A system comprising: a main receiver configured to amplify and downconvert an analog radio frequency receive signal (S RX, RF) to provide a digital receive signal (S RX) at the output of the main receiver; a co-located transmitter comprising a digital predistortion, DPD, subsystem, a digital-to-analogue converter, DAC, 242, an upconversion subsystem, and a power amplifier, the transmitter being configured to upconvert and amplify a digital transmit signal (S TX) provided at an input of the transmitter to provide an analog radio frequency transmit signal (S TX, RF) at an output of the transmitter, the analog radio frequency transmit signal comprising a desired signal in a transmit band of the transmitter and transmitter noise in a receive band of the main receiver; a transmit observation receiver for the receive band configured to sample the transmitter noise in the analog radio frequency transmit signal, wherein the transmitter noise in the analog radio frequency transmit signal is at a much lower power level than the desired transmit signal in the transmit band of the transmitter; and a digital feedforward transmit noise cancellation subsystem configured to: generate a digital transmitter noise cancellation signal representative of the transmitter noise in the receive band of the main receiver at the output of the main receiver based on the digital transmit signal input to the co-located transmitter; and subtract the digital transmitter noise cancellation signal from the digital receive signal output by the main receiver to provide a compensated digital receive signal (S' RX), wherein the digital feedforward transmit noise cancellation subsystem comprises a nonlinear model configured to process the digital transmit signal to generate the digital transmitter noise cancellation signal representative of the transmitter noise in the receive band of the main receiver at the output of the main receiver, and wherein the nonlinear model is a model of a signal path i) from the input of the co-located transmitter including a nonlinearity of the power amplifier of the co-located transmitter ii) through the transmit observation receiver for the receive band iii) to the output of the transmit observation receiver for the receive band and wherein the non-linear model is configured to be trained based on an output signal for the receive band of the main receiver provided by the transmit observation receiver for the receive band. a main receiver configured to amplify and downconvert an analog radio frequency receive signal (S RX, RF) to provide a digital receive signal (S RX) at the output of the main receiver; a co-located transmitter comprising a digital predistortion, DPD, subsystem, a digital-to-analogue converter, DAC, 242, an upconversion subsystem, and a power amplifier, the transmitter being configured to upconvert and amplify a digital transmit signal (S TX) provided at an input of the transmitter to provide an analog radio frequency transmit signal (S TX, RF) at an output of the transmitter, the analog radio frequency transmit signal comprising a desired signal in a transmit band of the transmitter and transmitter noise in a receive band of the main receiver; a transmit observation receiver for the receive band configured to sample the transmitter noise in the analog radio frequency transmit signal, wherein the transmitter noise in the analog radio frequency transmit signal is at a much lower power level than the desired transmit signal in the transmit band of the transmitter; and a digital feedforward transmit noise cancellation subsystem configured to: generate a digital transmitter noise cancellation signal representative of the transmitter noise in the receive band of the main receiver at the output of the main receiver based on the digital transmit signal input to the co-located transmitter; and subtract the digital transmitter noise cancellation signal from the digital receive signal output by the main receiver to provide a compensated digital receive signal (S' RX), generate a digital transmitter noise cancellation signal representative of the transmitter noise in the receive band of the main receiver at the output of the main receiver based on the digital transmit signal input to the co-located transmitter; and subtract the digital transmitter noise cancellation signal from the digital receive signal output by the main receiver to provide a compensated digital receive signal (S' RX), wherein the digital feedforward transmit noise cancellation subsystem comprises a nonlinear model configured to process the digital transmit signal to generate the digital transmitter noise cancellation signal representative of the transmitter noise in the receive band of the main receiver at the output of the main receiver, and wherein the nonlinear model is a model of a signal path i) from the input of the co-located transmitter including a nonlinearity of the power amplifier of the co-located transmitter ii) through the transmit observation receiver for the receive band iii) to the output of the transmit observation receiver for the receive band and wherein the non-linear model is configured to be trained based on an output signal for the receive band of the main receiver provided by the transmit observation receiver for the receive band.