Chapter 2 Fundamentals of MIMO OFDM Systems
2.2 Studies and Simulations of MIMO Channels
2.2.2 Studies and Simulation Results
Our Matlab simulation flow is shown in Figure 2.7. First of all, a single fading channel is constructed based on Jakes’ model. After that, spatial correlation property is added to the channel simulator. At last, the channel response is produced by this MIMO channel simulator.
Figure 2.7 Simulation flow of the adopted MIMO channel simulator
0 1 2 3 4 5 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Magnitude
Probability Distribution
Fading coefficient by Simulator
Theoretical Curve ( Rayleigh Distribution )
Figure 2.8 Magnitude distribution of four correlated fading channels
In the simulation, it shows that Jakes’ model can model the Rayleigh fading channel precisely. The distribution of amplitude fits Rayleigh distribution and the phase variation is also uniformly distributed. In Figure 2.8 and 2.9, it can be observed that the distributions of magnitude and phase are close to the theoretical curve.
20 40
60 80
100
30
210
60
240
90
270 120
300 150
330
180 0
Theoretical phase distribution Fading coefficient by Simulator
Figure 2.9 Phase distribution of four correlated fading channels (polar plot)
To verify the spatial correlation property, a 4 by 4 correlation matrix (as listed in Table 2.1) is selected to be target correlation matrix as an example.
Table 2.1 Desired spatial correlation matrix of the channel simulator
Channel 1 Channel 2 Channel 3 Channel 4
Channel 1 1 0.3 0.3 0.3
Channel 2 0.3 1 0.3 0.3
Channel 3 0.3 0.3 1 0.3
Channel 4 0.3 0.3 0.3 1
Table 2.2 Resulting spatial correlation matrix of the channel simulator
Channel 1 Channel 2 Channel 3 Channel 4
Channel 1 1 0.324 0.2655 0.2863
Channel 2 0.324 1 0.2898 0.2436
Channel 3 0.2655 0.2898 1 0.2831
Channel 4 0.2863 0.2436 0.2831 1
In the simulation, the resulting correlation matrix (as listed in Table 2.2) approximates to the desired matrix. This method can model the spatial correlation well. If we can adjust the number of oscillator in the Jakes’ model, the matrix can be more precise, but it will take more computation time (i.e., take more iterations for simulation).
Chapter 3
Standards of IEEE 802.11n (WWiSE) and IEEE 802.16a
For the rapid increase of broadband wireless communication, MIMO techniques are integrated into communication system to enhance system performance. However, the adoption of MIMO OFDM architectures may cause some difficulties in synchronization and channel equalization. For this reason, some efficient channel estimation schemes must be studied. Since a few years ago, some new communication standards have been discussed in the forums held by global engineering society, such as IEEE. One of them is MIMO 802.11n, which is a performance-enhanced version of 802.11-series standards. Another standard is 802.16a for wireless metropolitan area network (Wireless MAN). It also defines a specific optional mode with space-time block coding (STBC). In this chapter, we will make a simple introduction for both existing industrial standards with MIMO OFDM architectures.
3.1 IEEE 802.16a standard
The first version of P802.16a draft was issued on 30 November 2001. The last version of draft P802.16/D7 (draft version 7) was issued on 11 December 2002. The formal document of IEEE 802.16a (also known as WinMax) was approved as an IEEE standard on 29 January 2003 by IEEE Standard Association. The standard is developed by IEEE 802.16 Working Group and then the IEEE 802 Executive Committee. IEEE 802.16a focuses on the application of wireless metropolitan area,
network (Wireless MAN). This application may replace present ‘last mile’ technology between users’ terminals and Internet service providers (ISP). Wireless MAN may be a threatening competitor against wired communication technologies, such as ADSL or VDSL. We will introduce main features of 802.16a in the following subsections.
802.16a defines three system modes: single carrier (SC), OFDM, and OFDMA.
Each mode corresponds to different applications. OFDMA mode with space-time coding will be focused in this thesis. Table 3.1 shows the key baseband parameters of 802.16a-2003 standards. Some common abbreviations and expressions of 802.16a OFDMA PHY standard are listed below before introducing technical detail for conciseness.
(1)SS (subscriber station): usually known as user station or mobile stations.
(2)BS (base station): equipment sets providing connectivity, management, and control of subscriber stations.
