First, fundamentals of both OFDM and MIMO are studied in Chapter 2, and so are the techniques based on V-BLAST data detection. Besides, MIMO OFDM systems are also described in Chapter 2, followed by discussion of some existing enhanced algorithms for data detection. Chapter 3 introduces the proposed new enhanced MIMO OFDM data detection algorithms based on some major existing algorithms and the devised new idea, while Chapter 4 includes simulations. Simulations are performed according to EWC 802.11n specifications. Finally, we conclude with some remarks of the work in Chapter 5.
Chapter 2
OFDM and MIMO Fundamentals
2.1 OFDM System Models
The principle of multicarrier system is to seperate the data stream into several parallel ones, each modulated by a specific subcarrier and discrete Fourier Transform (DFT) is used in the baseband modulation and demodulation. Through this approach, only a pair of oscillator (for I-part and Q-part) is needed instead of multiple oscillators to modulate different signals at different carriers.
When signals pass through a time-dispersive channel, inter-symbol interference (ISI) and inter-carrier interference (ICI) usually occur in the receiver and cyclic prefix (CP) is introduced to combat ISI and ICI. Cyclic prefix, shown in Figure 2.1, is a copy of the tail part of a symbol, which is inserted in between the symbol to be transmitted and its preceding symbol. As long as the cyclic prefix length is longer than its experiencing time-dispersive channel length, ISI can be avoided. At the same time, the cyclic prefix along with its symbol makes a periodic signal and maintains the properties of circular convolution and subcarrier orthogonality that prevents the ICI effect.
Figure 2.1 Cyclic prefix of an OFDM symbol [18]
2.1.1 Continuous-Time Model
In this chapter, a continuous-time model is used to introduce the whole OFDM baseband system including the transmitter and receiver. In the transmitter, the transmitted data is split into multiple subchannels with overlapping frequency bands.
The spectrum of OFDM signal is shown in Figure 2.2. It is clear that the spectrum of each subchannel is spreading to all the others, but is zero at all the other subcarrier frequencies, because of the sinc function property, which is the key feature of the orthogonality.
Assume the given channel is quasi-static, i.e., constant during the transmission of an OFDM symbol and variable symbol wise, where the quasi-static impulse response is
) , ( mn
h , n is the time index and m is the channel path delay. The received signal )
(t
y can be expressed as
) ( ) ( ) , ( )
(t h n m x t nt
y = ∗ + (2.1)
where x(t) is the transmitted data and n(t) is the additive white Gaussian noise.
Figure 2.3 (a) shows a typical continuous-time OFDM baseband modulator, in which the transmitted data is split into multiple parallel streams which are modulated by different subcarriers and then transmitted simultaneously. At the receiver, the received signal is demodulated simultaneously by multiple matched filters and then the data on each subchannel is obtained by sampling the outputs of matched filters, as shown in Figure 2.3 (b).
Cyclic prefix
Ts Tg
Figure 2.2 Spectrum of an OFDM signal [18]
Figure 2.3 (a) Continuous-time OFDM baseband modulator [18]
Figure 2.3 (b) Continuous-time OFDM baseband demodulator [18]
2.1.2 Discrete-Time Model
As mentioned previously, to simultaneously transmit multiple data, the transmitter must modulate data with multiple subcarriers and the receiver must demodulate with multiple matched filters. In fact, the modulation and demodulation can be implemented efficiently by using digital IDFT/DFT operations, because they can be respectively represented as
∑
which are the same as IDFT operation of the transmitted data X(k) and DFT operation of the received data y(i), respectively.
Figure 2.4 shows the discrete-time baseband OFDM model. The IDFT transforms the frequency-domain data into time-domain data which is delivered over the air and passed through a multi-path channel, denoted as h( mn, ). At the receiver, to recover the signal in frequency domain, DFT is adopted in the demodulator as a matched filter. Then the frequency-domain signal of each subchannel is obtained from its DFT output.
