Chapter 1 Introduction
1.3 Thesis Organization
The rest of this thesis is organized as follows. In Chapter 2, the principles of OFDM will be introduced. The MIMO system in 802.16e and SCO effects will be introduced in Chapter2. In Chapter 3, SCO effects will be well analyzed and the way of estimating and compensating SCO will be illustrated. The architecture and hardware design is discussed in Chapter 4. Finally, Chapter 5 is our conclusions.
Chapter 2
Principles of MIMO OFDM and SCO Effects
2.1 Principles of OFDM
2.1.1 OFDM Technology Overview
OFDM used in 802.16e will be briefly introduced in this section. OFDM is based on the idea of frequency division multiplexing (FDM). The concept of using parallel data transmission was published in the mid 60s [8]. In FDM, the total frequency bandwidth is divided into N non-overlapping sub-channels which are modulated with a separate symbol. In order to prevent from the adjacent channel interference, frequency spacing is allocated between sub-channels. However, this is inefficient to use the spectrum. In OFDM, the total frequency bandwidth is divided into N overlapping sub-channels which are mutual orthogonal. The orthogonality allows simultaneous transmission of a lot of subcarriers without interference from each other.
The sub-channels in FDM and OFDM are shown in Fig. 2.1.
Fig. 2.1 Sub-channels and bandwidth in (a) FDM (b)OFDM (a)
(b)
2.1.2 OFDM Specifications in 802.16e
In 802.16e standard, lots of different frequency sinusoidal wave with finite length will be stacked up in time domain as shown in Fig. 2.2. On the other hand, the wave in frequency domain will be stacked up with lots of Sinc wave, since the length is finite making the corresponding wave in frequency domain become a Sinc function.
DC gain will be zero as shown in Fig. 2.3, because there is no DC component in time domain. In order to keep the orthogonality in frequency domain, the frequency of higher frequency sinusoidal wave will be a multiple of that of the lowest sinusoidal wave.
Fig. 2.2 Time domain representation of OFDM
Fig. 2.3 Frequency domain representation of OFDM
In 802.16e standard [6], there are several processing units specified in the PHY layer of OFDMA. They include one-dimension domain units and two-dimension
domain units because of data allocated on both time and frequency. An essential OFDMA symbol is based on the format of OFDM symbol and the most basic unit is
“subcarrier”. The “subcarrier” is the one-dimension unit and consists of three types as shown in Fig. 2.4 and Fig. 2.5:
1. Data subcarriers: for carrying data.
2. Pilot subcarriers: for the purpose of channel estimation, channel tracking and synchronization.
3. Null subcarriers: no power is allocated to the DC subcarrier and guard subcarriers. The frequency of DC subcarrier is equal to RF, and this will induce the local oscillator re-radiation effect such that this subcarrier is not suitable to carry data. The reason for guard band is to reduce the interference between adjacent channels.
1~420 -420~-1
Fig. 2.4. Data subcarriers in 802.16e
Fig. 2.5 Subcarriers in 802.16e
A set of subcarriers in frequency domain are grouped as a “subchannel”.
Two-dimension units from large number of subcarrier to small number of subcarrier are “frame”, “sub-frame”, “zone”, “segment”, “burst”, “slot” and “cluster”. Brief definitions are described as follows respectively and the relationship between these units is shown in Fig. 2.6:
1. Frame: It is an essential packet format of transmitted data sequence.
2. Sub-frame: It is a component to make up a frame and is identified as downlink and uplink.
3. Zone: A zone is the region of contiguous OFDMA symbols with the same data allocation method. It is allowed to have different zones in a sub-frame.
4. Segment: It is a subdivision of the set of subchannels for certain particular allocation zone. The content of the Medium Access Control (MAC) layer is the same in a segment.
5. Burst: It is a region which includes the contiguous subchannel and OFDMA symbol to transmit the broadcast or unique data for corresponding users.
6. Slot: It is the minimum possible data allocation unit and described in both time and subchannel dimension. It contains 48 data subcarriers for all subchannelization schemes, but their arrangement is different in different schemes
7. Cluster: It contains 14 adjacent subcarriers over 2 contiguous symbols with 4 pilot subcarriers in partial usage of subcarriers (PUSC) permutation scheme.
Fig. 2.6 Frame structure[2]
Table 2.1 shows the adopted specification of 802.16e. We choose the FFT size 1024 and QPSK mode for our system. Thus we follow the specification of 802.16e with FFT size 1024. In the specification, there are 1024 subcarriers in a symbol. In 1024 subcarriers, there are 720 subcarriers for data, 120 for pilots, and 184 for guard band. The guard time for a symbol is 11.4 us, and useful symbol time is 91.4 us. Thus symbol duration is about 102.9 us. Each subcarrier requires 10.94 kHz bandwidth, and total system requires 10MHz bandwidth.
