Analysis and experimental evaluation of the frequency response of an indoor radiating cable in the UHF band
© Sesena-Osorio et al.; licensee Springer. 2015
Received: 21 May 2014
Accepted: 6 January 2015
Published: 10 February 2015
We present the modeling of the frequency response of the channel for a radiating cable system by using an autoregressive model for an indoor environment. The coefficients of the autoregressive model are determined from the experimental channel frequency response. Measurements were carried out in an indoor environment, in particular on the second floor of a university building in the frequency range of 1.3 to 1.8 GHz by using a vector network analyzer. It is demonstrated that the use of a second-order model provides a better representation of the behavior of the channel. In this context, the coherence bandwidth and the rms delay spread show dependence with the receiver position along the radiating cable length. This dependence is crucial and must be taken into account in the design and study of broadband systems with mobility because the rms delay spread and coherence bandwidth are used to describe the time dispersion and the frequency selectivity of the multipath fading channels, respectively.
The improvement in wireless technology systems and devices has contributed to a greater concentration of mobile devices in specific locations as well as an increase in the data transmission rate. Consequently, wireless service providers and researchers are becoming more interested in obtaining the best possible performance of wireless systems under such conditions. In this context, radiating cables have been used as alternative distributed antenna systems in order to obtain optimal coverage levels in any underground or closed environment [1-4]. However, it is well-known that, for indoor wireless communications, constructive and destructive interferences have a crucial effect on the signal being transmitted. Therefore, knowledge of the behavior of the wireless channel is essential for planning and studying of any wireless systems.
A radiating cable or leaky feeder is a coaxial cable where the outer conductor has been slotted, allowing radiation to occur along the cable length for uniform coverage. Thus, radiating cables are used to distribute radio waves in sites where common antennas fail, besides being used as part of wireless systems such as radio detection systems and wireless indoor-positioning systems [5,6]. In recent years, the use of radiating cables has increased especially to provide cellular coverage in train and underground stations for which either macrocell penetration or an indoor distributed antenna system is not suitable. The coverage footprint provided by a radiating cable can normally be better shaped, thus filling in coverage holes in specific corridor scenarios much better than antennas and better containing leakage . As prices are coming down in the manufacturing and installation of radiating cables, indoor radio solutions that include radiating cable are thus a very viable alternative nowadays. However, as stated in , antennas are more suitable to provide coverage in areas where the installation of radiating cables is much harder or unfeasible. On the other hand, the installation of radiating cables is a more sophisticated procedure and more costly than that of antenna installation. If coverage is to be focused on a specific area, the radiation characteristics of directional antennas can be utilized to maximize such coverage in the desired location, something that is much harder to achieve with the use of radiating cables. In summary, although radiating cables are a good alternative for some specific indoor environments such as corridors, there are other instances where antennas still are the preferred choice.
In order to accurately estimate the coverage and expected data rate that could be obtained using a radiating cable system, channel modeling needs to be performed. Narrowband modeling will allow engineers and designers to estimate local mean coverage if the radiating cable is installed in a venue. This issue is particularly important for voice systems, where full received signal strength and signal-to-interference and noise ratio (SINR) are important parameters that affect the performance of the system. However, if broadband data communications are to be deployed, it is very important that wideband channel characteristics be modeled, and hence, the maximum achievable data rate can be determined. Herein lies the main focus of this paper.
In , a typical narrowband propagation model for radiating cable systems is reported which takes into account the coupling and longitudinal losses of the radiating cable. At the same time, the slow and fast variations of the received signal levels are modeled by a log-normal distribution and a Rayleigh or Rician distribution, respectively. In the case of the signal being considered as a narrowband signal, such mentioned propagation models could be sufficient to design and study a radiating cable system. However, if a digital communication is being considered with high speed of data transmission, it is necessary to study the frequency response and the rms delay spread of the channel. In this context, little attention has been paid to such issues in radiating cable systems. For example, in  and , only the rms delay spread values have been reported and not it’s modeling. The frequency response modeling allows classifying the channel as frequency selective or flat fading channel by calculating the coherence bandwidth, and the rms delay spread allows knowing the limits of the transmission rate. This fact is very important in most modern technologies because such technologies require wide bandwidths and high-transmission rate. In summary, a wideband propagation model allows knowing some system characteristics, for example, the frequency selectivity, intersymbol interference, and error floor.
The modeling of wideband channel can be developed by using time-domain or frequency-domain measurements, where the direct measurement of the impulse response or the frequency response of the channel is carried out, respectively. Time-domain measurement methods require various parameters to describe wideband channels but do not provide information of the signal phase. In contrast, using a frequency-domain measurement system, the magnitude and phase of the signal are known. Furthermore, an autoregressive model can be used to represent the channel with fewer parameters than in the case of time-domain measurements. For indoor measurements, the frequency-domain approach yields very good results, having limited applicability for outdoor measurements since the coax cable length is a strong limitation for this.
To the best of the authors' knowledge, we report for the first time the autoregressive modeling of the frequency response of channel for a radiating cable system, as well as the rms delay spread (τ rms) which showed a dependency with the receiver position along the cable length. Autoregressive (AR) models in the frequency domain for indoor radio propagation have been reported in different studies [9,10]; however, such studies were based on wireless systems where the receiver and transmitter used conventional antennas. In contrast, the results of this work are for a wireless system which uses a radiating cable. Results showed that a second order of the autoregressive model gave the best fit to the complementary cumulative distribution of the coherence bandwidth (the 3-dB width of the frequency correlation function) and showed a better description of the signal delay.
