We present a detailed theoretical analysis of a quantum communication system based on continuous variables. We focus on the use of a quadrature phase-shift keying (QPSK) constellation for bit encoding, and homodyne detection for bit decoding. Moreover, we characterize theoretically and experimentally the homodyne receiver used by the quantum key distribution system, mainly its noise variance for several value of the local oscillator optical intensity. We observe a linear evolution of the shot noise variance with the increase of the local oscillator optical intensity.