T IME -V ARIANT C HANNEL E FFECT - 應用於LTE收發器之多輸入多輸出正交分頻多工系統的可適性通道估測設計

CHAPTER 1 INTRODUCTION

1.2 T IME -V ARIANT C HANNEL E FFECT

Multipath propagation with combination of Doppler shift induces time-variant channel effects. As the phenomenon shown in Figure 1-2, a vehicle receives three multipath components while it travels from point A to B. Each multipath component is affected by different time-varying frequency shift and phase shift, therefore the time-variant channel effect reveals.



B A

Figure 1-2 The occasion of time-variant channels

The time-variant channel effect can also be described as a Finite Impulse Response (FIR) filter, which has three time-variant tap gains since there are three multipath components, as shown in Figure 1-3.

D D

w0(t) w1(t) w2(t) s(t)

y(t)

Figure 1-3 A 3-tap Finite Impulse Response (FIR) filter model for time-variant channels

 

s t is the transmitted signal and the received signal ^{y t}

 

can be written as a convolution sum

 

² k

   

k=0

y t =



w t s t-k ^(1.4)

Each time-variant tap gain wk

 

t is a complex number, which describes the phase and amplitude response of the k^th path at time^t.

The time-variant tap gains, or Channel Impulse Response (CIR), can be transformed into Channel Frequency Response (CFR), which is also time-variant.

Figure 1-4 shows the 15-tap noise-free time-variant CFR at 120km/hr by Jakes’ model [2].

(a) (b)

Figure 1-4 (a) Amplitude and (b) Phase variations of time-variant CFR by Jakes’

model at 120km/hr

Chapter 2 System Platform

3rd Generation Partnership Project (3GPP)[3][4][5] has recently specified an Orthogonal Frequency Division Multiplexing (OFDM) based technology, Evolved Universal Terrestrial Radio Access (E-UTRA), for support of wireless broadband data service up to 300 Mbps in the downlink and 75Mbps in the uplink [6]. In Long Term Evolution (LTE), MIMO technologies have been widely used to improve downlink peak rate, cell coverage, as well as average cell throughput. LTE is not only able to operate in different frequency bands but can also flexibly support different bandwidths.

A unique LTE possibility is to use different UL and DL bandwidths, allowing for asymmetric spectrum utilization. This is possible due to the support of both paired Frequency Division Duplexing (FDD) and unpaired Time Division Duplexing (TDD) band operations. In this thesis we concentrate on TDD.

2.1 LTE PHY Specification

Orthogonal Frequency Division Multiplexing (OFDM) is a popular method for high data rate wireless transmission. OFDM may be combined with antenna arrays at the transmitter and receiver to increase the diversity gain and to enhance the system capacity on time variant and frequency-selective channels, resulting in a multiple-input multiple-output (MIMO) configuration.

2.1.1 Transmitter

The transmitter block diagram of LTE MIMO specified is shown as Figure 2-1.

code words layers antenna ports

Scrambling

Figure 2-1 LTE MIMO transmitter

The baseband signal representing a downlink physical channel is defined in terms of the following steps:

- Scrambling of coded bits in each of the code words to be transmitted on a physical channel to prevent a succession of zeros or ones

- Modulation of scrambled bits from some modulation alphabet, e.g. BPSK, QPSK, 16QAM, 64QAM, to generate complex-values modulation symbols.

- Mapping of complex-valued modulation symbols onto one or several transmission layers. Basically a layer corresponds to a spatial multiplexing channel.

- The pre-coder extracts exactly one modulation symbol from each layer, jointly process these symbols, and maps the result in the frequency domain and antenna domain. The space-frequency block code (SFBC) as shown in section 2.2 is used if there has more than one transmit antennas.

- Mapping of complex-valued modulation symbols for each antenna port to the resource elements of the set of resource blocks assigned by the MAC scheduler for transmission of transport block(s).

signals appended to the Cyclic Prefix (CP) of 144 or 160 sub-carries are transmitted by RF modules.

2.1.2 Receiver

Fig 2-2 LTE MIMO receiver

The receive signals are first synchronized to recognize each OFDM symbol.

Each OFDM symbols shall be processed and de-mapped to coded bits through the following steps:

- Each OFDM symbols is transformed to complex-valued frequency-domain OFDM signal by Fast Fourier Transform (FFT). If the OFDM symbol belongs to reference signal (described in section 2.1.4), then it is used for channel estimation.

