Frequency response mismatch correction in multichannel time interleaved analog beamformers for ultrasound medical imaging

Time interleaving is one of the most efficient techniques em ployed in the design of high-speed analog beamformers in ultrasound phas ed rray transducers. However, its implementation introduces several mismatch errors betwee n int rleaved subunits, limiting the accuracy of the overall system. In this paper, a method for estimation and correction of frequency response mismatch based on an adaptive equalization is reported. The adaptive algorithm requires only that the input signal is band-limited t o the Nyquist frequency for the complete system. The proposed method greatly reduce the computa tional complexity requirement of sampled signal reconstruction and offers simplified ha rdware implementation. Recently, iterative frequency response mismatch cor re tion methods (Satarzadeh, 2009)(Johansson, 2008) have been proposed based on adapt ive filters either on each stage or at the system output by employing an inverse Fourier trans form (Satarzadeh, 2009) or polynomial time varying filter structures (Johansson, 2008). In this paper, we demonstrate digital frequency res pon e mismatch correction in timeinterleaved analog beamformer as an adaptive equali zation process. The estimation method requires only that the input signal is band-limited t o the Nyquist frequency for the complete system. The equivalent signal estimation structure can avoid aliasing without over sampling the input signal or operating at full sampling rate. Th e sparse structure of interleaved signals in the continuous frequency domain is used to replace the continuous reconstruction with a single finite dimensional problem. The implemented method si gnificantly reduce the computational complexity requirement of sampled signal reconstruc tion and offers effective hardware implementation. 2 CORRECTION ALGORITHM In the analog, time-interleaved beamformer, there a M identical sampling and subbeamformers operating in parallel. Each subsystem s a ples and digitizes the input signal every MT seconds; i.e., the digitizing rate of each subsyste m is 1/MT samples/s. Although all subsystems operate at the same clock frequency, the sampl ing clock of subsystem m+1 is T seconds behind that of the subsystem for m =0,1,...,M-1. The timing alignment within the required accuracy is obtained by using a master clock to syn chronize the different sampling instants. As illustrated in Figure 1, at the back end of these p arallel sampling and sub-beamformers is a sequential M:1 multiplexer, which samples the outputs of beamformers stages at a rate of 1 sample/T s. The sub analog beamformer consists of a sampleand-hold circuit, which consists of sampling capacitors and switches and a clock contro ller. Time domain analog-beamformer output is shown in Figure 2. For M time-interleaved sub-beamformers, each working uni formly with a period of Ts=MT and frequency response offset { hm fin/f1=miT}, the clock generator provides the required M sample clocks for each sub-beamformer stage accord ing to the sampling pattern such that ti(n)=(nM+mi)=(n+mi/M)Ts for 1≤i≤M. Defining the i th sampling sequence for 1≤i≤M as xmi[n]=x(t=nT=kMT+mT), the sequence of xmi[n] is obtained by up-sampling the output of the i-the sub-beamformer with a factor of M and shifting in time with mi samples. The spectrum of the sampled time-domain signal is then represented as