**3.2 Channel measurement system using OFDM pilot**

In the section, we present an example of OFDM-pilot-based MIMO channel measurement scheme. The measurement is conducted under LTE system. We utilize the reference signal (pilot) to carry out the 4x4 MIMO channel measurement. In this example, the measurement of channel occupied by pilots is LS algorithm, with the purpose of decreasing complexity.

One transmitter sends data according to the LTE agreement, so that each transmitted subframe consists of pilots and useful data. Receiver breaks down each subframe to obtain pilot segments and data segments, respectively. Such measurement equipment can implement the channel measurement without interrupting communications.

A cascade 1-D filtering is used for the 2-D interpolation. This cascade 1-D filtering firstly interpolates the channel in frequency domain with LMMSE interpolation, and then finishes the whole interpolation with a linear time domain interpolation.

There are several reasons why we choose a cascade of frequency LMMSE interpolation and time linear interpolation. LMMSE interpolation certainly has the best MSE performance among all the interpolation schemes. However, the complexity of LMMSE interpolation is much larger than that of linear interpolation. Thus, a tradeoff between performance and complexity has to be made. In frequency domain, LMMSE can provide a large performance increase. When achieving the same BLER or throughput performance, LMMSE interpolation can save about 2 dB SNR. On the other hand, the performance improvement in time domain by applying LMMSE interpolation is marginal, saving only 0.25 dB average. Considering the above, the usage of a cascade of frequency LMMSE interpolation and time linear interpolation is reasonable.

A block diagram of this example is showed in Fig. 8.

Fig. 8. A block diagram of LTE MIMO channel measurement system.

In addition, the pilot pattern of LTE system with 4 antennas can be seen in Fig. 9.

Fig. 9. Pilot pattern of LTE system [4].

#### **3.2.1 Measurements on LTE pilots**

248 Wireless Communications and Networks – Recent Advances

In addition, the pilot pattern of LTE system with 4 antennas can be seen in Fig. 9.

0 *l*

6 *l*

0 *l*

6 *l* Resource element (*k,l*)

Not used for transmission on this antenna port

Reference symbols on this antenna port

0 *l* 0 *l* even-numbered slots Antenna port 0

odd-numbered slots

even-numbered slots Antenna port 1

odd-numbered slots

even-numbered slots Antenna port 2

odd-numbered slots

even-numbered slots Antenna port 3

odd-numbered slots

6 *l*

0 *l*

6 *l*

0 *l*

6 *l*

0 *l*

6 *l*

0 *l*

2 *R*

6 *l*

0 *l*

6 *l*

0 *l*

6 *l*

0 *l*

3 *R*

6 *l*

1 *R*

1 *R*

0 *R*

0 *R*

0 *R*

0 *R*

1 *R*

1 *R*

2 *R*

> 0 *R*

> 0 *R*

> 1 *R*

> 1 *R*

2 *R*

3 *R*

0 *R*

0 *R*

1 *R*

1 *R*

2 *R*

3 *R*

3 *R*

6 *l*

0 *l*

6 *l*

0 *l*

6 *l*

0 *l*

6 *l*

1 *R*

1 *R*

0 *R*

0 *R*

0 *R*

0 *R*

1 *R*

1 *R*

> 0 *R*

> 0 *R*

> 1 *R*

> 1 *R*

0 *R*

0 *R*

<sup>1</sup>*R*

1 *R*

0 *R*

0 *R*

0 *R*

0 *R*

> 0 *R*

Fig. 9. Pilot pattern of LTE system [4].

0 *R*

0 *R*

0 *R*

Since LTE symbols are typical OFDM symbols, classic measurement schemes such as LS and LMMSE can be applied directly on LTE pilots. A matrix form of (12) for measured channel by LS algorithm is showed as followed:

$$\tilde{\mathbf{H}}\_{\rm p}^{\rm LS} = \mathbf{X}\_{\rm pp}^{-1} \mathbf{Y}\_{\rm p} = \mathbf{H}\_{\rm p} + \mathbf{X}\_{\rm pp}^{-1} \mathbf{N}\_{\rm p} = \mathbf{I} \frac{\mathbf{Y}\_{\rm p}^{1}}{\mathbf{X}\_{\rm p}^{1}}, \frac{\mathbf{Y}\_{\rm p}^{2}}{\mathbf{X}\_{\rm p}^{2}}, \dots, \frac{\mathbf{Y}\_{\rm p}^{M\_{\rm p}}}{\mathbf{X}\_{\rm p}^{M\_{\rm p}}} \mathbf{I}^{T} \tag{47}$$

Since LMMSE algorithm is very vulnerable to the speed of mobile stations, the benefit brought by LMMSE will be negligible while comparing to its large processing burden. Furthermore, LS algorithm can be helpful in cancelling the effect of noise brought by LMMSE interpolation, so that the overhead of LMMSE interpolation can be reduced.

#### **3.2.2 Design of frequency domain interpolation**

Considering equation (34), there are three major challenges in realizing frequency domain LMMSE interpolation: estimating autocorrelation matrix h hL L **R** , determining Signal-to-Noise-Ratio in receiver and obtaining the inversion of matrix.