- De-mapping complex-valued frequency-domain OFDM signal of each antenna port to complex-valued symbols.

- Complex-valued symbols are decoded by SFBC decoder, which needs the CFR information estimated by the channel estimation block. The SFBC decoder can be seen as the equalizer of MIMO-OFDM systems and it is introduced in section 2.2.

- After SFBC decoder, the spatial streams shall be Layer de-mapped and demodulation to complex-values modulation symbols.

- Finally, the data stream is decoded by de-scrambler.

2.1.3 Frame Structure

Shown as Figure 2-3, frame structure is applicable to TDD. Each radio frame of length T_f 307200 T_s 10ms consists of two half-frames of length

153600 T_s 5ms each. Each half-frame consists of five sub-frames of length 307200 T_s 1ms_.

One half-frame, 153600Ts = 5ms

One radio-frame, Tf = 307200Ts = 10ms

One slot,

Tslot = 15360Ts 307200Ts

One subframe, 307200Ts

Subframe #0 Subframe #2 Subframe #3 Subframe #4 Subframe #5 Subframe #7 Subframe #8 Subframe #9

DwPTS GP UpPTS DwPTS GP UpPTS

Figure 2-3 LTE frame format

Physical Downlink Share Channel (PDSCH), Reference Signal (RS) and Physical Downlink Control Channel (PDCCH) compose a sub-frame, shown as Figure 2-4. PDSCH is used for all user data, as well as for broadcast system information. Data is transmitted on the PDSCH in units known as transport blocks. A PDCCH carries a message known as Downlink Control Information (DCI), which includes resource assignments and other control information for a mobile or group of mobiles. RS(s) are known signals which do not carry any data. It can be used to do channel estimation.

The transmitted signal in each slot is described by a resource grid of ^{L M}^ subcarrier and N OFDM symbols, where ^L is downlink bandwidth configuration,

M is resource block size in the frequency domain, expressed as a number of subcarriers, and N is the number of OFDM symbols in a downlink slot. Resource blocks are used to describe the mapping of certain physical channels to resource elements. The resource grid structure is illustrated in Figure 2-5. In the thesis, ^Lis 50 blocks, ^Mrepresents 12 subcarriers, and N denotes 14 OFDM symbols.

One downlink slot Tslot

N OFDM symbols

Resource block (N*M resource elements) M subcarriers

Resource element L*M subcarriers

N = Number of OFDM symbol L = Number of resource block M = Number of subcarrier

Figure 2-5 LTE resource block format

2.1.4 Reference Signal

LTE downlink reference signals have three types, Cell-specific reference signals, MBSFN reference signals, and UE-specific reference signals. In this thesis we concentrate on Cell-specific reference signals.

The mapping of downlink reference signals is shown in Figure 2-6. Resource element used for reference signal transmission on any of the antenna ports in a slot shall not be used for any transmission on any other antenna port in the same slot and set to zero.

One antenna port

Not used for transmission on this antenna port

Antenna port 0 Antenna port 1 Antenna port 2 Antenna port 3

Figure 2-6 LTE Reference signals

2.2 Space-Frequency Block Coding

In LTE transmit diversity, the pre-coding is the same as Space-Frequency Block Coding (SFBC) [7], it has been applied to frequency selective channels by using OFDM with cyclic prefix, which transforms a frequency selective channel into flat fading sub-channels. The SFBC coding is done across the sub-carriers inside one OFDM symbol. In 2^2 SFBC, SFBC encodes two components onto two antennas over two different frequencies, these two frequencies are chosen to correspond to adjacent subcarriers. Since channel realizations on adjacent subcarriers may differ, SFBC is more sensitive to large delay spreads.

2.2.1 2

^

2 SFBC

The block diagram on a transmitter using OFDM and space-frequency block coding is shown in Figure 2-7. The mapping scheme of the data symbols Xn for SFBCs with 2 transmit antennas is shown in Table 2-1. The mapping scheme for SFBCs is chosen such that on the first antenna the original data is transmitted without any modification so that the scheme is compatible to systems without SFBC where the second antenna is not implemented or switched off.