Figure 2.4 Discrete-time OFDM system model [18]
2.1.3 Effect of Cyclic Prefix
Because of multipath channels, orthogonality as shown in Figure 2.2 will be destroyed by ISI and ICI. However, as long as the cyclic prefix length is longer than that of h( mn, ), ISI effect can be avoided. It is known that circular convolution in time domain results in multiplication in frequency domain when the channel is stationary so that the received signal y(k) in frequency domain is the product of transmitted data x(k) and subcarrier channel response H(k). Thus, the orthogonality is maintained (if h( mn, ) is fixed within the symbol length) and data can be easily recovered by one-tap channel equalizer, i.e., dividing y(k) by the correspondingH(k).
) ( ) ( ) ( )
(k H k x k n k
y = × + (2.4)
2.2 Concept of Multiple-Input Multiple-Output (MIMO) Systems
MIMO system architectures provide better spectral efficiency than conventional systems, because of the benefit of multiple antenna or space diversity both at the transmitter and receiver.
MIMO systems provide the ability to turn multipath propagation, which is traditionally a drawback of wireless transmission, into a benefit. Since MIMO systems effectively take advantage of random fading and multipath delay spread, the signals transmitted from each transmit antenna appear highly uncorrelated at each receive antenna and the signals travel through different spatial channels. Then the receiver can exploit these different spatial channels and separate the signals transmitted from different antennas at the same frequency band simultaneously.
2.2.1 MIMO System Model
MIMO is a promising technology suited for high-speed broadband wireless communications. Through space division multiplexing, MIMO technology can transmit multiple data streams in independent parallel spatial channels, thereby increasing total system transmission rate.
MIMO systems can be easily defined. Considering an arbitrary wireless communication system, a link is considered for which the transmitter is equipped with Nt
transmit antennas and the receiver is equipped with Nr receive antennas. Such a setup is illustrated in Figure. 2.5. Consider this system some important assumptions are made first:
1. Channels are constant during the transmission of a packet. It means the communication is carried out in packets that are of shorter time-span than the coherence time of the channels.
2. Channels are memoryless. It means that an independent channel realization is drawn for each use of the channels.
3. The channel is flat fading. It means that constant fading over the bandwidth is desired in the case of narrowband transmissions. It also indicates that the channel gains can be represented by complex numbers.
4. The received signal is corrupted by AWGN only.
With these assumptions, it is common to represent the input/output relations of a narrowband, single-user MIMO link by the complex baseband vector notation
n Hx
y= + (2.5)
where x is the Nt×1 transmit vector, y is the Nr×1 receive vector, H is the Nr×Nt channel matrix, and n is the Nr×1 additive white Gaussian noise (AWGN) vector at some instant in time. All the coefficients hij comprise the channel matrix H and represent the complex gain of the channel between the jth transmit antenna and the ith receive antenna. The channel matrix can be written as
⎟⎟
jij
ij ij ij
ij j h e
h =α +β = ⋅ φ (2.7)
Coefficients {hij} reflect unknown channnel properties of the medium, usually Rayleigh distributed in a rich scattering environment without line-of-sight (LOS) path. If
αij and βij are independent and Gaussian distributed random variables, then |hij| is a Rayleigh distributed random variable. Actually, coefficients {hij} are likely to be subject to varying degrees of fading and change over time. Therefore, determination of the channel matrix is an important and necessary aspect of MIMO techniques. If all these coefficients are known, there will be sufficient information for the receiver to eliminate interference from other transmitters operating at the same frequency band.
Figure 2.5 Wireless MIMO transmission model [17]
Although the introduced MIMO transmission requires flat-fading channels, and it is limited to applications with narrowband transmissions, in real broadband transmission systems, channel conditions are often frequency-selective fading. A technique alleviating severe effect of frequency-selective fading is demanded. OFDM technique is a good solution for this purpose in wireless transmission owing to its advantages [3,4,5].
2.2.2 MIMO-OFDM Architecture
According to Section 2.1, OFDM technique turns frequency-selective fading channel into several flat-fading subchannels, and it solves the major problem in wideband transmission systems. Boubaker et. al [10] proposed V-BLAST technique to detect transmitted signals on each subcarrier of a MIMO OFDM system. MIMO OFDM transceiver and receiver architecturs are shown in Figures 2.6 and 2.7, respectively.
