Originally posted Nov 21, 2014
“Tone reservation” is not an agency to book a band for your wedding
I recently explained some of the reasons why OFDM has become ubiquitous in wireless applications, but didn’t say much about the drawbacks or tradeoffs. As an RF engineer, you know there will be many—and they’ll create challenges in measurement and implementation. It’s time to look at one or two.
Closely spaced subcarriers demand good phase noise in frequency conversion, and the wide bandwidth of many signals means that system response and channel frequency response both matter. Fortunately, it’s quite practical to trade away a few of the data subcarriers as reference signals or pilots, and to use them to continuously correct problems including phase noise, flatness and timing errors.
However, pilot tracking cannot improve amplifier linearity, which is another characteristic that’s at a premium in OFDM systems. A consequence of the central limit theorem is that the large number of independently modulated OFDM subcarriers will produce a total signal very similar to additive white Gaussian noise (AWGN), a rather unruly beast in the RF world.
The standard measure for the unruliness of RF signals is peak/average power ratio (PAPR or PAR). The PAPR of OFDM signals approaches that of white noise, which is about 10-12 dB. This far exceeds most single-carrier signals, and the cost and reduced power efficiency of the ultra-linear amplifiers needed to cope with it can counter the benefits of OFDM.
A variety of tactics have been used to reduce PAPR and civilize OFDM, and they’re generally called crest factor reduction (CFR). These range from simple peak clipping to selective compression and rescaling, to more computationally intensive approaches such as active constellation extension andtone reservation. The effectiveness of these techniques on PAPR is best seen in a complementary cumulative distribution function (CCDF) display:
The CCDF of an LTE-Advanced signal with 20 MHz bandwidth is shown before and after the operation of a CFR algorithm. Shifting the curve to the left reduces the amount of linearity demanded of the LTE power amplifier.
Peak clipping and compression have not been especially successful because they are nonlinear transformations. Their inherent nonlinearity can cause the same problems we’re trying to fix.
As you’d expect, it’s the more DSP-heavy techniques that provide better PAPR reduction without undue damage to modulation quality or adjacent spectrum users. This is yet another example of using today’s rapid increases in processing power to improve the effective performance of analog circuits that otherwise improve much more slowly on their own.
In the tone reservation technique, a subset of the OFDM data subcarriers is sacrificed or reserved for CFR. The tones are individually modulated, but not with data. Instead, appropriate I/Q values are calculated on the fly to counter the highest I/Q excursions (total RF power peaks) caused by the addition of the other subcarriers.
Since all subcarriers are by definition orthogonal, the reserved ones can be freely manipulated without affecting the pilots or those carrying data. Thus, in theory the cost of CFR is primarily computational power along with the payload capacity lost from the sacrificed subcarriers.
The full nature of the cost/benefit tradeoff is more complicated in practice but one example is discussed in an IEEE paper: “By sacrificing 11 out of 256 OFDM tones (4.3%) for tone reservation, over 3 dB of analog PAR reduction can be obtained for a wireless system.” 
That’s a pretty good deal, but not the only one available to RF engineers. I mentioned the active constellation extension technique above, and other approaches include selective mapping and digital predistortion. They all have their pros and cons, and I’ll look at those in future posts.
 An active-set approach for OFDM PAR reduction via tone reservation, available at IEEE.org.