The Capacity of Wireless Channels: A Physical Approach

In this paper, the capacity of wireless channels is characterized based on electromagnetic and antenna theories with only minimal assumptions. We assume the transmitter can generate an arbitrary current distribution inside a spherical region and the receive antennas are uniformly distributed on a bigger sphere surrounding the transmitter. The capacity is shown to be $(\alpha P/N_0) \log e$ [bits/sec] in the limit of large number of receive antennas, where $P$ is the transmit power constraint, $\alpha$ is the normalized density of the receive antennas and $N_0$ is the noise power spectral density. Although this result may look trivial, it is surprising in two ways. First, this result holds regardless of the bandwidth (bandwidth can even be negligibly small). Second, this result shows that the capacity is irrespective of the size of the region containing the transmitter. This is against some previous results that claimed the maximum degrees of freedom is proportional to the surface area containing the transmitter normalized by the square of the wavelength. Our result has important practical implications since it shows that even a compact antenna array with negligible bandwidth and antenna spacing well below the wavelength can provide a huge throughput as if the array was big enough so that the antenna spacing is on the order of the wavelength.