# 1 Mobile Communication Systems 1 Prof. Carlo Regazzoni Prof. Fabio Lavagetto.

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1 Mobile Communication Systems 1 Prof. Carlo Regazzoni Prof. Fabio Lavagetto

3 Basics of radio propagation The free space attenuation It is the attenuation, only due to the path length and in presence of a free space propagation conditions (no obstacles between the transmitter and the receiver); The free space introduce the following attenuation term: The following expression is defined as available loss for the radio link : Where the two last terms represent the antenna’s gain.

4 Basics of radio propagation Antennas There are two main types of antennas: 1. Isotropic antenna; 2. Directional antenna. The first one irradiates its energy in all spatial directions in the same manner. The second one irradiates the signal in a particular direction. The antenna gain is defined as the ratio between the power radiated by a directional antenna and the one radiated by an isotropic antenna. In general:

5 Introduction Propagation effects: There are four phenomena (reflection, refraction, diffraction, scattering) associated with the propagation of wireless signals which give rise to Multipath; Fading; Delay spread; Doppler shift. The wireless channel is considered to be gaussian, additive, and band-limited (AWGN). Whereas in real world the channel exhibits non gaussian characteristic (not AWGN).

6 The radio channel: multipath propagation èUsually studied channels are characterized by a time-invariant impulse response; èInstead multipath channel is characterised by a time-variant impulse response; èOn the transmission of a single impulse (ideally a dirac delta), the response would be typically a time variant impulse train of impulses dispersed in time (defined as time spread, t) with different attenuations.

7 Multi-path propagation: the channel impulse response c(  t) represents the channel response by choosing time t as the reference time where  represents the delay with respect to the origin of time axis. Let the transmitted signal be represented by s(t) and received signal as x(t). The received signal can be represented as: Where l means the equivalent low pass response.

8 Multi-path effects If the propagating channel is slowly time variant, the value of  n (t) oscillates with time and its variability has small effects; However,  n (t) can vary up to 2  in a time interval if  n (t) varies along a factor 1/f c, which is a very small value. This can be true for bandpass signals modulated around f c  n (t) is a very sensitive parameter that characterizes the time- variant channel even if it has small oscillation; Moreover, the propagation delay related to each path can be often assumed to change in a complete random uncorrelated way (thus it is considered as a random process ) This means that the received signal cannot be modelled as Gaussian random process.

9 The received signal: envelope modelling  The received signal is dispersed in time with varying attenuation and phase. The signal is amplified (if constructive interference occurs) and attenuated (if destructive interference occurs). When the channel impulse response can be modeled as a Gaussian random process the envelope of the received signal can be modeled as: èRician: if the Gaussian process has non-zero mean. Practically, the channel can be modeled with a Line on Sight (LoS) path and other non- line of sight paths. èRayleigh: if the Gaussian process has zero mean. Practically, the channel can be modeled with non-line of sight paths; èNakagami: it is a general case which can be expressed for both Rician and Rayleigh fading with unequal fading amplitudes.

10 Channel correlation functions

11 Time-variant correlation function of the channel FT Time-variant correlation function of the channel FT Doppler power spectrum Scattering function IFT The relation between various considered fourier function

12 The delay spread Delay spread In general, the delayed paths are longer than the LoS path; As consequence the delayed paths arrive at the receiving antenna with different delays and in different time instants; The delay spread can be computed according the following relation: S max = distance covered by the longest path;. S min = distance covered by the shortest path. The major effect due to the delay spread is the presence of Intersymbol Interference (ISI)

13 Narrowband and wideband channel and coherence bandwidth A channel is defined as narrowband if Where T is the symbol time duration; A channel is defined as wideband if The coherence bandwidth is defined according to the following relations: T > T m T < T m

14 Channel frequency selectivity and temporal fading If the channel is frequency selective otherwise is not frequency selective. Channel frequency selectivity

15 Channel frequency selectivity and temporal fading Temporal fading The temporal fluctuations of the amplitude of the received paths are combined at the receiver antenna; This combination can be destructive or constructive

16 Channel frequency selectivity and temporal fading Channel frequency selectivity and fading The frequency selectivity and the temporal fading are two different types of distortion that are usually present on the same channel; On a wideband channel both the effects of frequency selectivity and temporal fading are present; On a narrowband channel the temporal fading is present

17 Time variance of the channel Temporal variation speed of fading depends on the spreading of frequencies due to the time varying nature of the environment; Phase time varying of replicas provides a spectral increase in a transmitted carrier; This phenomena is characterized by doppler spectrum defined previously; The doppler spread depends on: the relative velocity of the receiver with respect to the transmitter; the movements of the objects between the transmitter and the receiver.

18 Time variance of the channel In both cases the doppler spread can be computed as: Path 1Path 2 The coherence time is defined as: