The original q-Markov COVariance Equivalent Realization (q-Markov Cover) method for identification required white noise test signals, which cannot be generated exactly. This paper replaces the unrealizable white-noise signal with a realizable signal (the pseudo-random binary signal, PRBS), and proves that when the period of the PRBS approaches infinity the q-Markov Cover algorithm, operating with PRBS, matches the first q Markov and covariance parameters (as in the original theory with white-noise test signals). The existing q-Markov Cover algorithm will fail to match covariance and Markov parameters exactly due to non-white test signals. The new algorithm will fail to match covariance and Markov parameters exactly due to the finite period of PRBSs. We demonstrate however that the results with PRBSs are far superior to results with ’white’ noise signals. Apparently, the ’non-whiteness’ of the test signal degrades the identification performance worse than the ’non-infinite’ period of the PRBS.