A system for non-linear digital self-interference cancellation comprising: • a pre-processor communicatively coupled to a digital transmit signal of a full-duplex wireless communication system that generates a first pre-processed digital transmit signal from the digital transmit signal; the system being characterized in that it further comprises: • a non-linear transformer that transforms the first pre-processed digital transmit signal into a non-linear self-interference signal according to a transform configuration, wherein the non-linear transformer comprises a first transform path and a second transform path, wherein the first transform path includes a model component that generates a first order non-linear self-interference signal component from the first pre-processed digital transmit signal, wherein the second transform path includes an upsampler that upsamples the first pre-processed digital transmit signal by a factor of three to create an upsampled signal, a model component that generates a third order non-linear self-interference signal component from the upsampled signal, a low-pass filter that removes undesired high frequency components from the third order non-linear self-interference signal component, and a downsampler that downsamples the third order non-linear self-interference signal component by a factor of three; • a transform adaptor that sets the transform configuration of the non-linear transformer; and • a post-processor that adds the first order and third order non-linear self-interference signal to a digital receive signal of the full-duplex wireless communication system. • a pre-processor communicatively coupled to a digital transmit signal of a full-duplex wireless communication system that generates a first pre-processed digital transmit signal from the digital transmit signal; the system being characterized in that it further comprises: • a non-linear transformer that transforms the first pre-processed digital transmit signal into a non-linear self-interference signal according to a transform configuration, wherein the non-linear transformer comprises a first transform path and a second transform path, wherein the first transform path includes a model component that generates a first order non-linear self-interference signal component from the first pre-processed digital transmit signal, wherein the second transform path includes an upsampler that upsamples the first pre-processed digital transmit signal by a factor of three to create an upsampled signal, a model component that generates a third order non-linear self-interference signal component from the upsampled signal, a low-pass filter that removes undesired high frequency components from the third order non-linear self-interference signal component, and a downsampler that downsamples the third order non-linear self-interference signal component by a factor of three; • a non-linear transformer that transforms the first pre-processed digital transmit signal into a non-linear self-interference signal according to a transform configuration, wherein the non-linear transformer comprises a first transform path and a second transform path, wherein the first transform path includes a model component that generates a first order non-linear self-interference signal component from the first pre-processed digital transmit signal, wherein the second transform path includes an upsampler that upsamples the first pre-processed digital transmit signal by a factor of three to create an upsampled signal, a model component that generates a third order non-linear self-interference signal component from the upsampled signal, a low-pass filter that removes undesired high frequency components from the third order non-linear self-interference signal component, and a downsampler that downsamples the third order non-linear self-interference signal component by a factor of three; • a transform adaptor that sets the transform configuration of the non-linear transformer; and • a post-processor that adds the first order and third order non-linear self-interference signal to a digital receive signal of the full-duplex wireless communication system.