Table 2.1 Adopted 802.16e system specifications
Parameters Deriving formulas Values
FFT size (NFFT) 1024
System channel bandwidth (B) 10 MHz
Sampling factor (n) n=28/25 if B is a multiple of 1.25、1.5、2、2.75 MHz n=8/7 for the other cases
28/25
Sampling frequency (Fs) floor(n⋅BW/8000)×8000 11.2 MHz
Subcarrier spacing (Δf) Fs/ NFFT 10.94 kHz
Number of null subcarriers (Nn) 184 Number of clusters (Nc) (NFFT-Nn)/14 60
Modulation mode QPSK
Raw data rate 13.6 Mbps
Coding rate 3/4 CC
Peak data rate * Nd×2×3/4×(N-2)×1/ TF 9.93 Mbps
* Assuming 46 data OFDMA symbol in a frame
2.2 Principles of MIMO
2.2.1 Concepts of MIMO
The technology of MIMO is supported in WMAN, which provides several benefits as described below:
1. Increase the system reliability.
2. Increase the achievable data rate and enhance system capacity.
3. Increase the coverage area.
4. Decrease the required transmitting power.
For different application purposes, different MIMO schemes are adopted such as beamforming, spatial multiplexing and space-time code since these schemes usually conflict with one another. For example, increasing the data rate will decrease the reliability or increase the transmitted power.
1. Beamforming:
When multiple antennas are used in the closed-loop mode, the transmitter will know the channel state information. Thus, the interference caused from directional noise signals can be reduced by the technology of adaptive antenna systems, beamforming. A beamformer is similar to the spatial filter, which adjusts the strength of the transmitted and received signals based on direction as shown in Fig. 2.7. Two principles of beamforming, direction of arrival (DOA) based and eigenvalue beamforming based are generally used.
2. Spatial multiplexing:
Spatial multiplexing is a technique to increase the throughput rate by using multiple antennas at both ends. The transmitted data stream is divided into Nt
independent sub-streams. Multiple sub-streams are parallel transmitted through multiple antennas. If these data sub-streams can be separated successfully in the receiver, the data rate and system capacity will be higher than single antenna system.
3. Transmit diversity:
Transmit spatial diversity means that the transmitted signals can pass through different transmit antenna to overcome the deep fading channel. The transmit diversity is attractive for subscriber stations, because the cost of multiple antennas is on the transmitter. The space time block code (STBC), a transmit diversity technique, proposed by Alamouti in 1998 [6] is supported in WMAN. The case of 2*1 antenna system is described in Section 2.2.2 and is realized in our system.
2.2.2 STBC for MIMO
In the case of 2*1 antenna system, S1 and S2 are two consecutive symbols, and S1* and S2*mean complex conjugate of S1 and S2. h1 is the channel response of antenna 0 to Rx, and h2 is the channel response of antenna 1 to Rx. The receiver will receive data h1S1+ h2S2 for the first time slot, and -h1S2*+ h2 S1* for the second slot. The
1
( ) M i i( ) H ( )
i
y k w x k∗ w x k
=
=∑ =
Fig. 2.7 Concepts of MIMO
relation between transmitter and receiver is shown in Fig 2.8. The matrix in Fig. 2.8 is
Fig. 2.8 Transmit diversity
2.2.3 Symbol Representation of STBC and Effects in 802.16e
In 802.16e, pilots play an important role for detection, such as symbol boundary, channel estimation, and SCO. However, the pilot representation in 802.16e has predefined rules, and by using STBC, the consequence will be more complicated.
The pilots in subcarriers are shown in Fig. 2.9, and the location of the pilots repeats every four symbols. In each symbol, the pilot location repeats every fourteen subcarriers, and different antennas and time slots make the location of the pilots different in four consecutive symbols as shown in Fig. 2.10. For example, antenna 0 transmits pilots in the (9+14i) subcarriers in the first symbol time; in the (5+14i) subcarriers in the second symbol time; in the (13+14i) subcarriers in the third symbol time; in the (1+14i) subcarriers in the forth symbol time. Antenna 1 transmits pilots in the (5+14i) subcarriers in the first symbol time; in the (9+14i) subcarriers in the second symbol time; in the (1+14i) subcarriers in the third symbol time; in the (13+14i) subcarriers in the forth symbol time. The receiver will receive signals which are the sum of antenna 0 and antenna 1. Therefore, the pilots in the receiver will be in the (5+14i) and the (9+14i) subcarriers in both of the first and the second symbol time;
in the (1+14i) and the (13+14i) subcarriers in both of the third and the forth symbol time. This arrangement makes an important decision in the estimation for SCO, which
Time Antenna 0
Antenna 1
will be introduced in Section 2.3.6 and Section 3.3.