Table 2-1 Mapping with space-frequency block code and two transmit antenna

Antenna 1 Antenna 2

Subcarrier n

Xn X_n^*_₁

Subcarrier n+1

Xn_ X_n^*

Tx 1

Tx 2

frequency f₁ f₂ f₃ f₄ fn-1 fn

X

-X

^*₂

X

₃

-X

^*₄ Xn_1^-X^*n

X

₁^*

X

₃^* Xn Xn^*_1

X

Figure 2-7 Space-frequency block coding in an OFDM transmitter

Two subcarriers x1 and x2 are about to be transmitted in two subcarriers periods from two transmit antennas. The SFBC-encoded codeword is shown as

Figure 2- 2-8. At frequency f1, x1 and -x2^* are transmitted through channels h1

andh2. And at frequency f2, x2 and x1^* are transmitted through channels h1 andh2, respectively.

Subcarrier

Figure 2-8 2^2 SFBC MIMO systems for two receivers

Therefore the received signals r1 and r2 at time f1 and f2 can be expressed as

Rewrite in matrix form

1 1 2 1

The channel matrix ^H can be estimated using reference signals, hence the transmitted symbols can be calculated by

-1 corresponded channels, are ignored during the derivation of the decoding process, since the decoding method is the same as the first receiver. In simulation platform, two receivers are deployed and the SFBC-decoded symbols for each receiver are averaged

2.3 Channel Models

In this section, the time-variant channel models are introduced, this channel model [2] is the well-known Jakes’ mode. It will describe as following.

2.3.1 Jakes’ Model

Time-variant channel effect can be modeled as a FIR filter with time-variant tap gains. For Jakes’ model, the variance of each tap gain obeys Rayleigh distribution.

Figure 2-9 shows an n-tap FIR filter with Rayleigh-distributed tap gains, and the corresponded velocity is 120km/hr, shown for50ms .

Figure 2-9 FIR filter with Rayleigh-distributed tap gains at 120km/hr

D D

w0(t) w1(t) wn-1(t)

...

 

s t

 

y t

50 ms

-



10dB 0dB -10dB -30dB

PhaseAmplitude 0

 

sinusoids [8], that is

 

description of the sum of sinusoids is referred to [8].

Chapter 3 The Proposed Algorithm

In this chapter, an adaptive channel estimation technique is proposed. ²^² SFBC for MIMO-OFDM systems is considered. The proposed algorithm consists of three parts, the channel estimation of initial channel, the decision-feedback adaptive channel estimation for estimating the noisy time-variant channel, and the frequency domain lose-pass filter for decreasing the SNR requirement.

Section 3.1 gives an overview of proposed decision-feedback adaptive channel estimation and the use PDCCH for channel estimation and frequency domain adaptive channel estimation is proposed in section 3.2 and 3.3, the²^²SFBC is proposed in 3.4, and the lose-pass filter is discussed in section 3.5.

3.1 Adaptive Channel Estimation Overview

The synchronized time-domain signals are transformed into frequency-domain OFDM symbols by FFT. Figure 3-1 describes the data path after FFT for 2^2 LTE MIMO-OFDM systems.

FFT

Figure 3-1 2^2 adaptive channel estimation block diagram

After FFT, OFDM symbols classified as Physical Downlink Control Channel (PDCCH) are used for channel estimation. The 2^2 SFBC decoder operates for every two payload symbols, as shown as r1 and r2 above. Then the decoded symbols, x1^'

and x^'2, are decided by decision unit. The functionality of the decision unit is illustrated in Figure 3-1, it uses QAM constellation for decisioning.

Decision Unit

The decided symbols are averaged with which of the second receiver. x1 and

 are the differences between decided symbols and decoded symbols, and they are used by adaptive channel estimation to obtain the variances of the time-variant channels. After adding up with h1andh2, the time-variant channels, h1^' andh^'2, are ready to update the channel information stored in channel estimation block. The usage of Low pass filter is to mitigate the influence of Additive White Gaussian Noise (AWGN), since the adaptive channel estimation algorithm is sensitive to noise.

The flow chart for adaptive channel estimation is show below.

PDCCH

Figure 3-3 Adaptive channel estimation flow chart

After use PDCCH to do initial channel estimation, the OFDM symbols can only be one of the following categories: reference signal (RS) for channel estimation, or adaptive channel estimation. If the ^N^¹^th OFDM symbol has RS, use these RS to do interpolation, otherwise, use ^N^th OFDM symbol channel to do adaptive channel estimation and create ^N¹^th OFDM symbol channel.

