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# MODULATION IMPERFECTIONS IN IS54/136 DUAL-MODE CELLULAR RADIO

#### Typical modulation errors related to the RF and digital sections of a dual-mode (TDMA/AMPS) cellular phone front end, and development of calibration methods to effectively minimize internal modulator errors through analysis of the output signal

MODULATION IMPERFECTIONS IN IS54/136 DUAL-MODE CELLULAR RADIO

### Abstract:

Nonideal in-phase and quadrature (IQ) calibration circuits on one hand, and the synthesizer's phase noise spurious response and carrier leakage on the other, affect modulation quality by degrading modulation parameters such as error vector magnitude (EVM), spectral mask and residual AM. The transmitter's gain chain and its output power amplifier linearity and synthesizer phase noise degrade the spectral purity of the transmitter and its spectral mask even further, consequently degrading the system's bit error rate (BER) performance. This article identifies typical modulation errors related to the RF and digital sections of a dual-mode12,13 (TDMA/AMPS) cellular phone front end, and develops calibration methods that will effectively minimize the internal modulator errors by analyzing the output signal.

Quadrature modulators have been used for single-sideband (SSB) transmission and, in recent years, for quadrature AM (QAM) and other digital modulation schemes in digital radios. In dual-mode cellular phone radios, the modem is designed to use one modulator for both digital- and analog-mode transmissions. This single modulator simplifies the design and calibration of the RF section of the mobile unit.

Fig. 1 A quadrature modulator.

The block diagram of a quadrature modulator, shown in Figure 1, comprises two mixers and a summation circuit to combine the mixer outputs. The inputs to the mixers are the information-bearing baseband (lowpass) i(t) and q(t) signals and a carrier of the local oscillator signal cos(wct) mixed with the I input, and sin(wct) mixed with the Q input. Thus, the transmitted signal is expressed as17

The later presentation of the quadrature phase-shift keying (QPSK) modulator output signal implies that any complex modulation can be generated using properly chosen amplitudes and phases of the I and Q signals. Moreover, since the I and Q signals have lowpass characteristics, the low frequency modulation circuitry is usually easier to implement at the required accuracy. This ease of implementation is a major reason for the popularity of quadrature modulators.

ANALOG FM MODULATION IMPAIRMENTS

To establish an FM signal, the carrier's amplitude is held constant and the phase is varied. Thus, the FM transmitted signal is represented by17

where Dw is the peak radian deviation and the peak magnitude of m(t) is 1. m(t) is the information-bearing signal and the phase q(t) is given by the integral of Dwm(t). From Equation 3 it can be concluded that the required baseband I and Q signals needed to generate an FM transmitted signal using a QPSK modulator are given by17

In the case of ideal modulation, A(t) = A. However, in reality, there are several parameters that affect the amplitude A vs. time such as amplitude and phase imbalances between I and Q baseband inputs. These imbalances cause fluctuations in the magnitude A known as residual AM. Residual AM of an FM signal is defined as the amount of AM fluctuation on the FM signal amplitude. Residual AM is measured by the AM modulation index mi% as

where

m1 = maxOA(t)O

m2 = minOA(t)O

Figure 2 shows the residual AM plotted as a function of phase balance between I and Q, while the amplitude balance is a parameter.

It can be seen that the residual AM is more sensitive to the phase balance a than to the amplitude imbalance d for high phase imbalance. However, amplitude imbalance correction is crucial for small phase errors because, in the ideal case, the I and Q trajectory is a circle with a radius equal to AI = AQ = A. However, in the nonideal case there is an amplitude imbalance between I and Q, phase imbalance a and DC offsets. The phase imbalance causes the projection of I onto Q where I is decreased by cosa while Q is increased by 1 + sina. Hence, the circle turns into an ellipse with the offset axis due to the DC offsets caused by the carrier leakage.

Fig. 2 Residual AM vs. phase balance of a 1.004 kHz FM-modulated signal with 8 kHz peak deviation.

