Performance Of An Asynchronous DS/SSMA (DS/CDMA) System With Kronecker Sequences

A Kronecker sequence is constructed by sequence-inversion keying of an inner component sequence with an outer component code. Kronecker sequences a re a very a t t rac t ive choice f o r asynchronous DSlSSMA (DS/CDMA) systems when a short code acquisition time of a cor re la t ion receiver or matched f i l t e r receiver implementation issues a r e important design criteria. I t is shown tha t the auto-correlat ion a n d cross-correlation properties and SNR performance of Kronecker sequences a re only slightly poorer than those of conventional spreading codes (e.g. Gold, Kasami and M-sequences), provided that the component sequences a r e chosen carefully. Various kinds of component code combinations have been tested. I t is a useful rule of thumb for CDMA applications that more emphasis should be placed on the auto-correlat ion properties of Kronecker sequences than on their crosscorrelation properties, because emphasis on the la t ter easily detracts from the former. A Barker code as an outer code and a Gold or Kasami sequence as an inner code leads to sufficiently good auto-correlation and cross-correlation properties for asynchronous CDMA applications. The SNR performance is typically only about 0.5. ..1.0 dB poorer than using conventional sequences of equal length when E b / N O is about 15 dB. A little sacrifice in the SNR and BER performance of a CDMA system gives many important advantages which a r e not attainable using conventional spreading sequences.