3.2 Use PDCCH for Channel Estimation

Before adaptive channel estimation, it is necessary to estimation an OFDM symbol channel as initial channel. In this thesis, the PDCCH is used. Physical Downlink Control Channel (PDCCH) carries scheduling assignments and other control information. A physical control channel is transmitted on an aggregation of one of or several consecutive control channel elements (CCEs), where a control channel element corresponds to 9 resource element groups. The number of resource-element groups not assigned to PCFICH or PHICH isNREG. The CCEs available in the system are numbered from 0 andNCCE^¹, whereNCCE NREG^/⁹. The PDCCH supports multiple formats as listed in Table 3-1.

Table 3-1: Supported PDCCH formats

PDCCH format

Number of CCEs

Number of resource-element

groups

Number of PDCCH bits

0 1 9 72

1 2 18 144

2 4 36 288

3 8 72 576

As above describe, PDCCH are known signals which do not carry any data. In transmitted resource block, shows in Figure3-4. The PDCCH are second OFDM symbol and third OFDM symbol. We use the third OFDM symbol and zero forcing to

I=0 I=6 I=0 I=6

PDCCH PDSCH

Third PDCCH OFDM symbol

Figure 3-4 PDCCH in resource block

3.3 Frequency Domain Adaptive Channel Estimation

Each noisy time-variant channel estimated by adaptive channel estimation is then filtered by Low pass filter. For 2x2 LTE MIMO-OFDM systems, In an OFDM symbol, have 600 subcarriers. After SFBC decoder, there are 300 subcarriers. We get the 50 subcarriers, show in Figure 3-5, as virtual pilot to be adaptive channel estimation, pass through the SFBC coder and interpolation to 600 subcarriers, and then filtered by Low pass filter.

OFDM symbol (600 subcarriers) Virtual pilot (50 subcarriers)

Figure 3-5 Virtual Pilots

3.4 Adaptive Channel Estimation for 2

^

2 SFBC

In this section, the adaptive channel estimation algorithm can be seen as a transformation of the variances of SFBC-decoded symbols into the variances of time-variant channels. When we finish the one-shot channel estimation, if without adaptive channel estimation, we should keep a large memory to store the channel information until the step of channel equalizer. In architecture level, it will result huge number of gate count. The adaptive channel estimation algorithm applies to each frequency component individually for MIMO-OFDM systems.

For each receiver, the received signal within one SFBC block contains two

rfindicates the received signal at frequency index ^f within SFBC block and the channel from transmitter j is calledhj, which are assumed to be known. x1andx2

stands for the transmitted ^{2 2}^ SFBC codeword which are wanted.

By defining ¹* can be expressed in matrix form, that is

1 1 2 1

Due to time-variant channel effect, the channels of the consecutive SFBC block are not consistent with the previous ones. For the consecutive SFBC block, the channels are assumed to be h₁^' andh^'₂, which are defined as

Therefore, the received consecutive SFBC block in matrix form becomes

' '

Applying the decoding process again, that is, multiplying the inverted channel matrix H^-1 on both left side of equation (3.5), hence

As shown above, in consequence of the time-variant channel effect, the decoded symbol X^' contains a residual part with compared to^X. The residual part ^X indicates the variance of the decoded symbol due to time-variant channel effect. ^X can be obtained if the time-variant channel effect is not strong enough to make for a decision error on the decoded symbol X^'. That is, if the decision feedback result ofX^', which is defined asXDF, is equal to the ideal decoded symbol^X, then the relationship between ^X and ^H can be identified. By observing equation(3.6)

H can be solved since it is the only unknown matrix in equation (3.7). Further more, by defining ¹ that equation (3.8) uses the same process as which used in equation (3.3) for SFBC decoding.

3.5 First Order Low Pass Filter

Low pass filter is used on frequency domain to decrease the SNR requirements that adaptive channel estimation needed since it is sensitive to noise. The functionality of frequency domain Low pass filtering is illustrated below

a and b are vectors of low pass filter. It is show as Figure 3-6.

Z^-1

  Z^-1  Z^-1 

( ) x m

( )

b n ^b⁽³⁾ b(2) b(1)

( ) y m ( )

a n ^a⁽³⁾ a(2)

1( )

Zn_ m Z₂( )m Z m₁( )

Figure 3-6 Low Pass Filter

Chapter 4 Simulation Results

To evaluate the proposed algorithm, a typical MIMO-OFDM system based on LTE is used as the reference design platform. Performance of the proposed ^{2 2}^ adaptive channel estimation under time-variant frequency-selective fast-fading channels is simulated. The parameters used in the simulation platform are: OFDM symbol length is 14 and 600 subcarriers in an OFDM symbol. The major parameters are summarized in Table 4-1.

