Polar transmitters exploit the one-to-one mapping that exists between the traditional signal description in (I,Q) rectangular coordinates and the equivalent description in polar coordinates (r,θ) where r = ( I2 + Q2 )1/2 and θ = tan-1(Q,I). The major attractions to polar modulation are that (i) it is the preferred method for GSM and EDGE owing to its extremely low power spectral density at frequency offsets ≥20 MHz and attainable PA efficiency, (ii) its inherent ability to offer a unified means to extend the same architecture to more advanced waveforms like WCDMA, and (iii) its plausibility for extending these benefits through the entire transmit chain including the PA while also addressing the severe peak-to-average power ratio that accompanies more advanced transmission waveforms like orthogonal frequency-division multiplexing (OFDM). Even so, polar solutions are not without their own set of design challenges.

When the original baseband modulation signal is described in terms of (I,Q) components, it is straightforward to show that the required instantaneous frequency deviation that is required in the equivalent polar-coordinate system is given exactly by

where the apostrophes denote differentiation with respect to time. The lefthand side of the equation is equivalent to the instantaneous frequency required in rad/s and this result makes it possible to explore the peak-frequency deviation that is required in a polar implementation. It turns out that the most demanding signal trajectories in terms of peak-frequency deviation are those that pass near the origin of the (I,Q) signal space like the straight-line trajectory shown in Figure 4. The instantaneous FM that results from this straight-line trajectory is shown in Figure 5 and it becomes more δ-function-like as the path's minimum distance from the origin decreases.

Near-origin signal trajectories occur in the standard WCDMA signal constellation like those shown in Figure 7. Failure to properly handle signal trajectories that traverse near the origin normally have negligible effect on EVM (because the signal amplitude is low), but the impact on adjacent-channel noise can be substantial.

The δ-function-like instantaneous frequency behavior shown in Figure 5 is primarily responsible for the bandwidth expansion that is frequently attributed to polar modulation techniques. Although this expansion is fairly benign for GSM-EDGE because of its relatively low symbol rate and limited dynamic range (≈ 17 dB for EDGE), the demands imposed by WCDMA waveforms are considerably more severe in both regards.

Unless innovative measures are taken, most systems are unable to deliver the high peak-frequency deviations that occur for signal trajectories that come close to the origin. Normally, the magnitude and or the fidelity of the frequency deviations are compromised leading to poor out-of-band spectral performance as well as EVM degradation. In order to illustrate this point, the instantaneous frequency deviation (Figure 5) was strongly filtered with a first-order low-pass filter prior to AM-FM polar reconstruction. The strong filtering accentuates the pulse-like signal error behavior as shown in Figure 6. If allowed to occur, these signal errors degrade the out-of-band spectral performance substantially.

FM linearity is a second important performance requirement for any polar transmit scheme that directly modulates a voltage-controlled oscillator (VCO). If the instantaneous frequency versus applied control voltage is assumed to be modeled by a memoryless polynomial, it is easy to show that (i) accuracy of the first-order term is vital for achieving good EVM performance whereas (ii) accuracy of the other polynomial terms is necessary for good out-of-band spectral performance. These requirements are fairly reasonable to achieve for GSM-EDGE, but they require a substantially better solution to address the demands imposed by WCDMA waveforms.

Polar modulation entails breaking the (I,Q) baseband modulation signal into two paths (r and ) that have distinctly different characteristics. Re-assembly of these signals at RF demands exacting time-alignment between the AM and FM signal paths. GSM-EDGE typically requires a time-precision on the order of 15 ns or better whereas the more extensive characteristics of WCDMA dictate more demanding requirements.

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