An　improved　characteristic　waveform　decomposition　based　on　nonnegative　matrix　factorization　was　proposed.　Two　methods　based　on　Bayesian　Ying-Yang　(BYY)　harmony　learning　and　rival　penalized　competitive　learning　(RPCL)　to　compute　factorization　rank　of　nonnegative　matrix　factorization　(NMF)　were　proposed.　Computational　complexity　is　decreased　and　speech　quality　is　not　decreased　obviously.　Mixed　autoregressive　model　for　construction　of　WI　phase　was　proposed　according　to　the　energy　of　CW　and　coding　matrix,　which　improves　the　naturalness.　In　the　end,　a　low　complexity　NMF-WI　speech　coding　at　2　kb/s　was　developed.　NMF　based　on　Kullback-Leibler　divergence　and　Mel　scale　band-partitioning　initialization　used　for　basis　vectors　were　proposed,　and　CWs　were　classified　into　six　based　on　pitch　distribution.　In　CW　factorization,　computational　complexity　dropped　by　10　MOPS.　Speech　quality　is　increased,　and　equivalent　to　2.16　kb/s　NMF-WI　using　4bit　phase　VQ.