(3)MAC (media access control): used to control system access and provides links of data from upper layer (data link layer) and lower layer (physical layer).
(4)PHY (physical layer): handles the data transmission and may include use of
multiple transmission technologies, each appropriate to a certain frequency and application.
(7)TDD (time division duplexing): a single channel is used for both upstream and downstream transmission, but at different time.
(8)FDD (frequency division duplexing): requires two different channel pairs, one for upstream and another for downstream data transmission.
(9)STC (space-time coding): a coding skill applied on spatial and time domains
Table 3.1 Main baseband features of 802.16a-2003 Band Allocation 2-11Ghz
Throughput 1.0-75.0Mbps
Coverage range Most 32km,(6-9km is a typical range) Mobility Fixed
Channel model nLOS
Bandwidth 1.25-20Mhz
PHY SCa, OFDM,OFDMA
3.1.1 802.16a OFDMA Frame and Symbol Structures
The adopted duplexing methods are either FDD or TDD. The frame structures are different in these two duplexing methods. In license-exempt bands, the duplexing method is defined as TDD, which will be described in the following part. A typical OFDMA TDD time frame is shown in Figure 3.1. We can see that the DL and UL bursts are inserted into different time slots on all the subchannels. Between DL and UL bursts, narrow time gaps are inserted to protect different bursts from inter-frame interference. The time gaps are named as Tx/Rx transition gap (TTG) and Rx/Tx transition gap (RTG). The receivers at BS and SS should detect the beginnings of their corresponding bursts, and then start other following detection steps.
Figure 3.1 Frame structure of 802.16a OFDMA [11]
As described in Chapter 2 and Figure 3.2, a symbol (Ts) of 802.16a is composed of useful symbol (Tb) and guard interval (GI). The purpose of GI is to reserve orthogonality of each subcarrier, as we have described in Chapter 2.
Tg
Tb Ts
Figure 3.2 Time-domain structure of a 802.16a symbol
In frequency domain, all the subcarriers are either data carriers, pilot carriers, or guard band carriers. The purpose of guard band carriers are to avoid interference from other radiation sources or communication systems located at nearby bands, and the pilot carriers are for channel estimation or other tracking procedures. The data carriers are grouped into several subchannels, and data streams from different SS may transmit on different subchannels. The frequency domain description is shown in Figure 3.3.
Figure 3.3 802.16a symbol frequency domain structure
3.1.2 802.16a OFDMA Carrier Allocation
In 802.16a OFDMA, the standard specifies the data tones and pilot tones in different ways for downlink and uplink. In general, an OFDMA symbol obtains a set of used subcarriers excluding DC subcarrier and guard band subcarriers. In both uplink and downlink, these used subcarriers are divided into data tones and pilot tones.
However, the allocation of data and pilot tones is different in uplink and downlink.
The main difference is that the pilot carriers are allocated first and then all the other data carriers are grouped into 32 subchannels in downlink, and the pilot carriers are allocated in each subchannel. But in uplink, each subchannel has its own set of pilot carriers. This allocation corresponds to the fact that BS broadcasts to all SS in the downlink transmission, and SS delivers data stream individually to BS in the uplink transmission. In this thesis, we will mainly discuss the design of channel estimation in DL.
In DL of 802.16a OFDMA, all of the subcarriers can be divided into pilot tones and data tones according to the different purpose in data transmission. The pilot tones can be categorized into fixed location pilots and variable location pilots. There are 32 fixed-location pilot in an OFDM symbol, and their exact positions are listed in the 14th row of Table 3.2. The allocations of DC subcarrier and guard band subcarriers are also listed in the first three rows of Table 3.2. These special tones are allocated at the same places in every OFDM symbol. However, there are many variable location pilots other than those fixed-location ones. These variable location pilots repeat with a period of four OFDM symbols. The placement of variable location pilots is decided by equation (3.1).
(3.1)
{ }
3 12 , where
L is the offset that cycles through the values 0,1,2,3, periodically.
0,1, 2, 141
k k
k
varLocPilot L P
P
= +
∈
The variable location pilots described in (3.1) are specially designed that the number of overall pilot tones are the same in every OFDM symbol even if there are variable location pilots coinciding with fixed location pilots. Additionally, there won’t be all -pilot preamble in the DL OFDM symbols. Five 802.16a OFDMA DL symbols are illustrated in Figure 3.4 to show how these pilot tones are allocated, and the periodicity of variable pilots is also shown.
