ABSTRACT
The concept of signal space has its roots in the mathematical theory of inner product spaces known as Hilbert spaces. Many books on linear systems touch on the subject of signal spaces in the context of Fourier series and transforms. The applications of signal space concepts in communication theory find their power in the representation of signal detection and estimation problems in geometrical terms, which provides much insight into signaling techniques and communication system design. The first person to have apparently exploited the power of signal space concept in communication theory was the Russian Kotel'nikov, who presented his doctoral dissertation in January, 1947. J. M. Wozencraft and I. M. Jacobs expanded on this approach and their work is widely referenced. E. Arthurs and H. Dym made use of signal space concepts in the performance analysis of several digital modulation schemes. The procedure used in applying signal space concepts to estimation is similar to that used for signal detection.