2.3 Sampling Clock Offset (SCO) Effects
2.3.1 Synchronization in 802.16e
The synchronization in 802.16e mainly compensates the effect of symbol timing offset (STO) and carrier frequency offset (CFO) [5][6]. The following algorithm of estimation and compensation of SCO will use the concept of compensation of STO.
The effect of symbol timing offset is introduced in Section 2.3.4.
2.3.2 Introduction of SCO
The effects of SCO is caused by the difference of transmitter sampling rate and Fig. 2.9 Pilots in MIMO 802.16e
Fig. 2.10 Format of STBC in 802.16e
receiver sampling rate, as shown in Fig. 2.11. This means the sampled data will be different between the transmitter and the receiver. In a system, with large SCO, there will be lots of errors in the received data. The way to estimate SCO and compensate SCO will become an important issue.
2.3.3 SCO Effects on ICI and Phase Rotation in Frequency Domain
In fact, the effects of SCO are complicated to describe in frequency domain. For the convenience of analysis, we divide the SCO effects into two parts as shown in Fig.
2.12:
1. Fractional symbol timing offset (FSTO) cause phase rotation in frequency domain.
2. Sampling timing difference in a symbol (STDS) cause inter-channel interference (ICI) in frequency domain.
time domain data
Tx sample rate Rx sample rate
Fig. 2.11 The effect of different sample rate
In Fig. 2.13, we separate a general SCO effect in time domain as shown in Fig.
2.13(d), into the timing offset of the first sample time (Fig. 2.13(b)) and the difference of sampling rate while the first sampling time is the same (Fig. 2.13(c)) between Tx and Rx. The timing offset of the first sample in time domain for each symbol will cause FSTO. Since SCO will cause the difference of the sampling point in time domain, the timing offset of the first symbol and the second symbol will be different.
This difference can be accumulated by the accumulation of SCO. The difference of sampling rate while the first sampling is the same will cause ICI.
Fig. 2.12 Separations of SCO effects
Fig. 2.13 FSTO and STDS illustration
In Eqn. (2.1), x1 is the first symbol from Tx, x2 is the second symbol from Tx, x3
is the third symbol from Tx, x1’ is the first symbol after sampling in Rx , x2’ is the first symbol after sampling in Rx , x3’ is the first symbol after sampling in Rx , n is the sample index in time domain, ε is FSTO,δ is SCO, and N is the number of subcarriers with guard interval, Eqn. (2.2) shows that the accumulation of δ will become the change of ε.
2.3.4 The Illustration of ICI Caused by SCO Effect
ICI occurs when the first sample is correct but other samples are incorrect. This means ICI effect only affected by STDS δ as shown in Fig. 2.13(c).
In order to figure out this phenomenon and effect, we use a simple example as shown in Fig. 2.14 to illustrate how the sinusoidal wave behaves when sampling frequency change. In fact, OFDM system is the sum of different frequency and phase sinusoidal wave as shown in Fig. 2.2. The example shown in Fig. 2.14 can be easily extended to multiple carrier case as that in OFDM system. In Fig. 2.14, we can see that, if a multiple of sampling frequency change in continuous time domain, it can be thought as the boundary is changed so that there are more or less waves of the origin signal in the region. That is, the original sinusoidal wave becomes faster or slower in the region, and all different frequency sinusoidal wave will become faster or slower
1
by the factor of change of sampling rate, since the change of waves follows this rate.
So it will become a change of location change in frequency domain, and the change is the same as the change of sampling frequency. This means we can think it as the expansion or shrink by the multiplication in frequency domain as shown in Fig. 2.15.
In our system the data are in the discrete domain. In order to figure out the relationship between digital domain and analog domain, the relations between Fourier
time domain
time domain
sampling rate shift frequence direct to a ration of sampling
rate
time domain
time domain sampling times change to 1.5
times (a) sinusoidal wave frequency is f situation
(b) sinusoidal wave sampling time change to 1.5
times
Fig. 2.14 Frequency change illustration
Fig. 2.15 Expansion or shrink in frequency domain
Transform and Fast Fourier Transform shall be mentioned. The relationship is shown in Fig. 2.16 [7].
In baseband, we represent the signal in x(n) or X(k). In conventional digital signal process, we can transform from time domain signal x(n) to frequency domain signal X(k) by Discrete Fourier Transform (DFT) and transform from frequency domain signal X(k) to frequency domain signal x(n) by inverse Discrete Fourier Transform (IDFT). If we need to resample a signal in discrete frequency domain, the basic idea to resample is to transform signal to time domain x(n), reconstruct it to analog domain x(t), resample it to digital time domain x’(n), and then transform it to frequency domain X’(k). However, the computation will become very large, if we
Fig. 2.16 Time and frequency domain relationship
need to simplify and show the process just in frequency domain, we just follow the processes in frequency domain corresponding to those in time domain. In time domain, copying multiple finite length data to infinite length data corresponds to using Sinc function to reconstruct in each tone of digital data in frequency domain.
