A novel approach to decode information in a chipless RFID tag using signal space representation (SSR) is presented. SSR represents 2b possible tag signatures of a b-bit tag as linear combinations of a small set of L orthonormal basis functions. Each signature encoding a binary bit sequence is represented by a point in an L-dimensional constellation. Prototype 3-bit chipless RFID tags are used to validate the detection technique. The proposed method gives a solid mathematical framework to develop detection and decoding methods for more complicated tag reading scenarios.