Channel estimation in high date rate UWB system with unknown narrowband interference

Abstract

Interference degrades the performance of a correct data signal detection and decoding. This problem becomes rigorous when interferences are present during the period of channel estimation. This will wipe out the accuracy of channel estimation and will eventually result in a severe degradation in the performance of signal detection and decoding in the entire data packet/frame. In this article, we propose improved channel estimation techniques for multiband orthogonal frequency division multiplexing ultra-wideband system in narrowband interfering environment. In particular, we work towards preamble-based channel estimation techniques in the presence of unknown narrowband interference. The interference power on each subcarrier is considered as a nuisance parameter and is averaged out from the corresponding likelihood function. The later is then optimized in an iterative manner according to the quasi-Newton algorithm. Furthermore, we address highly accurate channel estimation in a time-variant channel due to sudden channel change and propose an iterative interpolation method and weighted channel estimation approach to reduce the effect of abrupt channel changes. Link level simulation results indicate that our proposed approaches outperform the conventional estimation methods.

Appendix

1.1 Cramer–Rao bound of proposed ML estimator

Taking the logarithm of in (6), we get the log-likelihood function:

Assuming ideal knowledge of σ ², the Fisher information matrix computed from the above equation leads to the inequality:

$$ E\left\{ {\left( {\widehat{h}-h} \right){{{\left( {\widehat{h}-h} \right)}}^H}} \right\}\geqslant \frac{1}{{2\sigma_s^2}}{{\left( {F^H {C^{-1 }}F} \right)}^{-1 }} $$

(34)

Using (4) and (5), (34) yields

$$ \begin{array}{*{20}c} {E\left\{ {\left( {{{\widehat{H}}_{\mathrm{MLE}}}-H} \right){{{\left( {{{\widehat{H}}_{\mathrm{MLE}}}-H} \right)}}^H}} \right\}\geqslant \frac{1}{{2\sigma_s^2}}F{{{\left( {F^H {C^{-1 }}F} \right)}}^{-1 }}} \hfill \\ {\Rightarrow E\left[ {tr\left\{ {\left( {{{\widehat{H}}_{\mathrm{MLE}}}-H} \right){{{\left( {{{\widehat{H}}_{\mathrm{MLE}}}-H} \right)}}^H}} \right\}} \right]\geqslant \frac{1}{{2\sigma_s^2}}\left[ {tr\left\{ {F{{{\left( {F^H {C^{-1 }}F} \right)}}^{-1 }}} \right\}} \right]} \hfill \\ {\Rightarrow E\left[ {tr\left\{ {{{{\left( {{{\widehat{H}}_{\mathrm{MLE}}}-H} \right)}}^H}\left( {{{\widehat{H}}_{\mathrm{MLE}}}-H} \right)} \right\}} \right]\geqslant \frac{1}{{2\sigma_s^2}}\left[ {tr\left\{ {F{{{\left( {F^H {C^{-1 }}F} \right)}}^{-1 }}} \right\}} \right]} \hfill \\ {\Rightarrow E\left\{ {<\left( {{{\widehat{H}}_{\mathrm{MLE}}}-H} \right),\left( {{{\widehat{H}}_{\mathrm{MLE}}}-H} \right)>} \right\}} \hfill \\ {\Rightarrow \frac{1}{{2\sigma_s^2}}\left[ {tr\left\{ {F{{{\left( {F^H {C^{-1 }}F} \right)}}^{-1 }}} \right\}} \right]} \hfill \\ \end{array} $$

(35)

where <A, B> is the inner product of A and B and the relation <A, B> = tr(B ^H A) has been used. Frobenius norm induced by the above inner product in (35) eventually leads to the following inequality:

$$ E\left\{ {{{{\left\| {{{\widehat{H}}_{\mathrm{MLE}}}-H} \right\|}}^2}} \right\}\geqslant \frac{1}{{2\sigma_s^2}}\left[ {tr\left\{ {F{{{\left( {F^H {C^{-1 }}F} \right)}}^{-1 }}} \right\}} \right] $$

(36)

1.2 IEEE 802.15.3a UWB channel model

The channel that we are concerned with is IEEE 802.15.3a UWB RF channel model that is given by,

$$ {h_{\mathrm{RF}}}(t)=X\mathop{\sum}\limits_{l=0}^{L_h }\ \mathop{\sum}\limits_{r=0}^R{\alpha_{r,l }}\delta \left( {t-{T_l}-{\tau_{r,l }}} \right), $$

(37)

where T _l , τ _r,l , and X are random variables representing the delay of the l − th cluster, the delay (relative to the l − th cluster arrival time) of the r − th multipath component of the l − th cluster and the log-normal shadowing, respectively. The channel coefficients are defined as a product of small-scale- and large-scale fading coefficients, i.e., α _r,l  = p _r,l ξ _l β _r,l where p _r,l takes on equiprobable ±1 to account for signal inversion due to reflections, and {1β _r,l } are log-normal distributed path gains. Then, we have E[α _r,l (T _l , τ _r,l )] = 0 and $E\left[ {{{{\left| {{\alpha_{r,l }}\left( {T_l, {\tau_{r,l }}} \right)} \right|}}^2}} \right]={\varOmega_0}{e^{{{{{-{T_l}}} \left/ {\varGamma } \right.}}}}{e^{{{{{-{\tau_{r,l }}}} \left/ {\gamma } \right.}}}}$. Γ and γ are the cluster decay factor and ray decay factor, respectively. With different parameters, four typical environments are defined; they are CM1, CM2, CM3, and CM4. Note that CMj stands for channel model j.