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Frames in CDMA Communication Systems: Tight Frames and Their Fundamental Inequality

For radio systems there are two resources, frequency and time. Division by frequency (or time), so that each pair of communicators is allocated part of the spectrum for all of the time (or all of the spectrum for part of the time), results in Frequency (or Time) Division Multiple Access (FDMA or TDMA). In Code Division Multiple Access (CDMA), every communicator will be allocated the entire spectrum all of the time (Fig. 1). CDMA has applications in wireless cellular communication as well as navigation (e.g., GPS) systems. CDMA uses codes (here referred to as signature sequences) to identify connections and is an interference limited multiple access system. Because all users transmit on the same frequency, internal interference generated by the system is the most significant factor in determining system capacity and communication quality (e.g., quality of voice in mobile phones). In what follows, we will review frame-theoretic results associated with the problem of designing optimal, i.e. minimum interference, signature sequences in CDMA communication systems.