We’ve reached part four of the series. So far we’ve looked at:

 

In a previous blog post on “The effects of phase noise and compensation on receiver performance for MIMO OFDM systems- part 3“, we have discussed the two major effects of phase noise in OFDM systems, namely, the common phase error (CPE) and the inter-carrier interference (ICI). Equally over all subcarriers, CPE causes constant constellation rotation. However, the ICI term is a random process. It has also been widely assumed that this term is distributed according to a zero-mean complex Gaussian distribution.

It is demonstrated in

[1] that the degradation caused in OFDM by phase noise is the same as in a single carrier system when phase noise effects are considered without attempting to correct them. However, it has thereafter been shown that this does not hold true if phase noise effects are corrected [2]. Some kind of channel correction mechanism is generally introduced in OFDM systems, which can also correct phase noise to some extent. Moeneclaey in [1] has proposed a closed form expression for the signal to noise ratio degradation SNRdegr due to small phase noise variance (σ2 << 1)

 

 

 

where Es represents the symbol energy and is the power spectral density of additive white Gaussian noise. (1) applies for both OFDM and single carrier systems as well.

On the other hand, a detailed MIMO-OFDM signal model over a flat fading channel which considers both TX and RX local oscillator phase noise can be borrowed from chapter 4 in [3]. It has been shown therein that the zero-mean complex Gaussian distribution of the ICI term is not a valid assumption where the limit distribution is derived for large number of the subcarriers [3]. Yu Zhang and Huaping Liu have studied the MIMO-OFDM system under the presence of both phase noise and doubly selective Rayleigh fading channels [4].

A phase noise suppression algorithm for OFDM based WLANs has been proposed by S. Wu and Y. Bar-Ness [5]. G. Liu and W. Zhu [6] discussed compensation of phase noise in OFDM systems using an ICI reduction scheme. A minimum mean square error (mmse)-based mitigation scheme to effectively minimize the impact of phase noise has been derived in [4] in the presence of a fading channel. Four detection schemes—the zero-forcing (ZF), the mmse scheme, the decorrelating decision-feedback (DF) and the mmse-DF scheme were compared in [4].

S. Wu and Y. Bar-Ness have also derived the signal-to-interference-plus-noise ratio (SINR) expression for single-antenna OFDM systems with various phase-noise levels and a different number of subcarriers [7]. The observed differences between the influence of TX and RX phase noise under flat fading channels has been intuitively explained in [3]. The ICI term effectively creates an extra TX or RX additive noise source for the TX and RX phase noise, respectively. For RX phase noise, the ICI source occurs after the fading MIMO channel. As such, its influence is similar to that of the commonly studied additive Gaussian RX noise source, i.e., the BER performance (and thus the BER flooring) depends on the MIMO configuration. However, since the TX noise source occurs prior to the propagation channel, it will result in high SNR flooring in the BER curves according to the AWGN BER performance, i.e., independent of the MIMO configuration. Therefore, the power of the resulting error term is also independent of the dimensions of the channel matrix [3].

 

 

References

[1] M. Moeneclaey, “The effect of synchronization errors on the performance of orthogonal frequency-division multiplexed (OFDM) systems,” in Proc. COST 254 (Emergent Techniques for Communication Terminals), Toulouse, France, July 1997.

[2] A. G. Armada, “Understanding the Effects of Phase Noise in Orthogonal Frequency Division Multiplexing (OFDM),” IEEE TRANSACTIONS ON BROADCASTING, VOL. 47, NO. 2, JUNE 2001.

[3] Book: “RF imperfections in high-rate wireless systems: impact and digital compensation”, Tim Schenk, Springer 2008

[4] Yu Zhang and Huaping Liu, “MIMO-OFDM Systems in the Presence of Phase Noise and Doubly Selective Fading,” IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 56, NO. 4, JULY 2007

[5] S. Wu and Y. Bar-Ness, “A phase noise suppression algorithm for OFDM based WLANs,” IEEE Commun. Lett., vol. 6, no. 12, pp. 535–537, Dec. 2002.

[6] G. Liu and W. Zhu, “Compensation of phase noise in OFDM systems using an ICI reduction scheme,” IEEE Trans. Broadcast, vol. 50, no. 4, pp. 399–407, Dec. 2004.

[7] S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: Consequences and solutions,” IEEE Trans. Commun., vol. 52, no. 11, pp. 1988–1996, Nov. 2004.

 

A MIMO radio with automatic IQ imbalance compensation.