Making digital infinite length data becoming analog data in time domain corresponds to making the data in frequency domain periodically.
From the relationship discussed above, we know to explain the signal behavior in frequency domain and it just need 3 steps:
1. Use Sinc function to reconstruct continuous signal.
2. Make it periodically in frequency domain to expand from finite length to infinite length.
3. Resample it by the new sampling rate for the wanted length.
Fig. 2.17 shows a general condition of resampling in frequency domain.
Fig. 2.17 ICI effect illustration
From Fig. 2.17, we know there will be aliasing on the higher frequency. However, in 802.16e the guard bands on higher frequency are all 0. So this effect can be neglected. So the effect is that the variant of sampling rate breaks the orthogonality in frequency domain. This causes ICI effect.
2.3.5 The Relationship between SCO and Symbol Boundary
In order to introduce the symbol boundary synchronization algorithm, the effect of symbol timing offset is derived in advance. STO means the estimated symbol boundary does not locate on the accurate location. It consists of two possible cases, earlier or later than the actual boundary index. If the estimated boundary is earlier than the ideal index but not locates at the channel response region, it means we choose the data in cyclic prefix (CP), which is the copy of final symbol data (Fig. 2.18); it induces the constellation of signals to rotate in the frequency domain, but can be compensated by channel estimation. On the other hand, the later case means we choose the data in the next symbol, and that means the irrelevant data is introduced, so the data is irrecoverable. In order to describe the earlier case, the received signal with this timing offset in mathematics is derived in Eqn. (2.2), where k is the subcarriers index, n is the sample index in time domain, and Nsc is the number of subcarriers in an OFDM symbol. If symbol timing offset is ε, then we have
ˆ ( ) ( )
X k = X k ej2πkε/Nsc which means the phase rotation is proportional to subcarrier index k.
Fig. 2.18 OFDM symbol with cyclic prefix
Another way to illustrate this phenomenon is by graph. In Fig. 2.19, we can see if the symbol boundary shifts the start phase of waves will be changed with a ratio of the wave frequency. This is a key point that the phase will rotate in frequency domain with a ratio of the frequency as shown in Fig. 2.20. That is when the frequency of sinusoidal wave higher the same length of boundary offset will insert more waves in that length. So the phase change will be larger.
sc
time domain
time domain
timing shift phase shift direct to a ration of frequence
time domain phase change π
phase change 2π
time domain
Fig. 2.19 Phase and symbol boundary shift
Fig. 2.20 Phase rotation
2.3.6 Phase Rotation Caused by SCO
For SCO, the FSTO part, which can be accumulated due to SCO, means the difference of boundary that shown Fig. 2.21. The main difference between FSTO and ISTO is the boundary offset is a fractional or an integer of sample rate The ISTO effect will makes the received data rotate in constellation, and the FSTO will make the phase rotate.
This conclusion makes an important role on detecting SCO. Since FSTO will change by the accumulation of SCO. SCO value can be generated by the difference of phase rotation in two consecutive symbols in the system. The best way to detect the difference may be from the fixed value data such as pilots. In next section (Section 2.3.6), the challenge using pilots in 802.16e MIMO system will be discussed.
2.3.7 Challenge on a MIMO System
In 802.16e, pilot locations repeat every four consecutive symbols. In four consecutive symbols, pilot location differs from the next symbol as shown in Fig. 2.22.
For example, pilot in antenna 0 arise in the (9+14i) subcarriers for first symbol, but arise in the (5+14i) subcarriers for the second symbol, in the (13+14i) subcarriers for
Fig. 2.21 Symbol timing relationship
third symbol, in the (1+14i) subcarriers for fourth symbol. On the other hand, pilots in antenna 1 arise in other different locations.
Though the pilot regulation of 2*1 antennas STBC in 802.16e as shown in Fig.
2.9, it seems that we can compare two consecutive symbols easily, for the pilots are in the same subcarrier location but from different antennas. However, in fact, the channel delay and channel response from two antennas are different as shown in Fig.
2.22. And this may cause different phase rotation in frequency domain as shown in Fig. 2.23., so that the phase rotation of two consecutive symbol are not with the same base phase rotation, and the difference of the phase of two symbols become meaningless. For the reason we decide to compare the phase every four symbols.
However, the channel would vary; if we assume the channel does not change in four symbols, the phase rotation with channel response will be discussed in Section 3.1.
CP DATA
CP DATA
antenna 0
anteanna 1
CP DATA CP DATA
Fig. 2.22 Different channel delay for two antennas
Fig. 2.23 shows that the locations of pilots from antenna 0 in symbol time 0 will
Fig. 2.23 shows that the locations of pilots from antenna 0 in symbol time 0 will