## Peak-to-average Power Ratio Reduction in Multi-antenna OFDM Via Multiple Signal Representation

Band 29, Erlanger Berichte aus Informations- und Kommunikationstechnik,
Herausgeber: A. Kaup, W. Koch, J. Huber. Shaker Verlag, Aachen, 2010.

### Abstract

Modern digital communication systems take advantage of the combined application of orthogonal frequency-division multiplexing (OFDM) and multi-antenna (or multiple-input/multiple-output (MIMO)) systems, often denoted as MIMO OFDM. OFDM is a very popular approach to equalize the temporal intersymbol interferences caused by frequency-selective channels. Using MIMO systems, it is possible to increase the channel capacity while keeping the transmission bandwidth and the transmit power. One of the most serious drawbacks of OFDM are high peaks of the transmit signal. Processing such a transmit signal with a nonlinear power amplifier at the transmitter front-end causes signal clipping, which in turn generates out-of-band radiation. In order to avoid the disturbance of adjacent transmission channels, this out-of-band radiation has to be strictly avoided. Considering multi-antenna transmitters, the issue of out-of-band radiation gets even more serious. For this reason, a transmitter-sided algorithmic control of the signal peaks, also known as peak-to-average power ratio (PAR) reduction algorithm, is desirable.

PAR reduction algorithms for single-antenna transmitters are well known in literature. However, there is a particular need for PAR reduction schemes, especially designed for MIMO systems. In this thesis, the schemes based on multiple signal representation, which are selected mapping (SLM) and partial transmit sequences (PTS), are extended to multi-antenna systems. In this context, we pursue the goal to exploit the multiple transmit antennas to achieve further gains in PAR reduction performance. Interestingly, based on the analysis of the multi-antenna extensions, further improvements on the respective single-antenna schemes can be derived. The analysis of the particular PAR reduction schemes and their extensions include further aspects, whose contributions are summarized as follows.

Alternative metrics to the PAR are regarded and are assessed with respect to the out-of-band radiation. This analysis is carried out with different power amplifier models and shows that the peak-to-average power ratio is the best suited metric to reflect the contribution of one OFDM frame to the out-of-band radiation caused by the clipping characteristic of a power amplifier.

For SLM and all its extensions, a deep analytical analysis of the PAR reduction performance is possible. In this context, the asymptotic behaviour of the cumulative distribution of PAR values is of particular interest. It can be shown, that with the original approach of SLM, the asymptotic slope of the cumulative distribution of PAR values is solely influenced by the number of assessed signal candidates. Considering multi-antenna transmitters and a parallel application of the original approach to each transmit antenna offers the same asymptotic behaviour. Additionally, an extension for multi-antenna transmitters is proposed. This extension directs the PAR reduction efforts on that transmit antenna which currently generates the most out-of-band radiation. This approach is favourable because the mean out-of-band radiation over all antennas is dominated by that transmit antenna with the highest contribution. It turns out, that the asymptotic slope of this extension is determined by the number of assessed signal candidates times the number of transmit antennas. Now, the PAR reduction performance increases the more transmit antennas are present. This effect is similar to the "diversity gain" when regarding bit error ratios of the transmission over flat-fading MIMO channels.

Besides multi-antenna point-to-point scenarios, multi-antenna multi-user scenarios are assessed. Of particular interest is the downlink direction, i.e., point-to-multipoint scenarios, where a joint signal processing is only feasible at the transmitter. Possible extensions of SLM and PTS are discussed and analyzed. Moreover, an additional approach, namely selected sorting (SLS), is proposed. This scheme combines the transmitter-sided precoding, which is mandatory in point-to-multipoint scenarios, with the generation of signal candidates.

In addition to a complete assessment of all possible signal candidates, a successive candidate generation is proposed, which stops after one signal candidate is found whose PAR falls below a tolerated threshold. Choosing this tolerated threshold above the critical PAR (natural logarithm of the number of subcarriers) leads to an average number of signal candidates to be assessed below 2.71 (Euler's number), independent from the maximum possible number of assessable signal candidates. The PAR reduction performance of this successive approach is identical to the complete assessment.

A comparison of the different PAR reduction schemes, considered in this thesis, is provided. This comparison is built upon the basis that all schemes exhibit the same computational complexity. It turns out that, under this constraint, PTS offers a better PAR reduction performance than SLM. Regarding point-to-multipoint scenarios, the performance of SLS lies between the ones of PTS and SLM.

Finally, this thesis addresses the issue of transmitting some extra or side information, which is required with the PAR reduction schemes based on multiple signal representations. First, an explicit transmission of the side information via reserved subcarriers is considered. Second, an implicit transmission is proposed, which embeds the side information inherently into the OFDM frame. Both schemes are analyzed with respect to their influences on the detection error ratio of the side information. It can be shown that both schemes provide reasonable results. Furthermore, improved estimation strategies of the side information are proposed, which include the consideration of a-priori probabilities and a joint detection when regarding MIMO systems.