A wireless transmitter comprising: a. a module configured to modulate input data bits into data symbols according to a predetermined modulation scheme, and group the data symbols into one or more precoding blocks; b. at least one symbol insertion module, each configured to insert one or more cancellation symbols into a corresponding precoding block in the data domain prior to precoding the corresponding precoding block; c. at least one precoding module, each configured to precode the corresponding precoding block to a precoded block; d. a subcarrier insertion module configured to concatenate the one or more precoded blocks and to insert at least one cancellation subcarrier into the concatenated precoded blocks to form a precoded OFDM symbol in the frequency domain; e. a module configured to process the precoded OFDM symbol so as to reduce the out-of-band power emitted by the transmitter in transmitting the precoded OFDM symbol, wherein the processing uses the inserted cancellation symbols and cancellation subcarriers; and f. a module configured to transmit the processed precoded OFDM symbol over a wireless communication channel; wherein the module configured to process the precoded OFDM symbol is configured to: construct an attenuation matrix from one or more out-of-band frequencies at which the emitted power is to be forced to zero; construct a distribution matrix from the locations of the cancellation symbols and the cancellation subcarriers within the precoded blocks and the precoded OFDM symbol respectively; compute an out-of-band emission reduction matrix from the attenuation matrix and the distribution matrix; and subtract the product of the out-of-band emission reduction matrix and the precoded OFDM symbol from the precoded OFDM symbol. a. a module configured to modulate input data bits into data symbols according to a predetermined modulation scheme, and group the data symbols into one or more precoding blocks; b. at least one symbol insertion module, each configured to insert one or more cancellation symbols into a corresponding precoding block in the data domain prior to precoding the corresponding precoding block; c. at least one precoding module, each configured to precode the corresponding precoding block to a precoded block; d. a subcarrier insertion module configured to concatenate the one or more precoded blocks and to insert at least one cancellation subcarrier into the concatenated precoded blocks to form a precoded OFDM symbol in the frequency domain; e. a module configured to process the precoded OFDM symbol so as to reduce the out-of-band power emitted by the transmitter in transmitting the precoded OFDM symbol, wherein the processing uses the inserted cancellation symbols and cancellation subcarriers; and f. a module configured to transmit the processed precoded OFDM symbol over a wireless communication channel; construct an attenuation matrix from one or more out-of-band frequencies at which the emitted power is to be forced to zero; construct a distribution matrix from the locations of the cancellation symbols and the cancellation subcarriers within the precoded blocks and the precoded OFDM symbol respectively; compute an out-of-band emission reduction matrix from the attenuation matrix and the distribution matrix; and subtract the product of the out-of-band emission reduction matrix and the precoded OFDM symbol from the precoded OFDM symbol.