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.