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In this paper, we consider the problem of blind identification of FIR systems using the cross-relations (CR) method first introduced in H. Liu et al. (1994). Our contribution in this paper is as follows: (i) we introduce an extended formulation of the CR identification criterion, which generalizes the standard CR criterion used in H. Liu et al. (1994). It can be shown that many existing multichannel blind identification methods belong to the class of generalized CR methods; (ii) we introduce a new identification method referred to as minimum cross-relations (MCR) method, which exploits with minimum redundancy the spatial diversity among the channel outputs. Simulation-based performance analysis of the MCR method and comparisons with CR method are also presented; (iii) Then, we present a modified version of the MCR referred to as the "unbiased MCR" (UMCR) method that leads to unbiased estimation of the channel parameters and better estimation performances without need of noise whitening as in the MCR. (iv) Finally, we discuss the multiinput case and show how additional difficulties arise due to the nonlinear parameterization of the noise vectors in terms of the channel parameters.