System for the multi-distributed amplification of a communication signal comprising at least a plurality N of input channels i connected to an input Butler matrix capable of delivering at the output N distributed signals, a plurality N of amplifiers capable of receiving at the input said distributed signals and capable of producing at the output N amplified and phase-shifted signals each of a complex gain G i and an output Butler matrix capable of receiving at the input said amplified signals and capable of producing at the output N output signals, said system being characterised in that it also comprises: ∘ a generator of reference signal of known amplitude and known phase, said reference signal being provided on a single one of said input channels of said system, said reference signal being transmitted simultaneously with said communication signal to be amplified, ∘ a measuring device for errors S of amplitude and phase of each of said output signals of said system, said device being capable of performing a coherent demodulation of the amplified signal in order to extract said reference signal from said communication signal and estimate said amplitude and phase errors impacting the reference signal, ∘ a signal processing device receiving at the input said amplitude and phase error measurements S, and producing, on the basis of said measurements S, for each channel i of said system, an amplitude a' i and phase Φ' i compensation calculated so as to minimise the differences between the complex gain G i of the amplifier of each channel i and the complex gain G 1 of the amplifier of a reference channel from among the channels of said system, ∘ a phase/amplitude compensating device, inserted between said input Butler matrix and the plurality of amplifiers and adapted to correct each of the channels i of said system on the basis of the received values of the amplitude a' i and phase Φ' i compensation. ∘ a generator of reference signal of known amplitude and known phase, said reference signal being provided on a single one of said input channels of said system, said reference signal being transmitted simultaneously with said communication signal to be amplified, ∘ a measuring device for errors S of amplitude and phase of each of said output signals of said system, said device being capable of performing a coherent demodulation of the amplified signal in order to extract said reference signal from said communication signal and estimate said amplitude and phase errors impacting the reference signal, ∘ a signal processing device receiving at the input said amplitude and phase error measurements S, and producing, on the basis of said measurements S, for each channel i of said system, an amplitude a' i and phase Φ' i compensation calculated so as to minimise the differences between the complex gain G i of the amplifier of each channel i and the complex gain G 1 of the amplifier of a reference channel from among the channels of said system, ∘ a phase/amplitude compensating device, inserted between said input Butler matrix and the plurality of amplifiers and adapted to correct each of the channels i of said system on the basis of the received values of the amplitude a' i and phase Φ' i compensation.