This paper presents multiplierless CIC compensator for software-defined radio (SDR) application. The compensator is composed of two simple filters with sinewave form of magnitude responses. The parameters of the design are the sinewave amplitudes expressed as powers-of-two and estimated in a way to fulfill the absolute value of the maximum passband deviation of 0.25 dB and 0.05 dB, for the wideband and narrowband compensations, respectively. The proposed compensator requires maximum nine adders. The comparisons with the methods proposed in literature show the benefits of the proposed compensator.
Software-defined radio (SDR) has found important role in modern wireless communications. The main idea in SDR is to move the analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) as close as possible to the antenna and thus perform all signal processing in the digital form [
SRC involves resampling in a digital domain thus causing aliasing and imaging which must be eliminated by filtering [
where M is the decimation factor and K is the number of the cascaded filters.
However, its magnitude characteristic:
exhibits a low attenuation in the stopband of interest and a passband droop in the band of interest. As K increases, the stopband attenuation increases, resulting in an increased droop in the passband, which may deteriorate the decimated signal. The motivation of this work is to achieve good CIC wideband and narrowband compensation while keeping low rate of addition operations.
Different methods were proposed to compensate for the CIC passband droop. The compensators which need multipliers were proposed for example in [
The paper is organized in the following way. Next section introduces transfer function of the proposed filter and describes the choice of the design parameters for wideband and narrowband compensation. Some comparisons are provided in Section 3.
Like compensator in [
In contrast to the method in [
where N1 and N2 are integers.
The corresponding transfer function at low rate becomes:
where
and
As a result, filters (8) and (9) require 6 and 3 adders, respectively, i.e. the compensator (7) requires total of 9 adders.
We consider the passband edge ωp = π/(2M), and impose the following condition:
where:
Considering M > 10 the compensator parameters do not depend on M, [
The method is illustrated in the following example.
Example 1: We consider the value of M = 18 and K = 5. According to
K | B1 | B2 |
---|---|---|
5 | 1/2 | 1 |
4 | 1 | 1/2 |
3 | 1 | 1/4 |
2 | 1/2 | 1/4 |
1 | 1/2 | 0 |
deviation is lesser than 0.23 dB. The proposed compensator requires 9 adders.
The overall magnitude responses in
We consider the passband edge ωp = π/(8M) for narrowband compensation and the following condition:
where:
and G1(ejwM) and G2(ejwM) are given in (11b) and (11c), respectively.
Applying the MATLAB simulation we got the values of parameters B1 and B2, shown in
Example 2: We consider values of M = 21 and K = 5 and the passband edge of ωp = π/(8M).
In next section are given some comparisons with the recently proposed compensators.
Consider M = 20 and K = 5.
The compensator in [
K | B1 | B2 |
---|---|---|
5 | 0 | 1 |
4 | 0 | 1/2 |
3 | 1 | 1/2 |
2 | 1 | 1/4 |
1 | 1 | 1/8 |
magnitude responses with amplitudes of sine squared functions B1 and B2. The value of B1 is equal to 2−3 for all values of K, while B2 = (1 + 4(K − 1))/16. For the sake of comparison we consider M = 16 and K = 5. The compensator in [
The proposed compensator is compared with that in [
Dolecek, G.J. (2017) Multiplierless Wideband and Narrowband CIC Compensator for SDR Application. Int. J. Communications, Network and System Sciences, 10, 19-26. https://doi.org/10.4236/ijcns.2017.108B003