A spread spectrum digital communication receiver, of the type comprising an input memory buffer (16) for storing samples of an input signal (y(k)) and a code generator circuit (30) for generating a re-generated user code, incorporates a device (24) for the estimation of a channel delay profile comprises: a basic correlator (32) having a first input (41) for sequentially reading from a memory location of the input memory buffer (16) a plurality of samples of the input signal (y(k)), a second input (43) for receiving from the code generator circuit (30) a re-generated user code, and an output terminal for generating, by means of a correlation operation between the plurality of samples of the input signal and the regenerated user code, a first value of the channel delay profile energy (DP(1)); and a memory controller circuit (36) for addressing said the memory buffer (16) so that the first input (41) of the basic correlator (32) is successively fed with the content of several memory locations of the memory buffer (16), each addressing operation corresponding to a new correlation operation of the basic correlator (32) for the computation of a new value of the channel delay profile energy (DP(1)).