The Bandwidth of Spread Spectrum Signals

Although spread spectrum systems depend on large bandwidth to achieve performance, they must also operate within bandwidth constraints imposed by frequency allocations. The measures of bandwidth relevant to performance are usually quite different from those defined in frequency allocations. In this paper a number of definitions of bandwidth are discussed, and a number of direct sequence pseudonoise (DSPN) modulation techniques are evaluated according to those definitions of bandwidth. A wide range of bandwidths per chip rate result, and trades among the modulation types are given. INTRODUCTION The engineering of spread spectrum communications systems invites involvement with a number of rather refined parametric concepts, such as bit error rate, antenna gain, radiated power, communication efficiency, and bandwidth. Of these, none has been the subject of more lively discussion and revision than bandwidth. The implications of bandwidth can vary considerably from context to context, as the profusion of definitions of bandwidth will attest. The purpose of the present article is to explore the subject of spread spectrum bandwidth through an examination of various definitions. WHY DISCUSS BANDWIDTH? Most of the current attention given to the bandwidth of conventional non-spread communication systems centers on the problem of spectrum allocation in an increasingly crowded radio frequency spectrum. The objective is often to achieve “bandwidth efficiency”, or a minimum bandwidth per data rate. The needs of the spread spectrum communication system place a rather contrasting premium on maximum bandwidth occupancy. To decrease the power spectral density of the signal without reducing the transmitter power, to reduce the effectiveness of enemy jammers, to multiplex many signals occuyping the very same band, and to increase the precision of timing information derived from a signal all imply greater system bandwidth per data rate of any one user. THE VARIETY OF DEFINITIONS OF BANDWIDTH The conventional interest in strict, or nearly strict, band limitation is most often an indirect expression of concern for adjacent channel interference in a conventional frequency division multiplexed (FDM) system. Here almost any definition of occupied bandwidth only imprecisely measures the interference. In fact, a recent investigation showed that total interchannel crosstalk can be minimized by optimization of the data modulation, and without any direct reference to bandwidth. Definitions of bandwidth, when used, serve the needs of the regulatory agency or the solicitor of a technical proposal who must seek to control interference while allowing the designer freedom to choose his own modulation scheme. Definitions of bandwidth arising in these circumstances are bound to be somewhat arbitrary. In the case of spread spectrum communication, there is an additional measure of bandwidth which is more likely to ask “is the signal spread out enough” rather than “within what bounds is it confined.” This is like saying that a gallon of paint should be applied in a layer not to exceed a certain thickness rather than insisting that the paint never splatter beyond certain boundaries. The definitions of bandwidth for spread spectrum systems can be very precise and practical in their own right, as further discussion will show. THE SIGNIFICANCE OF POWER SPECTRAL DENSITY Before proceeding to discuss various types of spread spectrum bandwidth, it will be good to discuss the underlying frequency function on which they all depend. This is called the power spectral density and is familiar as the typical display on a swept spectrum analyzer. The general feeling is that for every chip modulation scheme there exists a precisely known power spectral density from which the bandwidth can be deduced or computed according to any given definition of bandwidth. The power spectral densities generally given for spread spectrum signals are based on critical assumptions of random chip sequences and long averaging times. There may be circumstances under which one or both of those assumptions will fail to apply. For instance, the power spectral density usually given for 180E binary phase shift keying used in direct sequence pseudonoise (DSPN) modulation takes the form