1. A system, comprising: processor electronics configured to produce a digital transmit signal; a first convertor to convert the digital transmit signal to an analog transmit signal; a power amplifier to amplify the analog transmit signal to produce an amplified analog transmit signal, wherein the power amplifier has one or more nonlinear characteristics; receiver circuitry to receive an analog receive signal in different modes comprising an operational mode and a predistortion training mode, the receiver circuitry being configured to receive the amplified analog transmit signal as the analog receive signal in the predistortion training mode; a second convertor to convert the analog receive signal to a digital receive signal; and a receive filter coupled between the receiver circuitry and the second convertor, wherein the receive filter is configured to operate at a first bandwidth during the operational mode and operate at a second bandwidth during the predistortion training mode, and the second bandwidth being wider than the first bandwidth, wherein the processor electronics are configured to (i) operate the system in the predistortion training mode to gather information to estimate one or more predistortion parameter values, and (ii) use the one or more predistortion parameter values to predistort digital signals to compensate for the one or more nonlinear characteristics of the power amplifier when operating in the operational mode, wherein the information comprises transmit samples that are based on the digital transmit signal and receive samples that are based on the digital receive signal.