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It is revealed that there is a link between the quantization approach employed and the dimension of the vector parameter which can be accurately estimated by a quantized estimation system. A critical quantity called inestimable dimension for quantized data (IDQD) is introduced, which does not depend on the quantization regions and the statistical models of the observations but instead depends only on the number of sensors and on the precision of the vector quantizers employed by the system. It is shown that the IDQD describes a quantization-induced fundamental limitation on the estimation capabilities of the system. To be specific, if the dimension of the desired vector parameter is larger than the IDQD of the quantized estimation system, then the Fisher information matrix for estimating the desired vector parameter is singular, and, moreover, there exist infinitely many nonidentifiable vector parameter points in the vector parameter space. Furthermore, it is shown that under some common assumptions on the statistical models of the observations and the quantization system, a smaller IDQD can be obtained, which can specify an even more limiting quantization induced fundamental limitation on the estimation capabilities of the system. [ABSTRACT FROM AUTHOR]

Coarse time quantization of delay profiles within ultrasound array systems can produce undesirable side lobes in the radiated beam profile. The severity of these side lobes is dependent upon the magnitude of phase quantization error? the deviation from ideal delay profiles to the achievable quantized case. This paper describes a method to improve interchannel delay accuracy without increasing system clock frequency by utilizing embedded phase-locked loop (PLL) components within commercial field-programmable gate arrays (FPGAs). Precise delays are achieved by shifting the relative phases of embedded PLL output clocks in 208-ps steps. The described architecture can achieve the necessary interelement timing resolution required for driving ultrasound arrays up to 50 MHz. The applicability of the proposed method at higher frequencies is demonstrated by extrapolating experimental results obtained using a 5-MHz array transducer. Results indicate an increase in transmit dynamic range (TDR) when using accurate delay profiles generated by the embedded-PLL method described, as opposed to using delay profiles quantized to the system clock. [ABSTRACT FROM PUBLISHER]