Improved iterative detection and achieved throughputs of OFDM systems under imperfect channel estimation

Abstract

Assuming imperfect channel estimation, we propose an improved detector for ultra wideband (UWB) systems employing multiband orthogonal frequency-division multiplexing (MB-OFDM). By adopting a Bayesian approach involving the statistics of the channel estimation errors, we formulate an improved maximum-likelihood (ML) detection metric taking into account the characteristics of the channel estimates. As a first step, we propose a modified iterative detector based on maximum a posteriori which reduces the impact of channel uncertainty on the decoder performance, by an appropriate use of this metric. The results are compared to those obtained by using a detector based on a mismatched ML metric, which uses the channel estimate as if it was the perfect channel. In a second step, we calculate the information rates achieved by both the improved and mismatched ML detectors, in terms of achievable outage rates. These outage rates are compared to those provided by a theoretical (not practical) decoder defined as the best decoder in the presence of channel estimation errors. Numerical results over both uncorrelated Rayleigh fading channels and realistic UWB channels show that the improved detector provides significant gains in terms of bit error rate and achievable outage rates, compared to the classically-used mismatched approach, without any increase in the receiver complexity.

Optimal soft combination for multiple antenna energy detection under primary user emulation attacks

“…We can thus conclude that the pilot overhead due to employing multiple CR users is minimized in our system model since only one pilot symbol is necessary to achieve performance very close to the case of perfect CSI. More precisely, we have adopted the least-squares estimate of unknown channel which coincides with the maximum likelihood estimate under Gaussian noise by following the approach of [23]. Here, the channel coefficient in the kth time slot is necessary.…”

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“…Then, Σ H is a diagonal matrix with equal diagonal entries σ 2 h . By using the prior pdf of H from (11) and the pdf of (Ĥ|H) from (10), we can derive the posterior distribution of the perfect channel matrix, conditioned on its ML estimate, as follows (see Sadough & Duhamel (2008) for the details of the derivation):…”

“…In fact, equation (22) shows that p(y y y|Ĥ, x x x) can be simply derived from the general formulation in (19). It is shown in Sadough & Duhamel (2008) that the averaged likelihood in (22) is shown to be a complex Gaussian distributed vector given by…”

“…This sub-optimal approach is usually called the mismatched receiver. Its sub-optimality is due to the fact that the receiver does not take into account the presence of channel estimation errors Sadough & Duhamel (2008); Sadough (2008). A more appropriate approach is to take into account channel estimation inaccuracies in the formulation of the detector.…”

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“…It is shown, for instance in [3], that this scheme greatly degrades the detection performance in the presence of channel estimation errors. As an alternative to the aforementioned mismatched approach, Sadough and Duhamel recently proposed in [4] a general method for robust receiver design under channel estimation errors. This technique takes into account the presence of channel estimation errors in the formulation of the receiver.…”