The paper is organized as follows: Section 2 gives the methodology used in this study as well as the general description of the measurements and the autoregressive modeling of the channel frequency response. Section 3 is devoted to the analysis of results along with a brief discussion about the importance of the dependency of rms delay spread with the receiver position along the cable length. Finally, conclusions are given in Section 4.
2 Methodology, description of measurements, and the frequency-domain channel modeling
First, the experiment was designed by selecting the components, the configuration of the devices, and the sites or regions available for the development of frequency response measurements. Secondly, the assembly of the measurement system was made as well as its respective calibration. Then, the measurements were carried out and their positions were recorded. Once the frequency responses were obtained, the coherence bandwidth and the impulse response were calculated by using the autocorrelation function and the inverse discrete Fourier transform, respectively. The rms delay spread was then calculated by using the impulse response. The model parameters were obtained from measurements, and the autoregressive model was applied in each room. Finally, simulated frequency responses and coherence bandwidth were calculated.
Frequently, there is an inverse relationship between the rms delay spread and the coherence bandwidth of the channel. The coefficients of the inverse relationship are calculated by a linear regression (on logarithmic scales) between the rms delay spread and the 3-dB width of the correlation function of the frequency response. This is further expanded in Section 3.
2.2 Description of the radiating cable system
The measurements were achieved with f 0 = 1,300 MHz and Δf = 0.5 MHz. The frequency response consists of 1,000 complex samples (N). Around 30 m of flexible low-loss coax cable (LMR-400 from Times Microwave Systems, Wallingford, CT, USA) were used to connect the receiver antenna with port 2 of the network analyzer. A low-noise amplifier (ZRL-2400 from Mini-Circuits, Brooklyn, NY, USA) was used between the wideband omnidirectional antenna of the receiver and the flexible low-loss coax cable. Additionally, the receiver antenna was placed 1.5 m high on a trolley which carried the power source for the low-noise amplifier.
The frequency response measurements were collected at fixed locations inside each room on the second floor of the building. In each room, around 120 frequency response samples were measured and recorded, and the separation between the frequency response samples was 10 cm. These samples were distributed throughout the test area. In the corridor case, samples were collected along three parallel paths to the second segment of the radiating cable. The surrounding environment was kept stationary during the measurements by avoiding the movement of objects and the presence of people.
2.4 Frequency-domain channel modeling
In general, the order of the model depends on the measured site; however, the fifth-order process has been used as an upper bound .
3 Results and analysis
Figure 10 corresponds to the normalized impulse responses which were obtained along a parallel route to the radiating cable in the corridor. It illustrates how the impulse response starts with different delays. In the case of x = 5 m and y = 14 m, the impulse response starts around 15.5 ns; on the contrary, for x = 25 m and y = 14 m, the impulse response starts around 108 ns (refer to Figure 3 for both cases). Furthermore, the impulse responses finish in a similar time. This fact explains the different mean values obtained from the rms delay spread for every room (Figure 6). The former corresponds to the area of the radiating cable which is near to the feeder and the latter corresponds to the opposite situation.
It was shown in  that without diversity or equalization, the ratio of the rms delay spread to symbol duration in a digital transmission must be kept below 0.2 to have a tolerable intersymbol interference. Thus, assuming this criterion, in Room 2202, the maximum value of τ rms was 54.4 ns, and therefore, the channel can support a data rate up to 3.6 Mb/s. Meanwhile in Room 2207, the maximum value of τ rms was 28.5 ns; hence, the channel can handle a data rate up to 7 Mb/s. Such a situation must be considered in the design of modern wireless systems.
At the beginning of this paper, it was pointed out that radiating cables can be used as part of wireless systems such as in distribution systems, by providing coverage for in-building cellular scenarios, as well as in radio detection and wireless indoor-positioning systems. Nevertheless, modern digital communication systems require broadband to be deployed. In this context, the study and design of any wireless system needs to know the multipath fading behavior of the channel in order to obtain an optimal performance of the system.
The coherence bandwidth and the rms delay spread (τ rms) were obtained by measuring the frequency response of the channel, and it was demonstrated that there is dependence between τ rms and the receiver position along the cable length. This dependence must be taken into account in the design of broadband systems with mobility. Furthermore, such dependence can be used for wireless localization applications in indoor environments.
Moreover, an AR model for the frequency response was carried out. Complementary cumulative distribution functions showed that a second-order AR model gives the best fit at the 3-dB width of the frequency correlation function and showed a better-defined behavior in the complex plane. This better-defined behavior can be useful in the computer simulation of the channel or in the designing of simulation tools which allow evaluating specific systems under different schemas of modulation, coding, and equalization.
As it is known, the most modern wireless technologies are based on models because of the random variations of the wireless channel. Thus, the design and study of radiating cable systems can be carried out by using autoregressive modeling of frequency response; however, it is necessary to implement more studies in different environments in order to compare and verify the channel behavior obtained in this study, including the effects of moving scatters.
This work was partially supported by the Mexican Consejo Nacional de Ciencia y Tecnología (CONACYT), Project No. 154691. One of the authors, Jorge A. Seseña-Osorio wishes to thank the CONACYT for Scholarship Number 34612.
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