Optimizing Receiver Performance with Error Vector Analysis

JasonYoo

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Error vector analysis is a method of quantitatively representing the performance of a transmitter or receiver using amplitude error and phase error. By using a vector signal analyzer with error vector analysis, engineers can study the amplitude value and phase error of the signal space online while adjusting the receiver link parameters.

In order to adjust receiver parameters for optimal performance, it is necessary to compare the performance of a given receiver with that of an ideal receiver. There are several ways to do this. Bit error rate (BER) performance testers are commonly used to measure the bit error rate at different input signal-to-noise ratios (SNR), but this measurement method requires sending, receiving, and comparing very long bit sequences, which takes a long time. A faster method is able to monitor the error vector of shorter bit sequences, which can be done with a modern vector signal analyzer (VSA) with error vector analysis capabilities. This method allows engineers to study the amplitude value and phase error of the signal space online while adjusting receiver chain parameters such as intermediate stage matching circuits, distribution of cascaded gain and attenuation, and filter selection.

Error Vector Analysis

Error vector analysis is a method for quantifying the performance of a transmitter or receiver using amplitude and phase errors. In general, any digital modulation can be described by a signal waveform z(t)=A(t)cos(w _c t+Q(t)), where A(t) represents the instantaneous amplitude variable and Q(t) represents the instantaneous phase variable. In general, the baseband data is decomposed into I and Q vectors, which are then modulated to the desired carrier angular frequency w _c using an orthogonal modulator or direct synthesis . The resulting composite modulated waveform contains orthogonal I and Q data, which can be analyzed at the carrier frequency or it can be demodulated to baseband and directly analyzed for the I and Q baseband vectors. Several equipment manufacturers around the world offer VSAs with this capability.

The VSA measures the amplitude and phase of each transmitted symbol. The VSA with error vector analysis calculates the error vector between the measured vector and the closest ideal constellation point. First, the VSA must be provided with appropriate waveform parameters, such as symbol rate, pulse shaping filter parameters, and modulation mode. If the error vector magnitude (EVM) is too large, the VSA cannot correctly estimate the expected symbol vector, and the result obtained is very inaccurate and unreliable. Especially in very dense modulation modes, such as high-order QAM modulation. If you want to debug too many corrupted signals, the error vector can hardly provide information. In most cases, vector analysis is used to optimize performance rather than to verify functions, so EVM with high values but low accuracy is usually acceptable. Error vector analysis is very useful as a tool to optimize the design of existing functions, rather than a debugging tool.

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

(1)

Where Z(k) is the composite received signal vector, consisting of I and Q components; R(k) is the ideal composite reference vector. The error vector magnitude is the ratio of the error vector power rms to the reference vector power rms. It is a measure of receiver performance and is closely related to SNR and BER. For any coding gain, EVM is proportional to the square root of the SNR, as shown in Equation 2 (where L is the coding gain).

(2)

Coding gain comes into play when the original baseband data is spread using a pseudo-random sequence, such as that used in CDMA spread spectrum systems. Coding gain in such systems is the ratio of the chip rate to the baseband data rate. For example, a UMTS transceiver sending a 12.2kbps data stream at a chip rate of 3.84Mchips/s will have a coding gain of 3.84×10 ⁶ /12.2×10 ³ =314.75, or 25dB.

In order to relate EVM to BER, it is necessary to determine the relationship between SNR and the probability of symbol error for a given modulation scheme. For QAM modulation, the probability of symbol error can be expressed as follows:

(3)

Where M is the modulation order (e.g., for 64QAM, M=64); rb is the average SNR per bit; and k is the number of bits per symbol (e.g., for 64QAM, each composite symbol is 6 bits).

Equations 2 and 3 can be used to find the symbol error rate (SER) and EVM for different SNRs. The relationship between SER and SNR is shown in Figure 1a, which provides typical curves for different QAM modulation orders. The relationship between SER and EVM for the same modulation method is shown in Figure 1b, which enables designers to use error vector analysis to predict the BER performance of a given receiver. For example, if the EVM is measured to be 3% for uncoded 256QAM modulation, the predicted SER should be 600ppm. In other words, on average, 6 erroneous symbols are expected in every 10,000 symbol sequence, corresponding to 75 bit errors in a 1 million bit sequence, that is, a BER of 7.5× ^10-5 .

Figure 1: a) Theoretical symbol error probability vs. SNR for uncoded 16QAM, 64QAM, and 256QAM modulation. b) The corresponding symbol error probability vs. EVM measurement.