Fig. 3 The (a) origin offset and EVM errors and (b) I/Q phase error.

DIGITAL p/4 DQPSK SIGNAL IMPAIRMENTS AND EFFECTS

Signal impairment types can be divided into two groups: linear impairments (such as I and Q amplitude imbalance, phase imbalance, and I and Q DC offset14-16 causing the carrier leakage) and nonlinear impairments (such as AM to PM generally caused by the transmitter power chain, and LO phase noise affecting the phase imbalance by adding the LO's ±Dq RMS phase shift to the phase error between I and Q). The focus here is on the effects of linear impairments.

Fig. 4 Sideband suppression vs. amplitude balance factor d for various I/Q phase balance parameters.

The transmitter's modulation impairments affect the constellation diagram of the transmitted signal, as shown in Figure 3, and thus degrade the EVM and channel performance. I and Q amplitude imbalance affects the constellation symmetry and causes an ellipse-shaped constellation diagram, depending on which I or Q input is larger. The I and Q paths' phase mismatch causes constellation distortion in both the x and y directions because the orthogonal projection of one component on the other is not zero. The phase error rotates the constellation points from their original location. Because of DC offset of the I/Q inputs, the leakage of the carrier to modulator output affects the constellation origin offset. Since carrier leakage consists of two perpendicular components related to the I path and the Q path of the QPSK modulator, the constellation origin is shifted both in the x- and y-axis directions, respectively. By applying sine and cosine functions to the I and Q inputs, the resultant modulated signal becomes an SSB RF signal. Using these input signals, the modulator can be easily calibrated and checked for any malfunctioning and, thus, any constellation distortion and BER degradation can be eliminated.

The sideband suppression of an SSB signal is defined by14-16

where

a = phase imbalance between the I path and the Q path

d = amplitude imbalance (in decibels or as a relative value)

Figure 4 shows the sideband suppression as a function of amplitude balance between I and Q while the phase balance between I and Q is a parameter. It can be seen that phase imbalance a and amplitude imbalance d limit sideband suppression so that, for 30 dB of suppression, a should be below 3° and d below 0.3 dB.

Fig. 5 Sideband suppression vs. phase balance for various I/Q relative balance factors.

Fig. 6 Carrier suppression as a function of DC offset.

The same reasoning for an SSB signal sideband suppression (when I and Q transmission phases are not in perfect match) can be used by setting Equation 6 for constant amplitude error. Figure 5 shows the sideband suppression as a function of phase balance between I and Q while the amplitude balance between I and Q is a parameter. It can be seen that I and Q relative phase imbalance affects the sideband suppression for up to 10 percent amplitude imbalance. Phase errors over 3° limit the ability to calibrate the sideband suppression and require a phase-calibrating circuit. Hence, for low phase errors, only a simple amplitude matching circuit is required. For a 3° phase error and 0.3 dB amplitude error the sideband suppression is 30 dBc and thus the measured EVM is 4.5 percent.

The second calibration required is the DC offset between I and Q. This parameter affects the carrier leakage from the modulator. A carrier signal leaking to the antenna affects the origin offset of the constellation at the base station's receiver. The result may cause poor BER performance. The carrier suppression is given by14,15

The potential impairments of the modulator (shown previously) and input baseband signals (I vs. Q) are defined using

Dc1 = DC offset error of the LO at the I input

Dc2 = DC offset error of the LO at the Q input

Dm1 = DC offset error at the I input

Dm2 = DC offset error at the Q input

a = phase error between I and Q inputs

b = phase balance of the LO splitter within the modulator to quadrature

d = amplitude balance between I and Q inputs

KI < a = I path mixer transfer function, including the phase error a between I and Q inputs

KQ = Q path mixer transfer function, with zero phase

K = amplitude balance of the LO splitter within the modulator

Figure 6 shows the carrier suppression as a function of DC offset voltage where the phase quadrature error b of the LO divider is a parameter between 1° and 10°, and a = 1°, d = 1 dB and K = 1. It can be seen that the carrier leakage is highly sensitive to DC offset errors of the I and Q inputs and thus offsets of less than 20 mV are essential for a carrier reduction of 30 dB and higher. By analyzing Equation 6 for constant a and DC offset, it can be shown that the carrier suppression is only slightly affected by errors in LO quadrature b or LO amplitude imbalance factor K.