Subchannels are orthogonal to each other in OFDM systems. Hence, in a single-input-single-output (SISO) OFDM systems, the received signals are product of channel response and transmitted signal, as shown in equation 2.4. In MIMO systems, signals transmitted from different antennas on a subcarrier simultaneously interfere each other, but signals at different subcarriers are independent. At each receiver antenna, a linear combination of the transmitted signal and channel response on each subcarrier is observed. That corresponds to assumptions of MIMO systems. On each subchannel, a space division multiplexing (SDM) like V-BLAST is applied. That is, the task is to recover x from the received signal y and channel state information (CSI) H on each subcarrier.
Figure 2.6 Transmitter architecture of a MIMO OFDM system [10]
Figure 2.7 Receiver architecture of a MIMO OFDM system [10]
2.2.3 An example MIMO OFDM System EWC 802.11n
EWC 802.11n standard utilize both MIMO and OFDM techniques for high throughput transmission of wireless LAN. EWC 802.11n proposal [11] emphasizes backward compatibility with existing installed base, building on experience with interoperability in 802.11g and previous 802.11 amendments which are mainly designed for indoor wireless internet applications. Hence, we review the physical layer of wireless LAN 802.11a [12] system which is based on OFDM technology. The main system parameters of IEEE 802.11n Wireless LAN standard are listed in Table 2.1.
In 802.11n standard, a frame is composed of three fields. Table 2.1 shows the packet format which facilitates synchronization and channel estimation of the receiver. In the preamble field, the preambles are composed of ten repeated short symbols and two repeated long symbols. The total duration of short symbols is 8µs and so is that of long symbols. Since the SIGNAL field contains the most important information of a packet, such as frame length and modulation, synchronization and channel estimation must be finished before decoding of the SIGNAL field.
To examine validity of proposed algorithms in latter chapters, EWC 802.11n standard, is adopted for simulation.
Table 2.1 Parameters and specifications of EWC 802.11n systems [11]
In 802.11n, a PLCP (PHY Layer Convergence Protocol) frame shall have one of the following three formats, the field parameters are define below:
Figure 2.8 PLCP frame format of EWC 802.11n standard [12]
L-STF: Legacy Short Training Field.
L-LTF: Legacy Long Training Field.
L-SIG: Legacy Signal Field.
HT-SIG: High Throughput Signal Field.
HT-STF: High Throughput Short Training Field.
HT-LTF1: First High Throughput Long Training Field.
HT-LTF’s: Additional High Throughput Long Training Fields.
Data: The data field includes the PSDU (PHY Sub-Layer Data Unit).
The PHY will operate in one of 3 modes:
-Legacy mode: in this mode the packets are transmitted with 802.11a/g format.
-Mixed mode: in this mode packets are transmitted with a preamble compatible with the legacy 802.11a/g – the legacy Short Training Field (STF), the legacy Long Training Field (LTF) and the legacy signal field are transmitted so they can be decoded by legacy 802.11a/g devices. The rest of the packet has a new format.
In this mode the receiver shall be able to decode both the Mixed Mode packets and legacy packets.
-Green Field: in this mode high throughput packets are transmitted without a legacy compatible part. This mode is optional. In this mode the receiver shall be able to decode both Green Field mode packets and legacy format packets.
We can choose an appropriate mode for the compatibility with former standards.
For the purpose of compatibility with 802.11 legacy devices, the legacy part of the preamble format in EWC proposal is the same as that in 802.11a. If the legacy preambles are transmitted from multiple antennas, the mapping of this single spatial stream to multiple antennas has to be done such that beamforming in far-field is mitigated.
One method for achieving this is to use a cyclical-delay-diversity (CDD) mapping. The cyclical delay is adopted in EWC proposal, whose format is used for simulation. Figure 2.9 shows the cyclical delay format in EWC. The maximum number of the spatial data streams is four. STRN stands for the short training sequence. LTRN represents the long training symbol. GI2 is the guard interval of the long training symbol.