Using the data in Figures 1a and 1b and an appropriate VSA, designers can optimize performance in real time. While observing EVM performance, parameters such as filter selection, interstage matching circuits, and conversion gain can all be adjusted, allowing designers to quickly optimize their signal chain. The following example demonstrates the benefits of this approach by using error vector analysis to quantitatively analyze a receiver subsystem performance.

Practical Measurement and Application

Figure 2 shows the quadrature demodulator and high-precision RMS power detector, which form a closed-loop automatic level control (ALC) intermediate frequency (IF) to baseband receiver subsystem. The AD8348 provides high-precision quadrature demodulation from 50MHz to 1GHz, with a local oscillator (LO) frequency that is twice the desired carrier. The built-in LO divider allows the use of an LO, which can alleviate the LO frequency pulling (LO-pulling) problem in full-duplex transceivers. In this example, the IF input frequency is 190MHz, and a -10dBm@380MHz LO drive circuit is used. The integrated front-end variable gain amplifier (VGA) consists of a resistive variable attenuator and a high intercept-point post-amplifier to provide variable conversion gain while maintaining a constant spurious-free dynamic range. The AD8362 is a high-precision radio frequency (RF) power measurement device that can measure the RMS power of signals from any low frequency to 2.7 GHz. The AD8362 is insensitive to waveforms with varying crest factors, making it an ideal solution for measuring the true rms value of digitally modulated signal power.

Figure 2: The AD8348 quadrature demodulator combined with the AD8362 TruPwr detector provides high-precision automatic level control for the IF-to-baseband receiver subsystem.

The circuit shown in Figure 2 is used to measure the effective power of the I channel baseband signal. Assuming that both the I and Q vectors are pseudo-random, which is a reasonable assumption for most digital modulation methods, the I channel or Q channel detection can be arbitrarily selected. The internal error amplifier generates a control signal to drive the gain control port of the orthogonal demodulator by measuring the effective value of the baseband power. The conversion gain of the demodulator is adaptively adjusted in a closed loop to maintain a constant baseband effective power level, regardless of the waveform. The output level is set by applying an appropriate set point control voltage to the VSET pin. Error vector analysis is used to find the optimal ALC output setting and determine the filter suitable for 256QAM 1Msps digital modulation.

The demodulator provides a single-ended interface for low-pass filter application. 4th-order Bessel filters are used on both the I and Q paths to minimize broadband noise and help filter out unwanted adjacent-tone signals. Bessel filters were chosen because they have very low group delay characteristics, which is necessary to ensure low intersymbol interference. Butterworth and Chebyshev filters were initially tested, but their large passband group delays resulted in poor EVM performance. It is difficult to measure the subtle differences in receiver performance caused by different filter choices using classical methods. VSAs can quickly measure performance, allowing filter networks to be optimized in a short period of time.

The baseband EVM is measured using a Rohde & Schwarz FSQ8 vector signal analyzer. While observing the EVM, the set point control voltage can be adjusted to determine the optimal setting. As shown in Figure 3, choosing the right set point voltage can result in an EVM better than 2% over an input range greater than 40dB. The variable conversion gain of the demodulator allows the receiver design to have the best BER characteristics over a wider dynamic range than a fixed gain demodulator.

Figure 3: Error vector magnitude (EVM) vs. input power for 1Msps symbol rate, 256QAM.

SER performance can be easily estimated by measuring the EVM value over the expected input signal range. The measured EVM data can be used in conjunction with the curve in Figure 1 to predict the dynamic performance of the receiver. For 256QAM modulation, the EVM must be better than about 2% to ensure that the SER is less than 10-6 ^. Measurements of the IF to baseband receiver subsystem show that the receiver allows input power to vary by more than 40dB before the SER deteriorates to an unacceptable level. EVM analysis is an effective tool for signal chain optimization and dynamic performance prediction.

References :

"Digital Communications, 2nd Edition", John G. Proakis, McGraw-Hill Inc. 1989 "Universal Mobile Telecommunications System (UMTS); UTRA (BS) FDD; Radio transmission and reception (3GPP TS 25.104 version 4.7.0 Release 4)" , ETSI TS 125 104 V4.7.0, 2003 "Principles of Communication Systems, 2nd Edition", Herbert Taub and Donald L. Schilling, McGraw-Hill Inc. 1986

By Eric Newman,
Senior Applications Engineer,
Analog Devices