spread suffered by any wave when propagated in a medium. This corresponds to the interval of delay that causes that the auto-correlation function of the channel impulse response to differ from zero in the receiver. Frequency dispersion [20] describes the channel variation speed; the Doppler spread is the frequency range of the channel impulse response auto-correlation function that differs from zero [36].

### 2.2.1. PN-Sequence Wide-Band Analysis Proposal

There are several methods to conduct wide-band sounding and channel analysis. In this work, we have used the transmission of PN waveforms [37] with good cyclic cross-correlation characteristics, such as m-sequences [20]. The computation process for the wide-band sounding is detailed in Figure 1.

**Figure 1.** Diagram of the computation process for wide-band channel sounding.

The signal *r*[*n*] in the receiver is correlated with the original PN sequence *Se* shaped by a raised cosine filter with a determined roll-off factor, which is evaluated depending on the application. The correlation function is calculated as:

$$\phi\_{r[n],S\_{\ell}}[n] = \sum\_{k=0}^{N\_{\ell}-1} r[n+k]S\_{\ell}[k],\tag{1}$$

where *Ne* is the length of the PN sequence and *Se* is the sequence filtered with a raised cosine filter. Then, the channel impulse response *h*[*n*, *τ*] can be written as:

$$h[n\_\tau \pi] = \phi\_{r, \mathbf{S}\_\mathbf{t}}[n!\mathbf{N}\_\mathbf{t} + \pi],\tag{2}$$

where *τ* is the variable corresponding to the delay, *l* is the number of chips [20] (i.e., a pulse of a PN sequence), and *Nc* is the number of samples per chip. From Equation (2), we can evaluate the scattering function, which leads us to the multi-path and Doppler spreads caused by the variant channel. The scattering function *Rs*[*τ*, *v*] is calculated as the Fourier transform of the channel impulse response [20]:

$$\mathcal{R}\_h[\underline{\xi}, \underline{\tau}] = \sum\_{\underline{\xi}} h^\*[n, \underline{\tau}] h[n + \underline{\xi}, \underline{\tau}],\tag{3}$$

$$R\_s[\pi, \upsilon] = \sum\_{\mathfrak{F}} R\_h[\xi\_{\nu}^{\pi} \pi] e^{-j2\pi \mathfrak{F} \upsilon}. \tag{4}$$

Both the multi-path spread (*τc*) and the Doppler spread (*vc*) can be computed from the scattering function *Rs*[*τ*, *v*] using a certain observation window, which is wider or narrower depending on the channel variations and the application under study.

### 2.2.2. Underwater Acoustic Channel Sounding

The acoustic communication channel may have a sparse impulse response, where physical paths act as time-varying low-pass filters and where movement introduces both Doppler spread and shift. One of the applications of PN-sequence wide-band sounding is the field of underwater acoustic channel communications. Underwater acoustic channels are usually catalogued as one of the most hostile communications systems [38]. As the bandwidth is extremely limited, an acoustic system may operate in a frequency range between 10 and 15 kHz; although the total bandwidth is low (around 5 kHz), the system is considered wide-band as its bandwidth is not negligible in terms of coherence bandwidth.

Several studies, in which scientists used PN-sequence based systems to conduct sounding in a wide-band acoustic communications underwater channel can be found in literature. In [39], the authors described an underwater sensor network, which they took advantage of to perform acoustic tomography. In [40], the authors described Hermes, an asymmetrical point-to-point underwater acoustic modem designed for short-range operations, and explored the possibility of its possible evolution into a multiple-input-multiple-output (MIMO) device. In [41], the authors conducted a survey in northern Europe, covering the continental shelf, Norwegian fjords, a sheltered bay, a channel, and the Baltic Sea. The sounding measurements were performed in various frequency bands between 2–32 kHz, in order to define a typical acoustic communications channel.
