Complex RF mixers, zero-IF architectures, and advanced algorithms: The black magic in next-generation SDR transceivers

Figure 1 is a schematic diagram of a complex mixer in an upconverter (transmitter) configuration. Two parallel paths each have an independent mixer, and these paths are fed by a common local oscillator that is 90° out of phase with one of the mixers. The two independent outputs are then summed in a summing amplifier to produce the desired RF output.

Figure 1. Basic architecture of a complex transmitter.

This configuration has some simple but very useful applications. Assume that only a tone is fed on the I input and the Q input is not driven, as shown in Figure 2. Assuming the tone frequency on the I input is x MHz, the mixer in the I path produces an output at the LO frequency ±x. Since there is no signal applied to the Q input, the spectrum produced by the mixer in this path is empty and the output of the I mixer goes directly to the RF output.

Figure 2. I path analysis

Alternatively, assume that only a tone at frequency x is applied to the Q input. The Q mixer, in turn, produces an output with tones at the LO frequency ±x. Since no signal is applied to the I input, its mixer output is muted and the output of the Q mixer goes directly to the RF output.

Figure 3. Q path analysis

At first glance, the outputs of Figure 2 and Figure 3 appear to be identical. However, there is one key difference: phase. Assume that the same tone is applied to both the I and Q inputs simultaneously, and that there is a 90° phase shift between the input channels, as shown in Figure 4.

Figure 4. Path analysis with simultaneous application of I and Q signals.

Looking closely at the mixer output, we observe that the LO frequency plus the input frequency is in phase, but the LO frequency minus the input frequency is out of phase. This causes the tones above the LO to add, while the tones below the LO to cancel. Without any filtering, we have eliminated one of the tones (or sidebands), producing an output that is completely on one side of the LO frequency.

In the example shown in Figure 4, the I signal leads the Q signal by 90°. If the configuration is changed so that the Q signal leads the I signal by 90°, similar addition and cancellation can be expected, but in this case all signals will appear on the lower side of the LO.

Figure 5. The position of the tone depends on the phase relationship of I and Q.

Figure 5 above shows lab measurement results for a complex transmitter. The left side shows the test case where I leads Q by 90°, resulting in an output tone above LO. The right side of Figure 5 shows the opposite relationship, where Q leads I by 90°, resulting in an output tone below LO.

In theory, it should be possible to have all the energy fall on just one side of the LO. However, as shown in the lab measurements in Figure 5, in practice complete cancellation is not possible, and some energy remains on the other side of the LO, known as the image. It should also be noted that energy is also present at the LO frequency, known as LO leakage or LOL. Other energies can also be seen in the results—these are harmonics of the desired signal and are not discussed in this article.

To completely cancel the image, the I and Q mixer outputs must be exactly the same amplitude and exactly 180° out of phase with each other on the LO image side. If these phase and amplitude requirements are not met, the addition/cancellation process shown in Figure 4 will be less than ideal and energy at the image frequency will still be present.

With a conventional single mixer architecture, LO± products are generated. One of the sidebands needs to be removed before transmission, usually by adding a bandpass filter. The filter roll-off frequency must be appropriate to remove the unwanted image signal without affecting the wanted signal.

Figure 6. Single mixer image filter requirements.

The spacing between the image and the wanted signal directly affects the filter requirements. If the spacing is large, a simple, low-cost filter with a gentle roll-off can be used. If the spacing is narrow, the design must implement a filter with a steep response, usually using a multi-pole or SAW filter. It can therefore be said that the image and the wanted signal must be properly spaced so that the image can be filtered without affecting the wanted signal; this spacing is inversely proportional to the complexity and cost of the filter. In addition, if the LO frequency is variable, the filter must be tunable, which further increases the complexity of the filter.

The spacing between the image and the desired signal is determined by the signal applied to the mixer. The example in Figure 6 shows a 10 MHz bandwidth signal that is 10 MHz away from DC. The corresponding mixer output places the image 20 MHz away from the desired signal. In this configuration, to achieve a 10 MHz desired signal spectrum at the output, a 20 MHz baseband signal path must be connected to the mixer. The 10 MHz baseband bandwidth is unused and the data interface rate of the mixer circuit is higher than necessary.

