In wireless sensor networks or mobile networks, when the physical phenomena does not exist or where the base station is not transmiting any power, the mobiles or sensors will receive only a certain noise level. This noise at proximity sensors can be correlated to each other.
Please anyone can suggest a source/reference about how the spatial correlation between the noise at two different sensors can be modeled? I mean I want to know how much the noise experienced by two sensors is similar or different?
Thanks in advance.
Thanks Mr. Made Yadnya. but I mean which model (if you have any ref.) is suitable for what I asked?
In general, one component of the covariance matrix will be due to noise generated in the receiver, typically modelled as i.i.d. zero-mean proper complex Gaussian, and a second component will be due to thermal background noise impinging on the array, typically spatially colored, and a function of the antenna element gains, polarizations, electrical distance between elements (distance in wavelengths at the receive frequency), and background brightness distribution.
For an M-element array of antennas with equal polarization and rolled-up receiver noise factor F = 10^(0.10*NF), NF = noise figure, the noise covariance relative to kTBF is given by:
Rnn = (1 - (1/F)) * Rbb + eye(M)
where eye(M) is the MxM identify matrix and Rbb is the background noise covariance matrix, given generally by
Rbb(m,n) = 1/(4*pi) * \int_{-pi}^{pi} \int_{-pi/2}^{pi/2} a_m(az,el) * conj(a_n(az,el)) cos(el) T(az,el)/T del daz
where a_m(az,el) is the complex response of the mth antenna element in azimuth (az) and elevation (el) (sometimes known as the array manifold), and where T(az,el) is the noise temperature of the background noise (normalized by system noise temperature “T”, typically 290K). For spatially isotropic background noise and antenna elements, Rbb is given by
Rbb(m,n) = Sa(2*pi*norm(p(m) - p(n)))
where Sa(x) = sin(x)/x is the sampling function and {p(m)} are the element locations in wavelengths. Johnson’s book on antenna array processing derives this result.
The result generalizes to deal with polarization-diverse arrays, which most modern base stations are, in a straightforward manner. Some simplified results can be obtained by assuming azimuthally-omnidirectional noise and so on.
This result also assumes perfectly efficient antennas. If they are not, the result can be adjusted by treating the efficiency factor as a “hot plate” attenuation, which simply adds to the receiver noise figure.
Correction: the general formula is given by
Rnn = (1/F) * Rbb + (1 - (1/F)) * eye(M)
not
Rnn = (1 - (1/F)) * Rbb + eye(M)
where "F" is the rolled-up receiver noise factor.
- Badges
- Science topic