Receive Antenna Gain of Uniform Linear Arrays of Isotrops

The receive antenna gain of an antenna array critically depends on the receiver noise covariance. Receiver noise essentially originates from two sources: the receive low-noise amplifiers (LNA), and background radiation that is received by the array. In case that the LNAs are the sole origin of noise, it is state of the art to argue that the receiver noise is spatially uncorrelated, for noise originates in components of physically separate LNAs. However, this argument ignores coupling between antennas due to their spatial proximity, and moreover the coupling introduced by the impedance matching network which is located between the antenna outputs and the LNA inputs. Because of these coupling effects, the receiver noise is usually spatially correlated even when independent LNAs are the sole source of noise in the system. The noise covariance, depends on the following four factors: 1) antenna spacing of the array, 2) properties of the impedance matching network, 3) noise-resistance of the LNAs, 4) intensity of received background noise with respect to noise generated by the LNAs. Taking these issues into account, we derive, in this paper, the receive antenna gain of a uniform linear antenna array of isotrops in closed form. It turns out that the receive antenna gain can become much larger than the number of antennas. For the case of low noise-resistance, and low relative intensity of received background noise, we show that the receive antenna gain can even grow exponentially with the number of antennas. These results are exciting, because they imply that the performance of communication systems which use multiple receive antennas can be much better than previously reported.