1. A microphone-array-based speech recognition system comprising: a signal separator configured to separate mixed signals input through a plurality of microphone into sound-source signals by an ICA algorithm; a target speech extractor configured to extract one target speech spoken for speech recognition from the sound-source signals separated by the signal separator; and a speech recognition unit configured to recognize a desired speech from the extracted target speech, wherein the target speech extractor is configured to extract feature vector sequences from the separated sound-source signals, calculate logarithm likelihood ratios (LLRs) of the extracted feature vector sequences, calculate a maximum value by using the calculated LLRs, compare the maximum value with a predetermined threshold value, and determine the maximum value to be the target speech if the maximum value is larger than the threshold value.