Read Part 2 of this blog series: PAPR reduction techniques in MIMO OFDM systems – Part 2: PAPR reduction techniques in MIMO-OFDM systems

## Impact of PAPR on the performance of MIMO OFDM systems

The peak to average power ratio (PAPR) of a transmitted signal is one of main challenges in wideband multi-carrier systems that use orthogonal frequency division multiplexing (OFDM) or multiple-input multiple-output (MIMO) OFDM. Understanding the effects of PAPR on OFDM and MIMO-OFDM systems is critical when determining what techniques to use improve system performance. For the purposes of this blog post, we can use the terms OFDM and MIMO-OFDM interchangeably without affecting the meaning of PAPR.

## What is the PAPR in MIMO-OFDM systems?

The use of a large number of subcarriers introduces a high PAPR in OFDM systems. PAPR can be defined as the relationship between the maximum power of a sample in a transmit OFDM symbol and its average power (Cimini L. a., March 2000 ):

Where P peak and P average are the peak and average power of a given OFDM symbol.

The same definition of PAPR is applied to MIMO-OFDM systems. A high PAPR appears when a number of subcarriers of a given OFDM symbol are out of phase with each other. Figure 1 shows the time domain representation of the 3 subcarriers of an OFDM symbol. The right column indicates that the subcarriers are out of phase, which causes an increase in PAPR of about 2.5 dB compared to the subcarriers in the left column. Depending on the out-of-phase amount per subcarrier, the PAPR can vary up to its theoretically maximum of 10log10 (N)(dB) , where N is the number of subcarriers. In Figure 1, the 3 subcarriers reach their minimum amplitude at a same time, causing a large negative overshoot in the resulting composite OFDM signal.

Figure 1: Simple illustration of PAPR in an OFDM symbol.

## How does the PAPR effect MIMO-OFDM systems?

When a large number of subcarriers are out of phase, a significant PAPR can cause the transmitter’s power amplifier (PA) to run within a non-linear operating region. This causes significant signal distortion at the output of the power amplifier. In addition, the high PAPR can cause saturation at the digital-to-analog converter (DAC), leading to saturation of the PA.

PAPR also causes inter-modulation between the subcarriers and distorts the transmit signal constellation. Therefore, the PA must operate with a large power back-off, approximate to that of the PAPR, which leads to inefficient operation.

Therefore, it is necessary to reduce the PAPR of the transmit signal in MIMO-OFDM systems. Several PAPR reduction techniques for MIMO-OFDM exist, including clipping, block coding (Cimini X. L., May 1998) (Davis, Nov. 1999), tone reservation (Jayalath, March 2002), tone injection (Jayalath, March 2002), partial transmit sequence (Cimini L. a., March 2000 ) , and selected mapping (SLM) (Cimini L. a., March 2000 ) (Bauml, Oct 1996).

## Conclusion

This blog post discussed the effects of the PAPR on MIMO-OFDM system performance. A high PAPR is mainly caused by signal distortion at the PA output and makes the RF PA work inefficiently. A high PAPR significantly degrades the transmit signal quality by changing the constellation nature of the transmit signal. In the next blog post, we will discuss more details about performance and the complexity of the existing PAPR reduction techniques in OFDM systems.

## References

Bauml, R. F. (Oct 1996). Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping. 32 (22).
Cimini, X. L. (May 1998). Effects of Clipping and Filtering on the Performance of OFDM. 2 (5).
Cimini, L. a. (March 2000 ). Peak-to-average power ratio reduction of an OFDM signal using partial transmit sequences . 4 (3).
Davis, J. A. (Nov. 1999). Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes. 45.
Jayalath, A. D. (March 2002). Use of data permutation to reduce the peak-to-average power. 2 (2).