  Using ideas from Chu and Bode/Fano theories, we characterize the maximum
achievable rate over the single-input single-output wireless communication
channels under a restriction on the antenna size at the receiver. By employing
circuit-theoretic multiport models for radio communication systems, we derive
the information-theoretic limits of compact antennas. We first describe an
equivalent Chu's antenna circuit under the physical realizability conditions of
its reflection coefficient. Such a design allows us to subsequently compute the
achievable rate for a given receive antenna size thereby providing a physical
bound on the system performance that we compare to the standard
size-unconstrained Shannon capacity. We also determine the effective
signal-to-noise ratio (SNR) which strongly depends on the antenna size and
experiences an apparent finite-size performance degradation where only a
fraction of Shannon capacity can be achieved. We further determine the optimal
signaling bandwidth which shows that impedance matching is essential in both
narrowband and broadband scenarios. We also examine the achievable rate in
presence of interference showing that the size constraint is immaterial in
interference-limited scenarios. Finally, our numerical results of the derived
achievable rate as function of the antenna size and the SNR reveal new insights
for the physically consistent design of radio systems.
