In-phase/quadrature (I/Q) demodulators contribute to the noise figure of a direct-conversion receiver’s signal chain, although it can be difficult to predict the effects. While noisefigure meters can measure noise figures at microwave frequencies, they do not operate low enough for use at baseband frequencies. An alternative approach is to use a calibrated noise source and spectrum analyzer with preamplifier to measure the noise rise through the demodulator. This approach is limited by the sensitivity of the spectrum analyzer at baseband. Fortunately, a baseband noise assessment can be orchestrated using vector signal analysis (VSA). This article describes some measurement techniques using a baseband vector signal analyzer to assess the noise figure of an I/Q demodulator with and without interfering signals.

Figure 1 shows an example directconversion signal chain. Like many receivers, the design uses a band-selective low-noise front-end, followed by a quadrature mixing process, channel selection, and signal detection. It is similar to a real intermediate- frequency (IF) sampling receiver except the signal is split into quadrature pairs as it passes through the I/Q demodulator. This has the inherent convenience of providing direct output of the original I/Q vectors used to create the wanted modulated signal. To recognize this inherent feature it is helpful to understand the quadrature mixing process and the associated complex mathematics.

Consider an RF input signal given by Eq. A, where the timevarying envelopes for the upper sideband (USB) and lower sideband (LSB) are represented. As the signal passes through the demodulator core, it gets mixed by the local-oscillator (LO) signal. The LO signal has its in-phase component (cosine) and the quadrature component (sine), which is realized as the LO is passed through a 90-deg. phase shifter. As the LO is multiplied with the RF, high-frequency and lowfrequency terms are generated. The high-frequency terms are rejected as the signal passes through a lowpass filter. The quantitative relation and complex frequency spectrum of the signal is shown in Fig. 1.

As shown, the in-phase and quadrature components consist of USB and LSB components. If the in-phase signal is passed through a Hilbert transform, all negative frequencies get a +90-deg. phase shift and all positive frequencies get a –90-deg. phase shift. If the result is summed with the quadrature component, the LSB signal component remains, while the USB signal is rejected. In a similar fashion, it is possible to perform an inverse Hilbert transform on the quadrature signal and sum it with the in-phase signal component. By doing so, it is possible to retrieve the USB signal component and reject the LSB signal. This is the essence of image rejection and it is evident that quadrature accuracy determines successful rejection. Note that prior to the quadrature summation networks, both the wanted signal and image are overlapping making it difficult to separate the two sidebands.

Now if a zero-IF condition (?IF = 0) condition is considered, the USB and LSB vectors are readily available at the output of the Hilbert quadrature summation networks. If the original signal applied was an I/Q quadrature modulated signal of the form of Eq. B, the I and Q vectors would be present at the outputs of the quadrature summation networks. In this manner, an I/Q demodulator can directly demodulate an I/Q modulated signal when using an LO that is tuned to the carrier frequency.

Noise figure is a measure of the decibel degradation of the signal-tonoise ratio of a signal as it passes through a noise-contributing device. Mathematically, it is equal to 10log (F) where F is the noise factor and is equal to the ratio of the input SNR to the output SNR (SNRINPUT/SNROUTPUT). In a frequency-translation process, it is important to understand the mixing operation on both the signal and noise presented by the source. The trouble presented with the mixing process is twofold. First, it is necessary to measure the output noise at a different frequency than the source noise applied at the input. This requires careful calibration of the noise receiver as well as the noise source. Second, the noise delivered to the IF output frequency is the result of an upper and lower sideband noise contribution, referred to as a doublesideband noise-figure measurement. This is more apparent when inspecting the digitized signals prior to the Hilbert networks in Fig. 1. Note how both the upper and lower sidebands are present at outputs of the demodulator. This complicates the measurement as the conversion gain of each sideband may be different, which makes things slightly more difficult when attempting to predict the noise figure for a single-sideband.

While in practice an image rejection scheme will be employed to eliminate any noise or interference delivered from the unwanted sideband (the image). In a swept broad frequency range measurement, it may be impractical to measure only the singlesideband contribution unless the mixing process offers adequate inherent image-rejection performance.

VSA measurements assess the modulation accuracy and quality of a modulated signal. Many VSAs have basic spectrum analyzer functionality along with the capability to demodulate a signal and report a variety of information about the modulated signal. Whereas the modulated signal could employ amplitude modulation, phase modulation, or a combination of both, the VSA is designed to analyze the accuracy of the signal vectors used to describe the waveform. VSAs are most commonly used to measure the error vector. By measuring the magnitude and phase of each transmitted symbol, the VSA can calculate the error vector between the measured vector and the next closest ideal constellation point. In order to identify the ideal constellation coordinates, the VSA must first be given the proper waveform characteristics such as symbol rate, pulse-shaping filter specifications, and modulation format. If the error vector magnitude (EVM) is so great such that the VSA cannot estimate the anticipated symbol vector correctly, the results will be very noisy and unreliable. This is especially true in very dense modulation schemes such as higher-order quadrature-amplitude- modulation (QAM) modulation formats.

In a time-sampled system the EVM can be defined as:

where

Z(k) = the complex received signal vector, containing both in-phase (I) and quadrature (Q) components, and R(k) = the ideal complex reference vector.

The EVM is the ratio of the rootmean- square (RMS) power of the error vector to the RMS power of the reference. In general, a receiver will exhibit three distinct EVM limitations versus received input signal power ( Fig. 2). At strong signal levels, the distortion components falling in-band due to nonlinearities in the receiver will cause a strong degradation to EVM as signal level increases. At medium signal levels where the receiver is behaving in a linear manner and the signal is well above any notable noise contributions, the EVM has a tendency to reach an optimum level dominantly determined by the quadrature accuracy of the demodulator and the precision of the test equipment. As signal levels decrease such that noise is a major contribution, the EVM performance versus signal level will exhibit a dB-for-dB degradation with decreasing signal level. At lower signal levels, where noise proves to be the dominant limitation, the decibel EVM proves to be directly proportional to the SNR. Using this relationship it is possible to estimate the input referred noise level of the receiver and calculate NF.

Figure 3 describes a VSA-based demodulator characterization setup. The combiner network feeding the input of the DUT allows simultaneous application of multiple test signals. The signal path through the isolator and combiner were calibrated to get absolute power levels at the demodulator input. This provision allows for performance measurements under various blocking conditions.

Blockers may originate from another wireless terminal within the same cellular radius, or a pilot tone for cell identification from another nearby base-station. A direct conversion receiver does not have the benefit of any channel selectivity until after the signals pass through the low-noise front-end and I/Q demodulator. This forces the front-end and demodulator to support the unwanted blocker at full signal levels, while maintaining sufficient sensitivity to successfully recover a faint wanted signal. At baseband, I/Q channel selection filters are often applied to attenuate any nearby blocking signals and pass the wanted signals to the I/Q digitizing analog-todigital converters.

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