Figure 2.9 Cyclical delay format of the preamble in EWC 802.11n standard [11]
2.3 Signal Detection Algorithms for MIMO Systems
Signal detection here means a process that try to recover the transmitted signals at receivers. As shown in equation 2.5, the task is to detect the transmitted vector x based on received vector y and channel state information (CSI) H.
In this section zero-forcing (ZF) criterion is considered due to consideration of low complexity. Zero-forcing techniques receive an input vector y and send it to a filter bank which eliminates the mutual interference without caring about noise.
STRN 400 ns cs
STRN
STRN 600 ns cs
GI21
GI2 LTRN
GI23
LTRN 100 ns cs
LTRN 1700 ns cs
GI22
LTRN 1600 ns cs STRN
200 ns cs
2.3.1 Maximum-Likelihood (ML) Detection
Since modern transmission systems are digital, each element of transmitted vector x is chosen from a finite set, which is denoted as A, such as BPSK, QPSK and 16-QAM.
Hence, a transmitted signal x belongs to the multiplicative set ANt. The optimum maximum-likelihood (ML) detector searches over the whole set of transmit signals x ∈ ANt, and decides in favor of the transmit signal xML that minimizes the Euclidian distance to the receive vector y , i.e.
min 2
arg y Hx
xML = x∈ANt − (2.8)
The computational effort is of order MNt, where M denotes the size of finite set A.
When using high modulation scheme or a large number transmitting antennas, ML detection is impractical.
2.3.2 V-BLAST Detection Method
Although ML detection reaches optimal performance, it is not feasible for large numbers of transmit antennas or high modulation schemes. In the sequel, some suboptimal algorithms are investigated. The target is to find algorithms that have performance near ML and low complexities.
Vertical – Bell Laboratories Layered Space-Time (V-BLAST) [9] is proposed to improve performance of the linear detection method by utilizing successive interference cancellation based on zero-forcing criterion. It suggests that transmitted signals are detected sequentially rather than in parallel. In each detection step, the signal which yields the smallest estimation error is linearly detected. It is shown in [9] that row gZF, the row with the minimum norm in GZF (GZF =H+ =(HHH)−1HH ), has the largest signal-to-noise ratio (SNR) and yields the smallest estimation error, because it causes minimum noise enhancement.
( )
i ii ZF i
i gZFy g Hx n x
x = = + = +η
∩
(2.9)
xi
∩
is quantized to obtain estimate of x , and the interference of this signal is i removed by subtracting it from the received signal y, so is the i -th column of the channel matrix is nulled. Nulling and canceling process are repeated until all signals are detected, as summarized in the following algorithm steps:
Begin
k quantize x
xi (2.10.h)
The main computational bottleneck in the iterative process is the computation of pseudo inverses for Nt matrices. For saving computation, channel response is assumed constant within a packet, as assumption 1 suggests. The optimal detection order and each nulling vector gZF are validly used to detect received signals in the whole packet, because they share the same channel matrix. That is, pseudo inverse of the channel is not updated.
2.3.3 Detection Methods based on V-BLAST
We will introduce four different algorithms based on V-BLAST technique. The first algorithm reduces the numbers of pseudo-inverse operations. The second algorithms can increase performance by reducing negative side effects. The first and second algorithms consider trade-off in the iteration process of V-BLAST techniques. The third algorithm is MMSE-VBLAST that includes the noise term in the design of the linear filter matrix G. The fourth algorithm is based on parallel symbol cancellation (PSC) instead of serial symbol cancellation (SSC). It focuses on detecting signals at the same time.
2.3.3.1 Simplified V-BLAST Detection
On each subcarriers of a MIMO ODFM system, a V-BLAST detector is used, because we can formulate the detection problem of each subchannel by equation 2.5.
Hence for practical OFDM systems, there will involve a lot of V-BLAST detectors.
Fortunately, channel responses of successive subcarriers are often similar. Some simplified algorithms [13,20] are proposed based on this observation.
[13] assumed that successive subcarriers have the same channel response so that calculated vectors of a subcarrier are applied to detect signals of nearby subcarriers. We can call this algorithm a simplified 0th-order algorithm.