Fig. 7 Bit error probability for coherently detected BPSK with constant phase errors.5

Fig. 8 A constellation diagram for QPSK with phase noise of DqRMS = 5.758.

NONLINEAR ANALYSIS

Frequency error causes a constant phase error offset ±Dq from the required phase of the symbol point. The result can be seen as a constant rotation of Dq radians of the constellation diagram around its center. A binary phase-shift keying (BPSK) modulated signal is a simple example to describe the frequency error effect.9 The error probability ratio Eb/No of the modulated signal is reduced by cos2Dq; thus, it results in degradation of bit error probability of the system, so a higher energy per bit to noise ratio is required to achieve the same Eb/No. Figure 7 shows bit error probability for various phase errors values.

Fig. 9 Bit error probability for coherently detected QPSK with phase noise.5

Fig. 10 A constellation diagram for p/4 DQPSK with a spurious of -20 dBc within the channel band.

A practical synthesizer displays random frequency fluctuations around its center frequency known as phase noise. There are several ways to define the LO's phase noise. The common definition is SSB phase noise +(f)[dBc/Hz]. However, with phase-modulated signals, the LO's phase stability DqRMS as incidental phase modulation is used to describe the LO phase noise. An indication of the total phase stability of the LO within the information bandwidth is given with this last definition. For a stable oscillator used for communication radios the phase noise follows the relationship17

This phase error is a stochastic value that exists in both the I and Q vectors. As a result, both the I and Q signals would have the same phase error due to phase noise and the phase relationship between I and Q components is preserved when phase noise exists. Hence, r(t) becomes17

The bit error probability vs. Eb/No can be calculated analytically using

where

Fe(Eb/No, q) = bit error probability for the given modulation technique as a function of Eb/No and a random phase error q

f(q) = distribution function of the phase noise q

A Gausian distribution of mean zero and variance DqRMS is assumed.

The phase noise results in random rotations of the constellation diagram around the center point. Figure 8 shows a constellation diagram of a QPSK-modulated signal when the RMS phase error is 5.75°. Figure 9 shows bit error probability of a QPSK-modulated signal for three DqRMS phase error values. Phase noise results in a degradation in bit error probability. In an ideal communication system, BER goes to zero as Eb/No goes to infinity. In the presence of phase noise, the error probability goes to a nonzero value. As the phase noise power increases, the bit error increases, thus improvement of the bit error probability performance by increasing the Eb/No is limited.

The effect of spurious outputs from the synthesizer on modulated signal quality depends on the frequency offset of the spurious signal from the synthesizer's desired frequency. Spurious signals within the channel band shift the symbols' position around their constellation target point and cause BER degradation. The shift radius of the symbols depends on the spurious-to-carrier power ratio. Figure 10 shows the constellation diagram of a QPSK-modulated signal in the presence of a -20 dBc spurious signal. Out-of-channel band spurious signals contribute to the increment of the out-of-band emission.

Fig. 11 Out-of-band emission for a p/4 DQPSK-modulated signal.

Fig. 12 A constellation diagram of a 20 dB signal-to-noise ratio p/4 DQPSK-modulated signal.

In cellular portables, which are battery fed, it is important to design the transceiver for minimum power consumption. A lower power consumption power amplifier (PA) is more efficient but less linear. Nonlinearity of the PA results in AM-to-AM and AM-to-PM conversions. These conversions cause degradation in modulation quality and produce poor bit error probability and increased out-of-band emissions that reduce spectral efficiency. The nonlinear characteristics of the PA are represented by

Fig. 14 p/4 DQPSK constellation response at 36 dBm and EVM = 6.1 percent. (IS136 specification is 12 percent.)

