1. A method for detecting transmit symbols at a receiver side in a communications system, comprising: obtaining a channel state information matrix H and a received vector y, so to have a relation that the received vector y is equal to the matrix H multiplied by a transmit symbol vector x, which carries unknown noise n, as y=Hx+n; setting a constraint matrix C, wherein the constraint matrix C is an arbitrary unitary matrix and constrained values f are specified as differences between the transmit symbol vector x and a least-squares (ls) solution x ls a relation of f=x−x ls , wherein the transmit symbol vector x is iteratively sought by successively exchanging linear constraints through selected constraints of a reduced set of i linear constraints from a full set of M constraints, where i<M, and an assignment of the proper constraint values to the selected constraints in each iteration, wherein M is an integer greater than 1 and is equal to a number of antennas or a number of the transmit symbols being detected in one time instant in the communications system, wherein a transverse matrix C T multiplied by a variable vector w is equal to the constrained values f as a product of C T w=f; partitioning the transmit symbol vector x as M-dimensional into an i-dimensional seed symbol vector and a corresponding (M−i)-dimensional seed complementary symbol vector, wherein the seed symbol vector is inherited from an estimate in a previous (i−1)-th iteration and the corresponding seed complementary symbol vector is to be generated in a current i-th iteration; in each iteration, forming a new estimate of a M-dimensional augmented symbol vector from a concatenation of the i-dimensional seed symbol vector and the (M−i)-dimensional seed complementary symbol vector, and a matrix A equal to a product of H and C T as A=HC T is multiplied by the variable vector w to have a product of Aw and a minimum of an absolutes square of the product of Aw as min w ⁢  Aw  2 to determine the variable vector w as solved; and calculating the constrained values f by the product of C T w=f; and obtaining the symbol vector x, based on the relation of f=x−x ls .