Blind multipath separation and combining technique for signal recovery

Abstract

To achieve better mitigation of both cochannel interference (CCI) and intersymbol interference, a new structure using generalized estimation of multipath signals in conjunction with maximal-ratio combining diversity for wireless communications over multipath channels is introduced. In this structure, the signal replicas received from multiple paths are first independently produced by a bank of blind spatial filters and then constructively combined by a diversity combining receiver for final signal estimate. The new scheme can be applied on single antenna array or between multiple antenna subarrays. It will be shown, from both theoretical analysis and numerical experiments, that the new scheme provides both space diversity gains and path diversity gains while suppressing the CCIs.

Appendix

Here we look at the case when the reference output contains the unresolved path-1 and 2 and we have

$$\begin{aligned} z(k)=\beta _{1}s(k-\ell _{1})e^{j2\pi \nu _{1}k}+\beta _{2}s(k-\ell _{2}) e^{j2\pi \nu _{2}k} \end{aligned}$$

(47)

and

$$\begin{aligned} y'(k)&= \beta _{3}s(k-\ell _{3}-\ell )e^{j2\pi (\nu _{3}+\nu )k}\nonumber \\&= \beta _{3}s(k-\ell _{3}-(\ell _{1}-\ell _{3}))e^{j2\pi (\nu _{3}+(\nu _{1} -\nu _{3}))k}\nonumber \\&= \beta _{3}s(k-\ell _{1})e^{j2\pi \nu _{1}k} \end{aligned}$$

(48)

Hence,

$$\begin{aligned} \epsilon&= \mathbf {E}\left\{ \Vert z(k)-y'(k)\Vert ^{2}\right\} \nonumber \\&= \mathbf {E}\left\{ \Vert z(k)\Vert ^{2}+\Vert y'(k)\Vert ^{2}-z^{*}(k)y'(k)-z(k) y'^{*}(k)\right\} \nonumber \\&= \beta _{1}^{2}\sigma _{s}^{2}+\beta _{2}^{2}\sigma _{s}^{2}+\beta _{3} ^{2}\sigma _{s}^{2}-\beta _{1}^{*}\beta _{3}\sigma _{s}^{2}-\beta _{1} \beta _{3}^{*}\sigma _{s}^{2}\nonumber \\&= \left[ (\beta _{1}-\beta _{3})^{2}+\beta _{2}^{2}\right] \sigma _{s}^{2} \nonumber \\&\mathrm s.t. \beta _{1}=f(\mathrm const ), \beta _{2}=c\beta _{1} \end{aligned}$$

(49)

where $\mathbf {E}$ denotes expectation, $\sigma _{s}^{2}$ is the signal power. The constraints in (49) can be interpreted as following: the complex scale factor $\beta _{1}$ is some constant value and $\beta _{2}$ is a scaled value of $\beta _{1}$ with some constant scalar $c$. Note here that (49) is derived with the assumption that the signal $s(k)$ is i.i.d.. Therefore, from (49), $\epsilon$ can be minimized when

$$\begin{aligned} \beta _{1}=\beta _{3} \end{aligned}$$

(50)

Note here that in the presence of additive noise that is i.i.d., the above analysis and conclusion are still valid.