Figure 2.10 The 0th-order simplified V-BLAST detection algorithm in [13]
The subcarrier which is decoded by approximation is assumed to have the same decode order as that of the subcarrier which provides the pseudo inverse. At each step of V-BLAST detection, a column of channel matrix is set to zero in order to ignore the effect of the corresponding transmitting antenna. If the pseudo inverse is used to estimate inverse of adjacent subcarriers, the subcarriers have to recognize the nulled columns, which stand for the detected signals. In other words, the optimal decoding order is assumed unchanged.
Under this assumption, there are some opportunities for further simplification.
The simplified algorithm has identical performance but with lower complexities. Owing to unchanged decoding order it merely needs a row of the approximated pseudo inverse which represents the transmitted signal to be detected, rather than the whole pseudoinverse, as shown below.
[
H(k+1,p)+] [
j ≈ H(k,p)++H(k,p)+(H(k,p)−H(k+1,p))H(k,p)+]
j(2.11) where []j denotes the j-th row, and p is a small enough positive integer.
[
H(k+1,p)+] [
j ≈ H(k,p)+] [
j+ H(k,p)+(H(k,p)−H(k+1,p))H(k,p)+]
j (2.12) then[
H(k+1,p)+] [
j ≈ H(k,p)+]
j(1+(H(k,p)−H(k+1,p))H(k,p)+) (2.13) As a result, computation complexity is reduced, but performance is not noticeably degraded. This simplified algorithm can be called a 1st-order simplified algorithm. Its algorithm steps are summarized below.Figure 2.11 The simplified V-BLAST detection algorithm in [18]
Begin
for (i=1 ; i <= subcarrier number ; i+=2) (2.14.a) calculate weight vectors giZF according to equation (2.10) (2.14.b) if successive subcarriers share a channel respose [13] (2.14.c)
i ZF i
ZF g
g+1= (2.14.d)
else // (2.14.e)
calculate weight vectors gZFi+1 according to equation (2.13) (2.14.f)
end (2.14.g)
end (2.14.k)
2.3.3.2 Enhanced V-BLAST Detection
Since V-BLAST’s performance is worse than ML detection, improved detection methods [19,21,22] based on V-BLAST technique are proposed to get better performance than the conventional V-BLAST technique.
2.3.3.2.1 Two Iterative V-BLAST Detection Algorithms
Shen’s Approach [19]:
An iterative V-BLAST detection algorithm improving the performance over error propagation is proposed [19]. In the algorithm, low-diversity substreams are iteratively decoded by using decisions from high-diversity substreams. As such the performance is greatly improved over the conventional one. Another advantage of this algorithm is that it is practical to make a trade-off between performance and complexity. The steps of the algorithm is listed below. Table 2.2 also illustrates the algorithm.
initialization:
Step 1:
detect x x xNt
∩
∩
∩
...
, 2
1 by V-BLAST
Step 2:
for i=1 to Nt-1
subtract signals from substreams 1 to i (x x xi
∩
apply the V-BLAST detection to generate xNt−i
∩
end
Table 2.2 Change of diversity degree in each V-BLAST’s loop [19]
No. of Loop Detection order Detected Symbol
Initialization Loop 1
Li’s Approach [21]:
In this approach proposed iterative method [21] to suppress error propagation and improve the performance in an uncoded case. From simulation results, this method exhibits considerable performance gains over the original V-BLAST detection algorithm and the iterative algorithm presented in [19]. At the same time, this method has a lower complexity compared with the iterative method in [19].
Nt
Since the detected symbol xNt
∩
has a diversity order of Nr, the new-version symbols of
are more accurate than the old version. Such an improvement is especially obvious for symbol 1
∩
x , because the new-version 1
∩
x has the diversity order of Nr while the old one only has the diversity order of 1. By using such an approach, closed-loop iteration architecture for V-BLAST detector can be constructed. In detail, if the new-version 1
∩
x is different from the old one, repeat above procedure. Otherwise, terminate the procedure and the symbol of xNt
∩
as well as the present new-version
as well as the present new-version