Returning to the complex mixer shown in Figure 5, we know that its architecture eliminates the image without the need for external filtering. Furthermore, efficiency can be optimized in a zero-IF architecture so that the signal path processing bandwidth is equal to the desired signal bandwidth. The conceptual diagram shown in Figure 7 illustrates how this is accomplished. As mentioned above, if I leads Q by 90°, then only the output will be above LO. If Q leads I by 90°, then only the output will be below LO.

Therefore, if two independent baseband signals are generated, one designed to produce only the upper sideband output and the other designed to produce only the lower sideband output, they can be summed in baseband and applied to the complex transmitter. The result will be outputs with different signals appearing above and below the LO. In actual applications, the combined baseband signal is generated digitally. The summing node shown in Figure 7 is only to illustrate this concept.

Figure 7. Zero-IF complex mixer architecture.

There is a considerable benefit to using a complex transmitter to generate a single sideband output, reducing the RF filtering required to cancel the image. However, if the image cancellation performance is good enough to make the image negligible, then the architecture can be further exploited by using zero-IF mode. Zero-IF allows us to use specially created baseband data to generate the RF output so that independent signals appear on both sides of the LO. Figure 8 shows how this is achieved. We have two independent sets of I and Q data, encoded with symbol data, which the receiver can decode based on the phase of the reference carrier.

Figure 8. Closer look at I/Q signals in a zero-IF complex mixer configuration.

Initial observations show that Q1 leads I1 by 90° and their amplitudes are identical. Similarly, I2 leads Q2 by 90° and their amplitudes are also identical. Combining these independent signals results in I1 + I2 = SumI1I2 and Q1 + Q2 = SumQ1Q2. The summed I and Q signals no longer exhibit phase and amplitude correlation—their amplitudes are not equal at all times and their phase relationship is constantly changing. The resulting mixer output places the I1/Q1 data on one side of the carrier and the I2/Q2 data on the other side of the carrier, as described above and shown in Figure 7.

Zero-IF enhances the advantages of a complex transmitter by placing independent blocks of data adjacent to each other on either side of the LO. The data processing path bandwidth can never exceed the data bandwidth. Therefore, in theory, the use of complex mixers in a zero-IF architecture provides a solution that does not require RF filtering while optimizing baseband power efficiency and reducing the unit cost of unusable signal bandwidth.

So far, this article has focused on complex mixers used as zero-IF transmitters. The same principles apply in reverse, and the complex mixer architecture can be used as a zero-IF receiver. The same advantages described for the transmitter apply to the receiver as well. When receiving a signal using a single mixer, the image frequencies must first be filtered out using the RF mixer. In zero-IF operation, there are no image frequencies to worry about, and signals above LO are received independently of signals below LO.

A complex receiver is shown in the figure below. The input spectrum is applied to both the I and Q mixers. One mixer is driven with the LO and the other with LO + 90°. The outputs of the receiver are I and Q. It is not easy for a receiver to empirically prove what the output will be for a given input, but if the input tone is above LO, as shown, then the I and Q outputs will be at (tone – LO) frequency, and there will be a phase shift between I and Q (I leads Q). Similarly, if the input tone is below LO, then the I and Q outputs are also at (LO – tone) frequency, but this time Q leads I. In this way, a complex receiver can distinguish between energy above LO and energy below LO.

The output of the complex receiver will be the sum of two I/Q information: one representing the received spectrum above LO and the other representing the received spectrum below LO. This concept has been explained earlier for a complex transmitter, where a summed I signal and a summed Q signal are applied to the complex transmitter. For a complex receiver, the baseband processor that receives the summed I information and the summed Q information can easily distinguish between the higher and lower frequencies using a complex FFT.

Figure 9. Zero-IF complex mixer receiver configuration

When we receive the summed I and summed Q signals, we have two knowns—the summed I and summed Q—but four unknowns, I1, Q1, I2, and Q2. Since there are more unknowns than knowns, it may seem impossible to solve for I1, Q1, I2, and Q2. However, we also know that I1 = Q1 + 90 and I2 = Q2 – 90, and with these two known relationships, we can solve for I1, Q1, I2, and Q2 using the summed I and summed Q signals we received. In fact, we only need to solve for I1 and I2, since the Q signal is a replica of the I signal, but with a phase shift of ±90.

