We investigate the problem of sum-rate maximization of a secondary link of full-duplex generalized frequency division multiplexing (GFDM) radios operating over a spectrum hole, which is surrounded by two active primary adjacent channels. Thus, the secondary transmissions must be below an adjacent channel interference (ACI) threshold. In-band distortions and several interference terms are also caused by phase noise, in-phase (I) and quadrature (Q) imbalance, carrier frequency offset (CFO) and the nonlinear power amplifier (PA). Analog domain and digital domain self-interference (SI) cancellation is also considered. We study the two cases of two independent oscillators for local transmitter and receiver and one common shared oscillator. We derive the powers of residual SI, desired signal, interference signal and noise, signal-to-interference-plus noise ratio (SINR) and the power spectral density (PSD) of the transmit signal. By using successive convex approximations, we solve the sum-rate maximization problem. Finally, we show that in full-duplex radios under certain RF impairments, GFDM may double the sum rate compared to that of orthogonal frequency division multiplexing (OFDM). INDEX TERMS Full-duplex radios, generalized frequency division multiplexing (GFDM), cognitive radio, spectrum hole, radio frequency (RF) impairments, rate optimization.