During Coffee Break (FAQ) ...

When attending a conference, talks are an appropriate way to introduce the basics of a research topic to a larger audience. However, due to the strict timeline, these talks are not very well suited for discussing details of a specific research topic. As such, coffee breaks are a perfect opportunity to debate with colleagues from all over the world. In the recent past, we have attended several conferences and presented our latest results regarding the new signaling scheme Unique Word OFDM (UW-OFDM). During typical coffee break discussions after the presentation we noticed that various researchers had very similar questions, doubts and concerns regarding UW-OFDM.

As a consequence, we have decided to start a new section called “During coffee break …” which aims at answering the most common questions regarding UW-OFDM. We note that all this information is already part of our published journals and conference papers, this section should just serve as a convenient and easy accessible collection.

What are the advantages/novelties of Unique Word (UW-OFDM) over conventional Cyclic Prefix OFDM (CP-OFDM)?

There are three major advantages of UW-OFDM over CP-OFDM:

• The CP is a random sequence whereas the UW is deterministic. Hence, the UW can be optimally designed for particular needs like synchronization and/or channel estimation purposes at the receiver side. These advantages have already been investigated in the context of UW based SC/FDE systems. As UW-OFDM and UW-SC/FDE show the same transmit signaling structure, many of the concepts are likely to be easily transferrable.

Fig. 1 Transmit data structure using CP (top) or UW (bottom)

• A second advantage of UW-OFDM over CP-OFDM is the fact that in UW-OFDM the guard interval is part of the DFT interval, whereas this is not the case for CP-OFDM. The generation of the UW within the DFT interval introduces correlations in the frequency domain which can beneficially be exploited by the receiver to improve the bit error ratio (BER) performance.
• A third advantage of UW-OFDM over CP-OFDM is the superior spectral density of the generated waveform. The out-of-band-emissions of UW-OFDM are 15 dB and more below the emissions of the CP-OFDM system (when neglecting an additional spectral shaping filter).

Fig. 2 Power spectral density comparison

It seems that UW-OFDM is just another name for Known Symbol Padding OFDM (KSP-OFDM). Is there any difference at all between those two concepts?

Although UW-OFDM may look similar to KSP-OFDM at first glance, the differences are substantial when comparing both concepts in detail. It is true that both schemes offer a deterministic sequence which may be exploited to improve system parameter estimation tasks like channel or carrier frequency offset estimation. However, the most important difference between both schemes is that the UW is part of DFT interval, whereas the KSP is not. This difference seems unessential at first, but in fact has a tremendous impact. On the one hand, this characteristic of the UW implies the cyclic convolution within the DFT interval, and on the other hand, and most importantly, the insertion of the UW within the DFT interval introduces correlations in the frequency domain. These correlations can advantageously be exploited by the receiver to improve the BER performance. KSP-OFDM does not feature these correlations.

Fig. 3 Transmit data structure using KS (top) or UW (bottom)

In conclusion, both, KSP-OFDM and UW-OFDM, offer the same advantages of a known deterministic sequence, however, the known sequence in UW-OFDM additionally offers the potential to improve the BER behavior.

It seems that the two-step approach of generating an OFDM symbol with a zero word as UW is just another name for Zero Padded OFDM (ZP-OFDM). Is there any difference at all between those two concepts?

We note that KSP-OFDM coincides with ZP-OFDM, if the KS sequence is set to zero. Hence, the same arguments as stated in the answer for the previous question apply

It seems that a comparison between UW-OFDM and CP-OFDM is not fair. Is the BER performance improvement of UW-OFDM just a result of decreasing the spectral efficiency?

The different signaling scheme illustrated in Fig. 1 may mislead to the initial impression that UW-OFDM is just a way of trading spectral efficiency against increased redundancy and thus improved BER performance. However, more detailed investigations unveil that UW-OFDM and conventional CP-OFDM show almost the same spectral efficiency. For that let us consider a simple example. Table 1 summarizes the most important parameters of the IEEE 802.11a based CP- and our proposed UW-OFDM system we have used in our considerations so far.

Table 1. Main PHY parameters of the investigated systems

In the UW-OFDM approach, dedicated pilot pilots are omitted, as the UW shall (at least) take the estimation and synchronization tasks which are normally performed with the help of the 4 pilot subcarriers. The CP-OFDM system offers 48 subcarriers per OFDM symbol to be loaded with data. Considering a symbol length of 4us (T=T_GI + T_DFT) and QPSK as modulation format, this leads to a theoretical data rate of 24 Mbit/s. In case of UW-OFDM, 36 data subcarriers and a symbol length of 3.2us (T=T_DFT) lead to a theoretical data rate of 22.5 Mbit/s. Fig. 2 illustrates the simulated and normalized power spectral densities of both transmit signals. Taking into account that CP-OFDM requires 17.38 MHz bandwidth, whereas the UW-OFDM only needs 16.55 MHz (both measured at -15 dB), the bandwidth efficiencies follow to 1.38 and 1.36 bits/s/Hz, respectively, a difference less than 1.5 %.

As such, we can conclude that the two concepts provide almost the same spectral efficiency.

What is the price in UW-OFDM for the additional BER performance gain?

As already mentioned in the answer for the previous question, the bandwidth efficiency for CP-OFDM and UW-OFDM is almost the same. However, the gain in the BER behavior may lead to a complexity increase in the receiver design. Considering a simple linear minimum mean square (LMMSE) estimator, this leads to a straightforward inversion of a diagonal matrix in the CP-OFDM case. In UW-OFDM, however, an LMMSE estimator may require the inversion of a full matrix in order to benefit from the inherent redundancy. Of course, this seems to be a serious drawback at first, but this handicap can be relativized very quickly. The computational complexity increases only moderately when designing the receiver properly. In Classical and Bayesian Linear Data Estimators for Unique Word OFDM it is shown for systematic coded UW-OFDM how to reduce the complexity tremendously by implementing the batch LMMSE estimator in a sequential way while still providing the exact same performance as the batch version. Furthermore, current developments in technology suggest that this complexity increase is only of minor concern, especially when comparing it against the complex decoding algorithms used in nowadays’ mobile wireless communication standards.

What is the difference between linear precoding and non-systematic coded UW-OFDM?

Linear precoding is a technique mostly known for its use in Multiple Input Multiple Output (MIMO) systems. Nevertheless, this technique is also well accepted in Single Input Single Output (SISO) OFDM systems as a means to combat or attenuate the effects of frequency-selective channels by appropriately distributing the data symbols over the available bandwidth. Linear precoding methods are often categorized by the type of available channel knowledge at the receiver side, ranging from no to full channel knowledge. Non-systematic coded UW-OFDM can be interpreted as a mixture of a linear dispersive preprocessor (or channel-independent precoder) and a channel-coder.

As a consequence, UW-OFDM benefits from both sides, the ability to attenuate the effects of frequency-selective channels by its precoding abilities, and the coding gain due to its channel coding functionalities.