Figure 3.4 Carrier Allocation of DL 802.16a OFDMA [11]
Table 3.2 Detailed Carrier Allocation of DL 802.16a OFDMA [11]
3.1.3 802.16a OFDMA Space-Time Coding (STC)
In 802.16a standard, a simple scheme of transmitter diversity is defined as an optional mode. The special optional mode is mainly based on Alamouti’s scheme [2].
In this optional mode, we assume that the number of antennas at BS is two and the number at SS is one. A simple illustration of BS and SS is shown in Figure 3.5. The process before TX diversity encoder is quite similar to the general mode configuration.
However, after the diversity encoder, the new space-time code words are modulated by two independent IFFT processors. Once the transform is completed, the OFDM symbols are converted into analog signal, and then they will be transmitted on different antennas of BS. For this special transmission mode, BS will require extra hardware in its design. This modification is also shown in the upper part of Figure 3.5.
Table 3.3 Encoding pattern of 802.16a STC mode Antenna 0 Antenna 1
time t S0 S1
time t+T -S1* S0*
Detailed encoding flow of Tx diversity encoder is described in Figure 3.6. The encoding procedures are applied to each subcarrier and both on space and time domains. Table 3.3 gives a clear description on this procedure.
Figure 3.5 Tx/Rx architecture of 802.16a with STC [11]
Figure 3.6 Transmitter symbol arrangement of 802.16a STC [11]
3.2 IEEE 802.11n WWiSE Proposal
According to WWiSE 802.11n proposal [12], the frame structure of this system is quite similiar to 802.11a system. The proposal keeps major features of 802.11a to sustain backward-compatibility to the legacy system. The frame structure of 802.11a will be explored, and then extended to WWiSE’s proposed system.
3.2.1 Physical Layer Parameters of WWiSE
The system operates at 5 GHz license-free band, which has an advantage of large bandwidth for license-exempt usages. The system has a sampling rate of 20 MHz and FFT length of 64 points. A typical OFDM block duration consists of 80 samples. 64 samples of them are modulated data and 16 samples for guard interval, and their purposes have been introduced in 2.1.2 already. Among the total 64 subcarriers of an OFDM symbol, 12 tones on both sides of channel band are guard band to avoid interference to other nearby system. Besides 4 pilot tones, 48 subcarriers are used for data transmission. The main features of WWiSE physical layer are listed in Table 3.4.
Table 3.4 Main features of WWiSE baseband Mandatory Mode
Sampling rate 20MHz
Number of FFT points 64
Number of data subcarriers 48 Number of pilot subcarriers 4
Subcarrier spacing 0.3125 MHz (=20MHz/64) OFDM symbol period 4µs (80 samples)
Cyclic prefix period 0.8µs (16 samples) FFT symbol period 6.2µs (64 samples)
Modulation scheme BPSK,QPSK,16QAM,64QAM
Short training sequence duration 8µs Long training sequence duration 8µs Long training symbol GI duration 1.6µs
3.2.2 Frame Structure of WWiSE Mandatory Mode
Figure 3.7 shows the basic structure of an 802.11a frame. A frame consists of three parts, which are Preamble, SIGNAL, and DATA, respectively. Preamble part is inserted into the frame to assist synchronization and channel estimation. SIGAL part contains the length, modulation type, ECC coding rate, and other information of following DATA part. The modulation of SIGNAL is fixed to BPSK, and the coding rate of convolution code is 1/2. DATA part is the main element of a whole frame and carries data from transmitter. This thesis will focus on channel estimation skills. Our studies will be concentrated on design of Preamble part.
Figure 3.7 Frame structure of WWiSE 802.11n proposal [13]
In Figure 3.8, a clear illustration of 802.11a frame is shown. This figure shows two types of training field, the short training field (STF) and long training field (LTF).
In the advice of IEEE standard [14], there are ten STFs for auto gain control (AGC), coarse frequency offset estimation, and timing synchronization. After these STFs, there are two LTFs for channel estimation. In Chapter 4, we will focus on the arrangement of LTFs to complete our channel estimation.