In practice, complex mixers attempt to completely eliminate image signals. This limitation has two significant effects on radio architecture design.

Even with performance limitations, a complex IF can still provide real benefits. Consider the low IF example shown in Figure 10. Due to performance limitations, we do see an image. However, the image is greatly attenuated compared to what would be expected for a single mixer design (see Figure 6). While a complex mixer still requires a filter, the requirements for that filter can be much more relaxed, and its implementation is simpler and less expensive.

Figure 10. Practical implementation of a complex mixer. Note the attenuated images.

The filter complexity is inversely proportional to the distance between the image and the desired signal. If a zero-IF configuration is used, this distance becomes zero and the image is in the desired signal band. The practical application of the zero-IF theory is not fully realized and the resulting in-band images degrades the performance to unacceptable levels (see Figure 11).

Figure 11. Limitations of zero-IF implementation

The principles of complex transmitters and receivers are only valid if the phase and amplitude requirements of the I and Q data paths are met. Mismatches in the signal paths can result in image signals on both sides of the LO that do not cancel each other accurately. Examples of this type of problem are shown in Figures 10 and 11. Without using zero IF, filtering can be used to remove the image. However, with a zero IF architecture, the unwanted image can fall directly into the spectrum of the wanted signal, and if the image power is large enough, a failure condition can occur. Therefore, using zero IF and complex mixing will only provide an optimal system design solution if the design can cancel the phase and amplitude mismatches in the signal paths.

The concept of complex mixer architecture has been around for many years, but the challenges of meeting phase and amplitude requirements in dynamic radio environments have limited its use in zero-IF mode. ADI has overcome these challenges using a combination of smart silicon design and advanced algorithms. The design allows for factors that affect the signal path, but the smart silicon design minimizes these effects. The remaining errors are removed by a self-optimizing quadrature error correction (QEC) algorithm. Figure 12 is a conceptual diagram.

Figure 12. Advanced QEC algorithms and smart silicon design enable zero-IF architecture

On ADI transceivers such as the AD9371, the QEC algorithm resides in an on-chip ARM® processor. It continuously monitors the silicon signal path, the modulated RF output, the input signal, and the external system environment, and uses this information to intelligently adapt the signal path profile in a controlled, predictive manner rather than in a knee-jerk reaction. The algorithm performs so well that it can be thought of as digitally assisting the analog signal path to perform at its best.

The dynamic QEC calibration algorithm is just one of the more prominent examples of advanced algorithms that reside and function within ADI transceivers. Other algorithms that coexist with them include LO leakage cancellation, which improves the performance of the zero-IF architecture to the optimal level. While these first-generation transceiver algorithms are mainly used to support the implementation of related technologies, second-generation algorithms (such as digital predistortion or DPD) can enhance not only the performance of the transceiver, but also the performance of the entire system.

All systems have imperfections that limit their performance. While first-generation algorithms focused on removing on-chip limitations through calibration, newer algorithms use intelligence to remove system performance and efficiency limiters outside the transceiver, such as PA distortion and efficiency (DPD and CFR), duplexer performance (TxNc), passive intermodulation issues (PIM), etc.

Complex mixers have been around for many years, but their image rejection performance did not allow them to be used in zero-IF mode. A combination of smart silicon design and advanced algorithms has removed the performance barriers that previously prevented high-performance systems from adopting zero-IF architectures. With the performance limitations removed, adopting zero-IF architectures has benefits in terms of reduced filtering, power consumption, system complexity, size, heat, and weight.

For complex mixers and zero-IF, we can consider QEC and LOL algorithms as supporting functions. However, as the scope of algorithm development has been expanded, it has brought higher performance levels to system designers, giving them more flexibility in designing radios. They can choose to enhance performance or use the benefits provided by the algorithm to reduce the cost or device size of the radio design.

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