A method of sensing a target in a target detection system comprising processing circuitry, a multiplexer coupled to the processing circuitry and to a plurality N T of transmit antennas forming a sparse transmit uniform linear array, ULA, the multiplexer being configured to generate multiplexed transmit signals ( T 1...T NT) based on signals from a local oscillator, the processing circuitry being further coupled for receiving signals via a receiver including a plurality N R of receive antennas forming a dense receive ULA, the method comprising: generating transmit signal vectors x, where each transmit signal vector x is given by x = s ⊗ p, where s is a signal modulation vector given by s ∈ Ω 0 I c N T × 1, where the set Ω 0 = u Ω comprises the zero to model the multiplexing, where Ω = {1, -1, j, -j} representing Quadrature Phase Shift Keying, QPSK, modulation and l c is the number of Frequency Modulated Continuous Wave, FMCW, pulses in a train from the local oscillator, and p is a pulse vector representing the FMCW pulses and whose i s -th entry is given by p i s = exp j ω 0 T s i s + B 2 T C T s i s 2 where ω 0 is angular frequency, where ω 0 = 2π f 0, and is proportional to the center frequency of the FMCW pulses, T s is the sampling time of the receiver, l s is the total number of samples, and B is the bandwidth of the FMCW pulses; transmitting the plurality of transmit signals defined by the transmit signal vectors x via the transmit antennas so as to form a general radiation pattern corresponding to a block circulant probing signal matrix; receiving via the receive antennas receive signals resulting from backscattering of the plurality of transmit signals transmitted towards K targets; and processing the received reflection signals to determine the presence, range and/or angular position of a target within a field of view of the transmit antennas; wherein transmitting the plurality of transmit signals includes subjecting each of the transmit signal vectors to a target transmit steering matrix A Tκ, and wherein the general radiation pattern corresponds to the block circulant probing signal matrix through the following being satisfied: min N T × I c ‖ P d − A TM H R s A Tκ ‖ F 2 s. t. ‖ s ̃ i c ‖ = N c where s̃ i c is the signal modulation vector for the i c -th pulse, where P d is a desired radiation pattern given by P d ( φ κ, φ M) = P d ( φ) if φ κ = φ M, else P d ( φ κ, φ M) = 0, where φ κ defines the κ -th target angle of arrival and is mapped to the matched filter output φ M of a matched filter of the receiver, where A TM is a matched filter transmit steering matrix, where R s is a covariance matrix of a probing signal matrix S̃ representing the transmit signals, where S̃ = ( s̃ 1 ··· s̃ i c, ··· s̃ I c), and N c is the number of modulated channels of the sparse transmit ULA. generating transmit signal vectors x, where each transmit signal vector x is given by x = s ⊗ p, where s is a signal modulation vector given by s ∈ Ω 0 I c N T × 1, where the set Ω 0 = u Ω comprises the zero to model the multiplexing, where Ω = {1, -1, j, -j} representing Quadrature Phase Shift Keying, QPSK, modulation and l c is the number of Frequency Modulated Continuous Wave, FMCW, pulses in a train from the local oscillator, and p is a pulse vector representing the FMCW pulses and whose i s -th entry is given by p i s = exp j ω 0 T s i s + B 2 T C T s i s 2 where ω 0 is angular frequency, where ω 0 = 2π f 0, and is proportional to the center frequency of the FMCW pulses, T s is the sampling time of the receiver, l s is the total number of samples, and B is the bandwidth of the FMCW pulses; transmitting the plurality of transmit signals defined by the transmit signal vectors x via the transmit antennas so as to form a general radiation pattern corresponding to a block circulant probing signal matrix; receiving via the receive antennas receive signals resulting from backscattering of the plurality of transmit signals transmitted towards K targets; and processing the received reflection signals to determine the presence, range and/or angular position of a target within a field of view of the transmit antennas; wherein transmitting the plurality of transmit signals includes subjecting each of the transmit signal vectors to a target transmit steering matrix A Tκ, and wherein the general radiation pattern corresponds to the block circulant probing signal matrix through the following being satisfied: min N T × I c ‖ P d − A TM H R s A Tκ ‖ F 2 s. t. ‖ s ̃ i c ‖ = N c where s̃ i c is the signal modulation vector for the i c -th pulse, where P d is a desired radiation pattern given by P d ( φ κ, φ M) = P d ( φ) if φ κ = φ M, else P d ( φ κ, φ M) = 0, where φ κ defines the κ -th target angle of arrival and is mapped to the matched filter output φ M of a matched filter of the receiver, where A TM is a matched filter transmit steering matrix, where R s is a covariance matrix of a probing signal matrix S̃ representing the transmit signals, where S̃ = ( s̃ 1 ··· s̃ i c, ··· s̃ I c), and N c is the number of modulated channels of the sparse transmit ULA.