This paper presents a theoretical analysis and derives the amplifier output noise power spectral density result in a closed form when the input to the amplifier is a band limited Gaussian noise. From the computed power spectral density the NPR is evaluated by a simple subtraction. The method can be applied to any amplifier with known input-output characteristics. The method may be applied to analyze various other important characteristics of the nonlinear amplifier such as spectral regrowth that refers to the spreading of the signal bandwidth when a band limited signal is inputted to the nonlinear amplifier. The paper presents numerical results on the NPR as a function of the noise bandwidth, depth level of the notch, and the output power back-off obtained from the analysis presented in the paper.

The power amplifier is one of the most important subsystems of modern communication systems [

Among the various methods to assess the performance of an amplifier is the evaluation of the signal to distortion ratio at the amplifier output as a function of the amplifier output power back-off. In case of digitally modulated signals at the amplifier input in the digital communication systems, one of the most important performance measures is in terms of the bit error rate (BER) achieved in the presence of both the distortion introduced by the amplifier and any channel interference plus noise. However, both these measures are functions of the detailed modulation techniques, multiple accessing or multiplexing techniques, and the number of user signals at the amplifier input in addition to the amplifier input-output characteristics and the output power back-off. The various performance measures may be obtained by detailed mathematical analysis, computer simulations, and/or experimental measurements. Both the simulations and experimental measurements are, in general, very time consuming and expensive while the analysis methods are generally difficult and are for more specific cases. For example, detailed analysis has been presented by the author for the case of the code division multiple accessing (CDMA) [

A performance characterization of the nonlinear power amplifiers that is independent of the specifics of the amplifier input signal, such as the multiple accessing and modulation techniques used, the number of users, and the relative power level of the various user signals, is commonly used in the practice. This measure is termed the noise power ratio (NPR). The noise power ratio is measured by inputting the amplifier with a white noise of bandwidth equal to the specified signal bandwidth. A notch in the input noise band is created with the bandwidth of the notch much smaller than the noise bandwidth. At the output of the amplifier one measures the noise power spectral density both inside and outside the notch with the ratio of the two by definition equal to the amplifier NPR that is a function of the total output noise power or the output power back-off.

While the NPR measurements are relatively less intensive compared to some other performance measurements such as the BER measurements, nevertheless these do require extensive measurements as well, in which from the measurements alone it is not possible to predict the performance for the amplifiers other than the one involved in the measurement; in other words it does not provide any measure of the sensitivity of the NPR to the amplifier input-output characteristics and does not address the validation issues of the experimental data. Thus it is of great interest to be able to evaluate the amplifier NPR by independent analytical means. This paper presents a theoretical analysis of the NPR for the nonlinear amplifier that is also applicable to any other nonlinear devices.

This paper presents a theoretical analysis and derives the amplifier output noise power spectral density result in a closed form when the input to the amplifier is a band limited noise with a notch in the spectral band. From the computed noise power spectral density (PSD) the NPR is evaluated as the ratio of the PSDs evaluated outside and inside of the notch. The method can be applied to any amplifier with known input-output characteristics. The paper presents numerical results on the NPR as a function of the noise bandwidth, depth level of the notch, and the output power back-off obtained from the analysis presented in the paper.

It is assumed in this analysis that the amplifier output

The correlation function of the amplifier output process denoted by

The nonzero elements

In (

Sample values of the coefficients

| | |||||
---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | 5 | |

0 | 1 | 0 | 0 | 0 | 0 | 0 |

1 | 0 | | 0 | 0 | 0 | 0 |

2 | 1 | 0 | | 0 | 0 | 0 |

3 | 0 | | 0 | | 0 | 0 |

4 | | 0 | | 0 | | 0 |

5 | 0 | | 0 | | 0 | |

In view of (

The power spectral density

It follows from (

In summary the PSD of the amplifier output fundamental zone component of the bandpass power spectral density

This section presents some numerical results obtained by using the analysis presented in the paper. The analytical results have been encoded in the form of a relatively simple MATLAB program that can provide the result for any specified amplifier input-output characteristics, notch bandwidth and depth, and the output power back-off. The MATLAB program then generates the desired numerical result almost instantaneously.

The first example generates the various terms

The process

It may be observed from Figure

Power spectral density (W/Hz) of various order convolution terms (

Power spectral density (dBW/Hz) of various order convolution terms (

Power spectral density (dBW/Hz) of various order convolution terms over a bandwidth of 200 MHz (

As an example of the application of the theory presented in this paper, the nonlinear amplifier is approximated by a soft limiter model with its input-output characteristic described by the following nonlinear function

The amplifier characteristics

Figures

The NPR values obtained for the three cases shown in Figures

Figure

Figure

Soft limiter input-output characteristics.

Plot of the Chebyshev transform

Amplifier output versus input power level.

Amplifier output noise power spectral density with

Amplifier output noise power spectral density with

Amplifier output noise power spectral density with

Amplifier output noise power spectral density with

Plot of NPR versus the input power level.

Plot of NPR versus the output power back-off BO.

This paper has presented a theoretical analysis of the amplifier output noise power spectral density result in a closed form from which the NPR is evaluated by a simple subtraction. The method can be applied to any amplifier with known input-output characteristics. The paper has presented numerical results on the NPR as a function of the noise bandwidth, depth level of the notch, and the output power back-off obtained from the analysis presented in the paper. The analytical results of the paper have been encoded in the form of a MATLAB program that can provide the result for any specified amplifier input-output characteristics, notch bandwidth and depth, and the output power back-off. The MATLAB program generates the desired numerical result almost instantaneously compared to extensive efforts and time required for obtaining experimental and simulation results for any power amplifier.

The author declares that there is no conflict of interests regarding the publication of this paper.