Figure 3.8 Detailed frame structure of 802.11n system [13]
In [12], WWiSE proposed a prototype system for 802.11n MIMO OFDM system based on 802.11a standard as we mentioned in this subsection. For example, if there are two transmitting antennas, training sequence of the first antenna is similar to 802.11a, and training sequence of the second antenna will be cyclic-shift version of the first antenna. This special structure is shown in Figure 3.9. Note that guard interval GI21 in this figure is cyclic-shift version (1600ns) of GI2. We can extend this case to four-antenna scenario as we show in Figure 3.10. The shift length is described in each field of this figure. In following discussion, the case of two antennas will be focused for simplicity consideration.
Figure 3.9 Frame structure of WWiSE system with two transmission antennas [12]
Figure 3.10 Frame structure of system WWiSE with four transmission antennas [12]
3.2.3 The Code Structure of Space-time Block Code
From Table 3.3, the transmission model of space-time block code can be described in following equations. Assume the channel responses and are static in a STBC symbol (two consecutive OFDM symbols).
h0 h1
* *
When the number of data streams is three and four, we use the following space-time block codes, H3 and H4, to encode the data. The decoders for H3 and H4
are derived in the Appendix of [14].
( )
Chapter 4
Channel Estimations for MIMO OFDM Systems
4.1 Preamble Design for MIMO OFDM Systems
In [15], several types of pilot arrangements are proposed for MIMO OFDM systems. In this thesis, three of them will be discussed. In this section, these pilot arrangement methods will be introduced briefly. The pilot arrangements concerned are all-pilot preamble, space-time coded preamble, and scattered preamble, respectively. The same spatial arrangement may combine different time-frequency preamble formats, such as block type (802.11n) and comb type (802.16a with STC).
A simple category of pilot arrangement is shown in Figure 4.1. After a general study, channel estimation in both 802.11n and 802.16a systems will be discussed.
Figure 4.1 Classification of pilot arrangement in MIMO OFDM
4.1.1 Scattered Preamble
This preamble format is proposed in [15]. The scattered pilot preambles organize subcarriers in a single all-pilot-preamble symbol into several groups for different antennas. The transmission signal on each antenna can be expressed in the form of (4.1) and (4.2). The illustration of scattered preamble and data symbols is shown in Figure 4.2.
For pilot symbol assisted modulation (PSAM) OFDM symbol
(4.1)
1
2
( 0 0
(0 0 )
X P d d P d d
X P d d P d d
=
=
)
) ) where P is pilot tone and d is data tone
For block type OFDM preambles (802.11n-like)
(4.2)
1
2
( 0 0 0 0
(0 0 0 0
X P P P P
X P P P P
=
=
An OFDM packet
Data symbols coded by STBC
All-pilot preamble
Pilots for first antenna Pilots for second
antenna
Figure 4.2 Frame structure of a 2x1 MIMO OFDM system with scattered pilot
4.1.2 Space-time Coded Preamble
According to [2], space-time block code (STBC) can be applied to MIMO system so that the diversity of multiple antenna systems can be utilized. If the transmitted symbols are known, one can obtain the channel response from space-time coded OFDM symbols. The transmission scheme of this space-time coded preamble is depicted in Figure 4.3, and it can be seen how channel estimator (for preambles) and combiner (for data symbols) work. Table 4.1 lists transmission sequence of the space-time symbols between two antennas, and Figure 4.4 shows total arrangement of a whole packet in this kind of pilot arrangement.
Figure 4.3 Receiving and decoding structure of a 2x1 space-time coded system
Table 4.1 Training symbol arrangement of space-time coded preamble Antenna 0 Antenna 1
time t P0 P1
time t+T -P1* P0*
An OFDM packet
Data symbols coded by STBC
Space-time coded preable P0
P1
-P1*
P0*
P0-P1*
P1 P0*
Figure 4.4 Frame structure a 2x1 MIMO OFDM system with space time coded pilot
4.1.3 All-pilot Preambles
In a SISO OFDM system with packet transmission, the all-pilot preambles are often used. As introduced in Section 3.2.2, 802.11a system adopts this frame structure to perform channel estimation with its LTF preambles. If 802.11n system is needed to backward-compatible to 802.11a, the 802.11n system must reserve the feature of all-pilot preambles. As explained in section 3.2.2, WWiSE uses cyclic-shift version of original LTF for antennas other than the first one. However, this structure may experience severely co-channel (CCI) effect because pilots from different antennas occupy the same tones at the same time. For scattered preambles and space-time coded preambles mentioned previously, this problem can be avoided by tone-interleaving skills and space time block coding. The issue of CCI cancellation will be discussed later in this chapter.
