Optimization of Number Representations - Signal Processing Systems - page 1307

Fig. 20 Grouping result for
one tap of LMS adaptive filter

Tabl e 8 Determined fixed-point attributes for the LMS adaptive filter

Integer
word-length

Minimum
word-length

Optimum
word-length Group Signal

u001 Sum 3 12 12

u005 Tap 2 7 7

u002 Error − 4 5 5

coef Coefficient 1 13 13

u004 ADC (channel) 3 8 10

u006 ADC (source) 2 7 13

are shown in Table 8 . The optimization results are compared for three search
algorithms: uniform word-length, exhaustive search, heuristic search based on
uniformly increasing the minimum word-length vector. The uniform word-length
optimization requires 13 bits for all the signals and the hardware cost required is
96,265 gates. The exhaustive and heuristic search algorithms, both are based on
the minimum cost criterion, need the cost of 46,278 and 49,520 gates, respectively.
The hardware cost required using the minimum cost optimization is just 48% of
that needed for the uniform word-length determination in this example. The number
of simulations for searching the optimum word-length vector from the minimum
word-length vector is 27 and 5 for the exhaustive and heuristic search algorithms,
respectively.

6 Summary and Related Works

Fixed-point hardware or integer arithmetic based implementation of digital signal
processing algorithms is important for not only hardware cost minimization but also
power consumption reduction. The conversion of a floating-point algorithm into
a fixed-point or an integer version has been considered very time-consuming; it
often takes more than 50% of the algorithm to hardware or software implementation
procedure [ 25 ] . The fixed-point format discussed in Sect. 2 bridges the gap between