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The concept of close-loop beamforming for MIMO system was well known proposed the singular value decomposition on channel matrix. This technique can improve the capacity performance, but the cost of feedback channel and the complexity processing discard the interest of implementation. Therefore, this paper aims to investigate the benefit of using an open-loop beamforming for MIMO system in practical approaches. The low-profile concept of open-loop beamforming which is convenient for implementation is proposed by just inserting Butler matrices at both transmitter and receiver. The simulation and measurement results indicate that the open-loop beamforming with Butler matrix outperforms the conventional MIMO system. Although, the close-loop beamforming offers a better performance than open-loop beamforming technique, the proposed system is attractive because it is low cost, uncomplicated, and easy to implement.

The MIMO (Multiple-input-multiple-output) system is a good quality of service such as channel capacity. In general, MIMO systems consideration of channel capacity is based on the array antennas at both transmitter and receiver.Many works have proposed the method of eigen-beamforming technique [

In the research areas of MIMO system, many works such as [

In summary, the contribution of this paper falls into three main issues. At first, the analytical analysis of how open loop beamforming impacts on the channel matrix is originally provided. This helps the reader to understand in a true benefit of open loop beamforming. Secondly, the practical realization of open loop beamforming for

For a memoryless SISO (single-input-single-output) system, the Shannon capacity is given by [

We consider the narrowband MIMO channel. Let

Figure

System overviews.

Conventional MIMO system

Close loop beamforming

Open loop beamforming

Figure

Figure

In (

It is similarly defined for the open loop beamforming representation of the transmitted signal. The signal transmitted at direction

We can transform the conventional MIMO system into the open loop beamforming by the following expression:

Figure

Examples of

It has been demonstrated in the literatures [

Let the channel matrix be modeled as

According to (

In literatures, the degradation of channel capacity depends on the magnitude of correlation coefficient. As seen in (

Because the property of each path is independent from each other and also the attenuation is independent from the directional cosine, then

In (

With the same derivation as receiver, the mean of correlation coefficient at transmitter is given by

According to (

For the mean value of open loop beamforming, the same assumption with conventional MIMO has been used. From (

The magnitude of mean correlation, for

Figure

Block diagram of Butler matrix [

It is easily shown that the weight vectors corresponding to each port presented in Table

Element phasing, beam direction, and interelement phasing for the Butler matrix shown in Figure

Beam direction | Inter-element phasing | |||||
---|---|---|---|---|---|---|

Port 1 ( | −45° | −180° | 45° | −90° | 138.6° | −135° |

Port 2 ( | 0° | −45° | −90° | −135° | 104.5° | −45° |

Port 3 ( | −135° | −90° | −45° | 0° | 75.5° | 45° |

Port 4 ( | −90° | 45^{o} | −180° | −45° | 41.4° | 135° |

Figure

Element phasing, beam direction, and interelement phasing for the Butler matrix shown in Figure

Beam direction | Inter-element phasing (average) | |||||
---|---|---|---|---|---|---|

Port 1 ( | 158° | 25° | −112° | 118° | 138° | −130° |

Port 2 ( | −87° | −137° | 176° | 137° | 105° | −42° |

Port 3 ( | 132° | 178° | −139° | −98° | 76° | 50° |

Port 4 ( | 136° | −90° | 40° | 176° | 42° | 138° |

The parameters used for measurements.

Parameters | Value |
---|---|

Antenna type | Monopole |

Number of transmitted antennas | 4 |

Number of received antennas | 4 |

Center frequency | 2.4 GHz |

The normalized separation between the transmit antennas | 0.5 |

The normalized separation between receive antennas | 0.5 |

Distance between Tx and Rx at location 1 | 2.3 m |

Distance between Tx and Rx at location 2 | 6.6 m |

Distance between Tx and Rx at location 3 | 6.8 m |

Distance between Tx and Rx at location 4 | 6.1 m |

Distance between Tx and Rx at location 5 | 13.3 m |

Configuration of manufactured Butler matrix.

Figure

Illustration of applying Butler matrix for

Figure

Block diagram of measurement setup.

Figure

Measurement scenarios.

The simulations are undertaken by MATLAB programming, and the capacity results are evaluated by using (

In Figure

Average capacity (bits/s/Hz) versus SNR (dB) for 4 conditions of angle spread,

The channel matrices

Figure

Measured

In Figure

Average capacity (bits/s/Hz) versus SNR (dB) at each location.

For the measurements resulting in Figure

Average capacity (bps/Hz) of all locations when rotating the direction of array antennas for SNR = 10 dB.

Location | Direction | |||||
---|---|---|---|---|---|---|

0° | 45° | 90° | ||||

Conv. MIMO | Open loop BF | Conv. MIMO | Open loop BF | Conv. MIMO | Open loop BF | |

1 | 8.72 | 10.12 | 9.99 | 11.68 | 11.01 | 11.59 |

2 | 8.43 | 8.52 | 10.54 | 10.98 | 9.61 | 10.84 |

3 | 6.46 | 6.65 | 6.88 | 9.69 | 9.67 | 10.00 |

4 | 6.88 | 7.37 | 6.66 | 10.69 | 6.67 | 10.69 |

5 | 10.57 | 11.03 | 11.11 | 11.52 | 11.31 | 11.59 |

The rotating directions of array antennas for measurement scenarios.

Average capacity (bits/s/Hz) versus SNR (dB) for various array directions at location 5.

This paper presented the performance of MIMO systems using open loop beamforming realized by Butler matrix. The simulation results reveal that the proposed system outperforms the conventional MIMO system for every fading case. Then, this paper verified the benefit of using open loop beamforming technique for

This paper is financially supported by Suranaree University of Technology, Thailand and the Royal Golden Jubilee Program of Thailand Research Fund, Thailand.