Abstract
Due to the inherent feedback in a decision feedback equalizer (DFE) the minimum mean square error (MMSE) or Wiener solution is not known exactly. The main difficulty in such analysis is due to the propagation of the decision errors, which occur because of the feedback. Thus in literature, these errors are neglected while designing and/or analyzing the DFEs. Then a closed form expression is obtained for Wiener solution and we refer this as ideal DFE (IDFE). DFE has also been designed using an iterative and computationally efficient alternative called least mean square (LMS) algorithm. However, again due to the feedback involved, the analysis of an LMS-DFE is not known so far. In this paper we theoretically analyze a DFE taking into account the decision errors. We study its performance at steady state. We then study an LMS-DFE and show the proximity of LMS-DFE attractors to that of the optimal DFE Wiener filter (obtained after considering the decision errors) at high signal to noise ratios (SNR). Further, via simulations we demonstrate that, even at moderate SNRs, an LMS-DFE is close to the MSE optimal DFE. Finally, we compare the LMS DFE attractors with IDFE via simulations. We show that an LMS equalizer outperforms the IDFE. In fact, the performance improvement is very significant even at high SNRs (up to 33%), where an IDFE is believed to be closer to the optimal one. Towards the end, we briefly discuss the tracking properties of the LMS-DFE.
Highlights
A channel equalizer is an important component of a communication system and is used to mitigate the inter symbol interference (ISI) introduced by the channel
We show that the decision feed back equalizer (DFE)-Wiener filter (WF) and an least mean square (LMS)-DFE attractor are close to each other at high signal to noise ratios (SNRs)
Our claim is that in case of a DFE, apart from being computationally efficient the LMS algorithm outperforms the ideal DFE (IDFE), IDFE. This is because we will see briefly that the LMS attractors are close to DFEWF while IDFE is away from DFE-WF. We achieve this goal by showing that the LMS-DFE attractors are close to that of the DFE-WF at high SNRs
Summary
A channel equalizer is an important component of a communication system and is used to mitigate the inter symbol interference (ISI) introduced by the channel. A DFE feeds back the previous decisions of the transmitted symbols, to nullify the ISI due to them (which can happen without amplifying the thermal noise) and makes a better decision about the current symbol. These equalizers have been used for quite sometime, due to feedback their behavior is much more complex than that of the LEs. these equalizers have been used for quite sometime, due to feedback their behavior is much more complex than that of the LEs A DFE mainly exploits the finite alphabet structure of the hard decoder output [2,13] and the hard decoder cannot be ignored (i.e., its performance is better than a system with a soft decoder)
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