According to one exemplary embodiment, a method for producing an up-converted and amplified transmission signal comprises performing a logarithmic transformation of an input transmission signal to form a logarithmically transformed transmission signal, adding the logarithmically transformed transmission signal to a logarithmic local oscillator signal to form a sum signal, and performing an antilogarithmic transformation of the sum signal to produce the up-converted and amplified transmission signal. In one embodiment, a log-antilog circuit for producing an up-converted and an amplified transmission signal comprises a transmission log block configured to receive an input transmission signal and to provide a logarithmically transformed transmission signal as a transmission log block output, and an antilog block coupled to the transmission log block. The antilog block is configured to receive a sum signal of the transmission log block output and a logarithmic local oscillator signal.