Fig. 15 The p/4 DQPSK spectral mask at 32.7 dBm at TDMA operation.

where

Og(t)O = magnitude of the input signal to the PA

A(Og(t)O) = AM-to-AM conversion

F(Og(t)O) = AM-to-PM conversion

f(t) = phase of the input signal r(t)

The effect of the AM-to-AM and AM-to-PM conversion of a PA results in out-of-band power emission known as spectral mask. The out-of-band power emission can be modeled by measuring A(|g(t)|) and F(|g(t)|) functions, and analyzing the power spectrum of the output signal when a baseband signal waveform function is applied to A(|g(t)|) and F(|g(t)|). An alternative way is to approximate A(|g(t)|) and F(|g(t)|) by a power series and then applying a power spectrum analysis6,10,11 efficiency. Figure 11 shows the power spectrum of a p/4 differential QPSK (DQPSK) modulated signal shaped by a square root raised cosine filter with a = 0.35 that feeds the approximated PA.

Fig. 16 Temperature effects on a QPSK modulator while switched between Rx and Tx phase; (a) Tx (08C) and (b) Tx (48C) operation.

The transmitted symbols represented by the constellation diagram points take the form of a cloud of points around each ideal target of the constellation, as shown in Figure 12. Thermal noise results in a modulation error that degrades the bit error probability of the system. Another effect of the transmitted noise is desensitization of the receiver. Generally, the transmit and receive channels within a transceiver are connected to the antenna through a duplexer. A wideband PA injects high level broadband noise into the receiver and, thus, reduces its sensitivity. The thermal noise effect on receiver sensitivity can be minimized by proper design of the out-of-band transmitter's noise rejection.

MEASURED RESULTS

A dual-mode subscriber unit containing a radio card with 440 to 450 MHz transmit and 485 to 495 MHz receive channels and 825 to 850 MHz transmit and 870 to 895 MHz receive channels was tested. The measured results are shown in Figures 13, 14, 15 and 16. Calibration methods and optimization based on the aforementioned analysis were used in the dual-mode radio card, achieving good agreement between the measured and calculated results. Figure 17 shows the measured residual AM before and after calibration.

Fig. 17 Residual AM (a) before and (b) after calibration.

CONCLUSION

When designing digital radio modulator and demodulator circuits, it is important to consider the effects of a nonideal modulator and the limited accuracy of its baseband interface network. The analytical approach to modulation impairments presented in this article can help in dealing with practical nonideal modulation effects, which are common to digital communication radios.

Special attention should be given to I and Q signal amplitude and phase balancing if a QPSK modulator is used to generate an analog FM signal. Special care also must be given to the modulator's I and Q input DC offset balancing to optimize carrier leakage (origin offset) problems. Optimizing the transmitter's power amplifier to an optimal biasing point and designing the synthesizers to exhibit low phase noise and spurious improves the spectral mask and constellation performance of the radio's transmitter.

Residual AM tested in an FM mode must be measured at a low power transmit level to ensure that the transmitter chain is operating in a linear region and there is no clipping or limiting mechanism that will improve the result and give a wrong impression. Some of the modulators are very sensitive to temperature changes while being switched on and off during Rx/Tx phases. This characteristic is due to the GaAs MESFET channel warm-up phenomena. It is recommended that the modulator be kept on at all times rather than using the power save option.

ACKNOWLEDGMENT

The authors wish to thank Gideon Argaman, former Optomic Microwaves Ltd. chief engineer and now Celletra's CTO, for his encouragement and guidance as well as his review of this article; Mark Kirzner and Florin Deligorgi, the project development technicians from Optomic who helped to carry out the project's tasks from the idea to its success; and Joseph Aharon of Telrad Inc. for his aid on tests. n

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