Detection Decide which s m t from the set of s 1 t … s m t signals was transmitted based on observing r r 1 r 2 ⋮ r N , the vector composed of demodulated received signal, that is, the vector of projection of the received signal onto the N bases. m ^ 1 m M r was observed s m t was transmitted Note that r s m ≜ r was observed s m t was transmitted f r | s m s m f r If s m was transmitted 1 M , that is information symbols are equally likely to be transmitted, then 1 m M r s m 1 m M f r | s m Since r t s m t N t for 0 t T and for some m 1 2 … M then r s m η where η η 1 η 2 ⋮ η N and η n 's are Gaussian and independent. r n r n f r | s m 1 2 N 0 2 N 2 n 1 N r n s m n 2 2 N 0 2 m ^ 1 m M f r | s m 1 m M f r | s m 1 m M N 2 N 0 1 N 0 n 1 N r n s m n 2 1 m M n 1 N r n s m n 2 where D r s m is the l 2 distance between vectors r and s m defined as D r s m ≜ n 1 N r n s m n 2 m ^ 1 m M D r s m 1 m M r 2 2 r s m s m 2 where r is the l 2 norm of vector r defined as r ≜ n 1 N r n 2 m ^ 1 m M 2 r s m s m 2 This type of receiver system is known as a correlation (or correlator-type) receiver. Examples of the use of such a system are found here. Another type of receiver involves linear, time-invariant filters and is known as a matched filter receiver. An analysis of the performance of a correlator-type receiver using antipodal and orthogonal binary signals can be found in Performance Analysis.