The use of phase codes in ultrasound imaging: SNR gain and bandwidth requirements

Barker coded excitation with linear frequency modulated carrier for ultrasonic imaging

“…which reflects that the matched filter SNRG of the Sinusoid-Barker coded signal can be approximated by the Barker code length [16]. It is well known that the SNR out of the matched filter is dependent on the energy of the transmitted signal [16].…”

“…The bandwidth of Barker coded signal is basically determined by its carrier frequency spectrum [9]. In this study, the bandwidth of Barker coded signal must be redefined as the bandwidth of carrier, since the definition of bandwidth for a phase encoded signal is complex, due to the sharp phase transitions in the signal [16]. The sinusoid carrier has the TB product on the order of one.…”

“…The sinusoid carrier is a broadband signal containing all frequencies in a bandwidth of 1/T p around f 0 [6,16]. It can be seen that the bandwidth of sinusoid carrier is determined by the chip duration of Barker code.…”

“…The TB product of the transmitted signal is often used in the literature to describe the SNRG of the matched filtered output [16].…”

“…However, its frequency spectrum cannot accord well with ultrasound transducer frequency spectrum. Moreover, the single-frequency carrier of sinusoidal wave has the time-bandwidth (TB) product on the order of one, and hence the gain in SNR (SNRG) through the Sinusoid-Barker coded excitation can be only achieved by Barker code length [16]. Theoretically, Barker coded waveforms with longer code length give better SNRG.…”