The conversion from an isotropic antenna
to a half-wavelength dipole through the effective area is not totally accurate for regions close to the near-field, while for larger distances results converge.
where [[parallel] x [parallel].sub.F] is the Frobenius norm, [n.sub.R] the number of receiving antennas, and [H.sub.ref] the channel matrix with the two isotropic antennas
at the BS and the '2-ISO' at the MS, respectively.
Directivity is how well an antenna radiates in a particular direction as compared to an isotropic antenna
. If a test antenna's planar radiation pattern exhibits greater than 0 dBi for 180[degrees] in the forward direction and less than 0 dBi for 180[degrees] in the rearward direction, then the test antenna can transmit farther than an isotropic antenna
in the forward direction and less in the rearward direction.
Thus, the total signal received by an isotropic antenna
near the surface of a flat earth is
In Section 3, we introduce a difference between isotropic antenna
and dipole antenna.
For an isotropic antenna
, the gain is unity, so the effective area is simply [[lambda].sup.2]/2[pi].
A real antenna's gain often is quoted relative to the field produced by a perfectly isotropic antenna
. All physical antennas are directional to some extent so the isotropic ideal is a convenient reference, not something that actually can be constructed.
The design method can be used directly in practice to synthesize reconfigurable concentric ring isotropic antenna
arrays with discrete amplitudes, discrete phases and the control over beams by the modification of the state of the switches.
(Note that the gain can be either positive or negative and that an isotropic antenna
) has unity gain, which is also stated as 0-dB gain.
Where: P = signal strength in W E = electric intensity in V/m A = antenna area in [m.sup.2] [Z.sub.0] = impedance of free space (120[Pi] ohms) G = antenna gain (= 1 for isotropic antenna
) c = speed of light (3 x [10.sup.8] m/sec) F = frequency in Hz.
For example, if a lossless isotropic antenna
had half of its radiation pattern pointed at the earth ([T.sub.b] = 290 K) and the other half pointed at a cool area of space ([T.sub.b] = 100 K), the antenna temperature would be:
Theoretically, non-directional radiation pattern is known as isotropic radiation pattern; but, isotropic antennas
are practically not available.