1. A method for generating soft output for a received signal in a multiple input, multiple output (MIMO) receiver, comprising: estimating a channel matrix H from signals y received at a plurality of antennas via corresponding channels; decomposing, using M parameters, the channel matrix H to obtain a unitary matrix Q and upper triangular matrix R; determining, in an M parameter QR decomposition (QRD-M) detection unit, a set of candidate decision vectors based on the matrices Q and R and the received signals y; determining, in a Markov chain Monte Carlo (MCMC) detection unit, an important subset of the set of candidate decision vectors; and determining, in a log-likelihood ratio unit, a soft output using the important subset, wherein a relation between transmitted signals d and the received signals y is y=Hd+n, where y ε C N r is a vector of the received signals, d ε C N t is a vector of the transmitted signals, H ε C N r ×N t is the channel matrix in which an element h i,j is an impulse response of the channels between an i th receive antenna and a j th transmit antenna, and n ε C N r is a noise vector, wherein the decomposition is performed over the channel matrix as 
 r=Q H y=Q H Hd+Q H n=Rd+Q H n, where H=QR, Q ε C N r ×N r is the unitary matrix and R = [ T 0 N r - N t , N t ] , where T ε C N t ×N t is the upper-triangular matrix, and wherein the MCMC detection unit determines a Euclidean distances according to  ω  2 = ∑ k = 1 N t ⁢  r k - ∑ l = k N t ⁢ t k , l ⁢ d l  2 , where |ω| 2 is the Euclidean distance, r k , t k,l ,d l are the entries of vectors r,d and matrix T.