_{1}

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 N_{1} and N_{2} 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 ω_{p} = π/(2M), and impose the following condition:

where:

Considering M > 10 the compensator parameters do not depend on M, [_{1} and B_{2}, for K = 1, ・・・, 5, shown in

The method is illustrated in the following example.

Example 1: We consider the value of M = 18 and K = 5. According to _{1} and B_{2} are equal to 1/2 and 1, respectively.

K | B_{1} | B_{2} |
---|---|---|

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 ω_{p} = π/(8M) for narrowband compensation and the following condition:

where:

and G_{1}(e^{jwM}) and G_{2}(e^{jwM}) are given in (11b) and (11c), respectively.

Applying the MATLAB simulation we got the values of parameters B_{1} and B_{2}, shown in

Example 2: We consider values of M = 21 and K = 5 and the passband edge of ω_{p} = π/(8M).

In next section are given some comparisons with the recently proposed compensators.

Consider M = 20 and K = 5. _{1} = 1/2, B_{2} = 1. The parameters of the compensator in [_{1} = 1 and, B_{2} = 2^{0} − 2^{−2} − 2^{−5}, thus requiring total of 11 adders.

The compensator in [

K | B_{1} | B_{2} |
---|---|---|

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 B_{1} and B_{2}. The value of B_{1} is equal to 2^{−3} for all values of K, while B_{2} = (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