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This paper investigates the impact of the channel estimation error and outdated channel state information (CSI) on the outage performances of partial relay selection (PRS) and efficient partial relay selection (EPRS). Considering imperfect channel estimation and outdated CSI with decode-and-forward (DF) relaying strategy, closed-form expressions for exact outage probabilities and asymptotic outage probabilities for PRS and EPRS are provided assuming independent and nonidentically distributed Rayleigh fading channels. Numerical investigations verify the analytical expression for outage probability and show how much performance is degraded by the channel estimation errors and the feedback delay that causes the outdated CSI.

Cooperative relaying has attracted great attention because it offers an excellent performance at low cost by forming a virtual multiple-input multiple-output (MIMO) system using all available nodes as relays. In industry, the cooperative relaying system has been included in both worldwide interoperability for microwave access (WiMAX) [

The assumption of perfect CSI for selecting a single relay and decoding a received signal may be impractical because the acquired CSI generally contains estimation errors because of noise, and also it can be outdated because of a feedback delay time. Therefore, performance evaluation and system design considering the impacts of both channel estimation errors and outdated CSI may be critical and necessary to satisfy performance requirements in practical communication environments. In [

We consider a dual-hop DF relaying system using relay selection that consists of a source,

Dual-hop relaying system using relay selection where relay

Let the channel coefficient for relay

The source and the relays transmit training signals orthogonally, and then the minimum-mean-square-error- (MMSE-) estimated channels at the relays and the destination are given by [

Since the estimated CSI is fed back for relay selection, the CSI may be outdated when the source and the selected relay transmit a data signal. Letting

For PRS, the first-hop CSI is used to select a single relay. Thus, each relay feeds back the estimated CSI for the first hop to the source. Then, the source broadcasts the index of a selected relay to all the relays. The relay selected by PRS is expressed as [

For EPRS, the first-hop estimated CSI for relay

In this paper, we assume equal transmit powers at the source and the relays and equal noise powers at the relays and the destination, denoted as

An outage probability expression of PRS can be easily obtained from that of EPRS. Thus, in this paper, we show only derivations of outage probability of EPRS.

Using [

Conditioned on

Let

Using (

In this section, different asymptotic analysis is performed according to the condition of

When

In contrast to the asymptotic analysis for

To verify the analysis presented in this paper and evaluate the outage performance, we consider three simulation cases as shown in Table

Description of simulation cases.

Cases | | | Average channel powers |
---|---|---|---|

I | 1 bps/Hz | 2 | |

| |||

II | 1 bps/Hz | 3 | |

| |||

III | 1 bps/Hz | 3 | |

Correlation coefficient

| | 4.5 km/h | 10 km/h | 30 km/h | 60 km/h |
---|---|---|---|---|---|

2.0 | 0.5 | 0.9998 | 0.9992 | 0.9924 | 0.9698 |

2.0 | 1 | 0.9993 | 0.9966 | 0.9698 | 0.8818 |

2.0 | 1.5 | 0.9985 | 0.9924 | 0.9326 | 0.7441 |

0.8 | 1.5 | 0.9998 | 0.9988 | 0.9891 | 0.9566 |

3.0 | 1.5 | 0.9965 | 0.9829 | 0.8516 | 0.4720 |

Outage probabilities of EPRS and PRS with perfect channel estimation for Case I when

Outage probabilities of EPRS and PRS with perfect channel estimation for Case II when

Outage probabilities of EPRS and PRS with perfect channel estimation for Case III when

Outage probabilities of EPRS and PRS with

Outage probabilities of EPRS and PRS with

Outage probabilities of EPRS and PRS with

Figures

Figures

This paper presents the exact and closed-form expressions for outage probabilities of PRS and EPRS in dual-hop DF relaying systems with channel estimation errors and outdated CSI under nonidentical Rayleigh fading channels. In addition, the expressions for their asymptotic outage probabilities are presented. Numerical results verify the analytic expressions and show that the performance improvement of EPRS over PRS becomes smaller as the feedback delay time increases, but it can be better as the number of relays and the average channel power gap between the first and the second hops increase. Furthermore, the impact of channel estimation errors on the outage performance is much more serious than feedback delay, since the channel estimation errors induce a considerable reduction in the diversity order. Finally, we recognize that a CSI feedback design is much more important for EPRS than PRS, and an advanced channel estimation scheme is necessarily required for both EPRS and PRS in order to maintain the diversity order. Furthermore, when the multiantenna relays are considered, an impact of channel estimation errors and outdated CSI on the system performance may be more serious than the single-antenna scenario. Therefore, further study of the performance analysis of the cooperative relaying system with MIMO configuration is required in the presence of channel estimation errors and outdated CSI.

The authors declare that they have no competing interests.

This work was supported by the ICT R&D program of MSIP/IITP [B0117-16-1005, A Study on Core Technology for Multidimensional Immersive Media Broadcasting and Communication].