Table 4-1 Simulation parameters

Parameter Value

Number of taps 6

Doppler speed 120km/s

Modulation 64-QAM

Equalization Zero-Forcing

FFT size 1024 Bytes

Signal Bandwidth 20 MHz

Subframe size 1ms

The results show that the best step-size in simulation is 0.1. Figure 4-2 expresses the Bit Error Rate (BER) performance with different step-size of the proposed adaptive channel estimation for 2^2 LTE MIMO-OFDM systems under time-variant channels for 120km/hr Jakes’ model.

Figure 4-1 MSE of OFDM symbol with step-size 0, 0.1, 0.15, 0.2

Figure 4-2 BER of OFDM symbol with step-size 0.1, 0.15, 0.2

Figure 4-3 addresses the Bit Error Rate (BER) performance of the proposed adaptive channel estimation 2^2 LTE MIMO-OFDM systems, which use the low pass filter to filter the noisy.

Figure 4-3 BER of OFDM symbol with Low pass filter

Figure 4-4 indicates the Bit Error Rate (BER) performance of the proposed adaptive channel estimation 2^2 LTE MIMO-OFDM systems, which use the different initial channel estimation. The first one is use first OFDM symbol’s reference signal, and be interpolation as initial channel, the other one use the PDCCH to estimate the initial channel. The results show that use PDCCH to estimate the initial channel has the better performance.

Figure 4-4 BER of OFDM symbol with two channel estimation methods.

The required SNR for BER of the proposed algorithm among various configurations are summarized in Table 4-3.

Table 4-3 Required SNR for BER (64-QAM modulation)

Simulation configurations

Jakes’ model 120km/hr with

step-size 0.1

Jakes’ model 120km/hr with

step-size 0.15

Jakes’ model 120km/hr with

step-size 0.2

2^{2 MI}

MO-OFDM systems One-shot channel estimation

One-tap compensation 27 dB 27 dB 27 dB

Adaptive channel estimation

Direct compensation 38 dB 40 dB 45 dB

Adaptive channel estimation

low pass filter compensation 29 dB 30 dB 33 dB

As introduction described, the contribution of proposed adaptive channel estimation is computing complexity reduced which compared with one-shot channel estimation. Table 4-2 exhibits the comparison between the one-shot channel and proposed adaptive channel estimation. The result shows that the one-shot channel estimation needs 600×14 storages to store the channel information, but proposed adaptive channel estimation only needs 600 storages. In channel estimation, the multiplier number of one-shot channel estimation needs 650000, but the proposed algorithm which use PDCCH only needs 900, and in adaptive channel estimation, one-shot channel estimation needs zero multiplier and proposed algorithm needs 75000 multipliers. For estimate channel, the total multiplier number of one-shot channel estimation is 650000, and proposed algorithm is 75900. The computing complexity of proposed algorithm is reduced.

Table 4-2 complexity comparison between two channel estimation Channel Estimation One-shot Adaptive

(use first OFDM symbol)

Adaptive (use PDCCH) Storages

600 × 14 600 600

Multiplier

(channel Estimation) 650000 1800 900

Multiplier (Adaptive channel Estimation)

0 75000 75000

Chapter 5 Conclusion and Future Work

5.1 Conclusion

In this thesis, adaptive channel estimation is proposed to oppose the Doppler effect under high velocity environments, and make full use of the time- and frequency-domain correlation of the frequency response of time-varying multipath fading channels without requirement of accurate channel statistics.

The presented 2^2 adaptive channel estimation scheme achieves. It is a prototype algorithm for SFBC-coded MIMO-OFDM systems. The distance between QAM constellation points dominates the maximum tolerance to time-variant channels;

therefore lower modulation scheme provides higher velocity tolerance. Further more, the proposed adaptive channel estimation algorithm shares the same process with SFBC decoding. It is a significant feature in hardware implementation phase.

5.2 Future Work

High QAM constellation like 256-QAM for higher data rate is going to be deployed. As a result, the distance between constellation points shrinks; therefore a

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