System for spatially detecting any foreign bodies within a product on the basis of dielectric characteristics of said product, said system comprising: - conveyor means adapted to convey said product through a scanning region along a crossing direction, in a predefined crossing time interval for crossing said scanning region; - a plurality of antennae arranged transversally to said crossing direction and comprising a number N of antennae, wherein each antenna of said plurality of antennae is adapted to operate in the microwave range, and wherein each antenna is adapted to transmit an electromagnetic scanning signal adapted to propagate in said scanning region, so as to diffuse in said product; - processing means adapted to generate a first set of values indicative of the dielectric characteristics of said product based on at least one diffused electromagnetic signal received by at least one antenna of said plurality of antennae, said processing means being adapted to compare said first set of values with a second set of values indicative of the dielectric characteristics of said product in the absence of any foreign bodies, wherein each antenna of said plurality of antennae is adapted to transmit said electromagnetic scanning signal at least once in said crossing time interval, according to a predefined transmission sequence, said system being characterised in that the first set of values is determined by means of said electromagnetic signal diffused by said scanned product, each electromagnetic signal being received by each antenna of said plurality of antennae excluding the self-interaction terms, namely when the transmitting antenna and the receiving antenna coincide, to determine, among all possible pairs of antennae, a first interaction matrix comprising N 2 -N first interaction values expressed as both the phase and the amplitude of said at least one diffused electromagnetic signal, in that the second set of values is determined by means of said electromagnetic signal diffused by said scanned product in the absence of any foreign bodies, each electromagnetic signal being received by each antenna of said plurality of antennae excluding the self-interaction terms, namely when the transmitting antenna and the receiving antenna coincide, to determine, among all possible pairs of antennae, a second interaction matrix comprising N 2 -N second interaction values expressed as both the phase and the amplitude of said at least one diffused electromagnetic signal, and in that said processing means are adapted to compare said first set of values and said second set of values by difference between the first interaction matrix and the second interaction matrix, thereby obtaining a differential interaction matrix indicative of the dielectric characteristics of one or more foreign bodies that may be present in the scanned product. - conveyor means adapted to convey said product through a scanning region along a crossing direction, in a predefined crossing time interval for crossing said scanning region; - a plurality of antennae arranged transversally to said crossing direction and comprising a number N of antennae, wherein each antenna of said plurality of antennae is adapted to operate in the microwave range, and wherein each antenna is adapted to transmit an electromagnetic scanning signal adapted to propagate in said scanning region, so as to diffuse in said product; - processing means adapted to generate a first set of values indicative of the dielectric characteristics of said product based on at least one diffused electromagnetic signal received by at least one antenna of said plurality of antennae, said processing means being adapted to compare said first set of values with a second set of values indicative of the dielectric characteristics of said product in the absence of any foreign bodies, wherein each antenna of said plurality of antennae is adapted to transmit said electromagnetic scanning signal at least once in said crossing time interval, according to a predefined transmission sequence, said system being characterised in that the first set of values is determined by means of said electromagnetic signal diffused by said scanned product, each electromagnetic signal being received by each antenna of said plurality of antennae excluding the self-interaction terms, namely when the transmitting antenna and the receiving antenna coincide, to determine, among all possible pairs of antennae, a first interaction matrix comprising N 2 -N first interaction values expressed as both the phase and the amplitude of said at least one diffused electromagnetic signal, in that the second set of values is determined by means of said electromagnetic signal diffused by said scanned product in the absence of any foreign bodies, each electromagnetic signal being received by each antenna of said plurality of antennae excluding the self-interaction terms, namely when the transmitting antenna and the receiving antenna coincide, to determine, among all possible pairs of antennae, a second interaction matrix comprising N 2 -N second interaction values expressed as both the phase and the amplitude of said at least one diffused electromagnetic signal, and in that said processing means are adapted to compare said first set of values and said second set of values by difference between the first interaction matrix and the second interaction matrix, thereby obtaining a differential interaction matrix indicative of the dielectric characteristics of one or more foreign bodies that may be present in the scanned product.