4.2 Channel Estimation Techniques for MIMO OFDM System
In [16], the authors mainly introduce the methods to detect channel response on pilot tones based on LS and MMSE methods for SISO OFDM systems. For MIMO OFDM systems, the channel estimation problems may be more complicated. Due to the special structure of space-time coding and co-channel interference, some additional processing must be integrated into the MIMO OFDM system to solve these problems. In this section, we will study channel estimation methods for MIMO OFDM systems.
4.2.1 Channel Estimation for Scattered Preambles
Scattered preamble described in (4.2) is explored further here. To explain the estimation process, an example is given. The number of transmitter antennas is two, and the total amount of subcarriers in an OFDM symbol is 64. In this case, the frequency domain expression of two OFDM preambles can be described by (4.3).
1 and P P2
m
(4.3)
1 1 1 1
1 0 2 4 62
2 2 2 2
2 1 3 5 63
th
( 0 0 0 0)
(0 0 0 0 )
is the pilot symbol at tone from the antenna
m k
P P P P P
P P P P P
P k
=
=
In preamble symbol which belongs to a transmission packet, the channel effect and additive white noise can be modeled as.
(4.4)
Therefore, the received symbol vector R is
1 2 1 2 1
1 0 2 1 1 2 2 3 1 62 2 63
[ (0) (1) (2) (3) (62) (63) 2]
R= H P H P H P H P H P H P (4.5)
For estimation, the tones may be used for LS
estimation. The general form of estimation is like (4.6). The result can be also applied to channel response for the second antenna, and the extension to more than two antennas is straightforward.
H1 R(0) R(2) R(62)
However, only half the tones are obtained when the estimation in (4.6) is applied. The response on the tones occupied by training symbol from another antenna must be derived with interpolation techniques. In following discussion, some popular interpolation techniques are considered.
4.2.1.1 Piecewise Linear Interpolation
Linear interpolation is quite simple and intuitive among all interpolation skills.
The interpolation skills are based on linearity assumption of unknown subcarrier responses between known two known subcarrier intervals. If known subcarrier data is inserted for each M subcarrier, the segment length is M, and then subcarrier response interpolation in the mth segment can be obtained by
ˆ( ) M l- ˆ( ) l ˆ(( 1) ) ,0
H mM l H mM H m M l M
M M
+ = + + < < (4.7)
4.2.1.2 SPLINE Interpolation
Figure 4.5 Illustration of channel segmentation and the required known parameters for cubic spline interpolation
For generalization, specific-order spline functions can be derived such as the widely used cubic spline for channel interpolation. It is based on the third-order curve-fitting polynomial . Sufficient equations are required to solve this problem because there are total 4N’ unknown variables. All the divisional polynomial coefficients are solved based on continuous assumption at the segment boundary, with the first and second derivative continuity of the pilot channel values on segment boundaries. Therefore, (2N’)+(N’-1)+(N’-1) equations can be set
3 2
i i i i
Y =Ax +Bx +Cx +D
up from the constraints, with two more from the assumption of zero first order derivative value of the very first and last carrier channel value.
4.2.1.3 Transform-Domain Interpolation
DFT-based channel estimators have been proposed in [17,18]. These estimators are based on the techniques performed in transform domain to accomplish the estimation. Fast DFT algorithms can be utilized to reduce the transform complexity.
In the following, we will describe this method in detail. The DFT-based channel estimator has a principal restriction on placement of pilot subcarriers. That is, pilot subcarriers must be equi-spaced along frequency direction. A typical pilot pattern is shown in Figure 4.6. As the figure describes, DFT estimator can be applied only when Df is a constant.In such case, pilot tones can be viewed as a downsampled version of frequency response on all tones.
Figure 4.6 Regular pilot placement
When scattered pilots are used in MIMO OFDM, interpolations are needed to obtain channel response of interleaving tones for different antennas. In this case, transform domain methods are good choices because of the equi-spaced pilot tones in preambles.
When scattered pilots are used in MIMO OFDM, interpolations are needed to obtain channel response of interleaving tones for different antennas. In this case, transform domain methods are good choices because of the equi-spaced pilot tones in preambles.