Enhancing Performance of Asynchronous Cooperative Relay Network with Partial Feedback

Abstract

Distributed close-loop extended orthogonal space-time block code (DCL EO-STBC) was demonstrated to achieve a significant improvement of performance for closed-loop cooperative relay network systems with limited feedback channel. This paper proposes a decode-and-forward (DF) cooperative strategy with using partial feedback in stead of DCL EO-STBC to obtain a distributed cooperative diversity gain. Based on the partial phase feedback technique, the new scheme has only previous inter-symbol interference (ISI) components in the received signals and obtains an enhancing system performance in term of signal-noise power ratio (SNR) at the destination node. Theoretical analysis and Monte-Carlo simulations confirm that the using near-optimum detection (NOD) at the destination can completely remove interference components before detection process. In comparison to previous DCL EO-STBC scheme, this work not only has simpler signal processing due to not using DCL EO-STBC endcoder and decoder, but also outperforms sytem performance without decrease transmission rate.

Appendices

Appendix

A The Processional Requirement of the Proposed Scheme

Firstly, from the step 1 to step 3 at the Subsect. 3.2 in Sect. 3 we can calculate the number of operation for choosing three feedback bits as follows:

$$\begin{aligned} {C_{new\_feedback}} = 30{C_M} + 20{C_A}. \end{aligned}$$

(14)

Then, transmitted symbols at the relays are multiplied by these three feedback bits as shown in the Eq. (2) which require the processional complexity as follows:

$$\begin{aligned} {C_{new\_relay}} = 6{C_M}. \end{aligned}$$

(15)

The decoding complexity of the proposed NOD scheme depends on both the Eqs. (10) and (11) as following:

$$\begin{aligned} {C_{new\_NOD}}&= {C_{new\_eq10}} + {C_{new\_eq11}}\nonumber \\&= \left( {32{C_M} + 22{C_A}} \right) M + \left( {58{C_M} + 52{C_A}} \right) M\nonumber \\&= \left( {90{C_M} + 74{C_A}} \right) M \end{aligned}$$

(16)

where, M is the size of constellation $\mathcal{A}$ (e.g. M-QAM or M-PSK). Therefore, the total processional requirement of the proposed scheme can be written as:

$$\begin{aligned} {C_{New}}&= {C_{new\_feedback}} + {C_{new\_relay}} + {C_{new\_NOD}} \nonumber \\&= 30{C_M} + 20{C_A} + 6{C_M} + \left( {90{C_M} + 74{C_A}} \right) M \nonumber \\&= 36{C_M} + 20{C_A} + \left( {90{C_M} + 74{C_A}} \right) M. \end{aligned}$$

(17)

B The Processional Requirement of the DCL EO-STBC Scheme

From the Eqs. (15) and (16) in [1], the requirement of feedback process can be written as:

$$\begin{aligned} {C_{DCL{} EO - STBC\_feedback}} = 96{C_M} + 48{C_A}. \end{aligned}$$

(18)

The process of the relays is used to encode the DCL EO-STBC as shown in Eq. (5) [1] and requires the number of operations as follow:

$$\begin{aligned} {C_{DCL{} EO - STBC\_relay}} = 16{C_M} + 8{C_A}. \end{aligned}$$

(19)

The complexity of DCL EO-STBC detection is the number of operations from the Eqs. (20) to (24) in [1] and can be written as following:

$$\begin{aligned} {C_{DCL{} EO - STBC\_detection}} = \left( {170{C_M} + 134{C_A}} \right) M. \end{aligned}$$

(20)

Then, the total processional requirement of the DCL EO-STBC scheme is written as:

$$\begin{aligned} {C_{DCL{} EO - STBC}}&= {C_{DCL{} EO - STBC\_feedback}} + {C_{DCL{} EO - STBC\_relay}}\nonumber \\&+ {C_{DCL{} EO - STBC\_detection}} \nonumber \\&= 96{C_M} + 48{C_A} + 16{C_M} + 8{C_A} + \left( {170{C_M} + 134{C_A}} \right) M \nonumber \\&= 102{C_M} + 56{C_A} + \left( {170{C_M} + 134{C_A}} \right) M. \end{aligned}$$

(21)