The system considerations and channel models are introduced in Chapter 2. A brief introduction of the MIMO-OFDM system is given. The fundamental understanding of MIMO technology and space-time processing is presented. In addition, the impact of impairments on the system performance is also discussed. In order to maintain the system performance, some essential algorithms are developed.
In Chapter 3, an anti-I/Q mismatch (IQ-M) auto frequency controller (AFC) is developed. Frequency synchronization is a critical problem for the MIMO-OFDM system. Various frequency offset estimation algorithms have been developed in the open literature. However, it is shown that some methods are not suitable for current wireless systems since the packet format is not compatible with current standards. The proposed carrier frequency offset (CFO) estimation method, based on pseudo CFO (P-CFO) technology, can estimate the CFO value under the conditions of IQ-M. Additionally, the proposed P-CFO algorithm is also compatible with the conventional method.
In Chapter 4, preamble-assisted estimation methods are developed to circumvent the effect of IQ-M. Because IQ-M can degrade the accuracy of CFO estimation and introduce image interference, the compensation for IQ-M is necessary. Many IQ-M estimation methods are published in the open literature. However, most methods focus on the constant IQ-M only. Because of the impairment in the analog components, the low-pass filters of I and Q channels are not identical, resulting in frequency-dependent
IQ-M. The proposed methods can estimate not only constant IQ-M but also frequency-dependent IQ-M.
In Chapter 5, an adaptive channel estimator in STBC MIMO-OFDM modems is developed. In order to realize the gains obtained from MIMO cannels, obtaining accurate channel state information in time-varying environments is extremely important. In order to reduce the hardware cost, the proposed adaptive channel estimator utilizes the property of the Alamouti-like matrix to decrease the cost of complex operators.
In Chapter 6, digital beamforming for wireless communications is presented. In order to improve the signal quality, digital beamforming is performed digitally to form the desired output.
Finally, Chapter 7 describes the conclusions of this work and indicates some promising directions for future research.
Chapter 2
Overview of MIMO-OFDM Systems
This chapter serves as a brief introduction to multi-input multi-output (MIMO) orthogonal frequency-division multiplexing (OFDM) wireless communication systems.
The impact of non-ideal front-ends on system performance is also discussed.
2.1 MIMO Wireless Communications 2.1.1 Antenna Configurations
Figure 2-1 shows different antenna configurations. Single-input single-output (SISO) which uses one transmit antenna and one receive antenna is the well-known configuration, single-input multiple-output (SIMO) uses one transmit antenna and multiple receive antennas, multiple-input single-output (MISO) has multiple transmit antennas and a single receive antenna, and, finally, MIMO has multiple transmit
antennas and multiple receive antennas.
With MIMO, the system can effectively provide the array gain [9]-[12]. Array gain is the average increase in the signal-to-noise ratio (SNR) at the receiver that arises from the coherent combining effect of multiple antennas at the receiver, transmitter or both.
If the channel is known to the multiple antenna transmitter, the transmitter can weight the transmission with weights, depending on the channel state information, so that there is coherent combining at the single antenna receiver. The array gain in this case is called transmitter array gain. For the SIMO system with perfect knowledge of the channel at the receiver part, the receiver can suitably weight the incoming signals so that the signals are coherently added up at the output. This case is called receiver array gain. In order to achieve the array gain, multiple antenna systems require perfect channel knowledge at the transmitter, receiver or both.
SISO
SIMO
MISO
MIMO Transmitter
Transmitter
Receiver
Receiver Receiver
Receiver Transmitter
Transmitter
Figure 2-1. Different antenna configurations.
2.1.2 Capacity Results
Based on Shannon’s theorem, capacity is a measure of the maximum transmission rate for reliable communication on a given channel. Firstly, let us consider the SISO system on the additive white Gaussian noise (AWGN) channel. The capacity of the channel is expressed as
( )
log 12 (bits/s/Hz)
C = +P (2.1)
where P is the average signal-to-noise ratio (SNR) at the receiver. The capacity, as defined in (2.1), is also known as the spectral efficiency. If the transmission rate is less than C bits/s/Hz, then an appropriate coding scheme exists that could lead to reliable and error-free communication. On the contrary, if the transmission rate is more than C bits/s/Hz, then the received signal, regardless of the employed coding scheme, will involve bit errors. MIMO communication technology has received significant attention due to the rapid development of high-speed wireless communication systems employing multiple transmit and receive antennas. Theoretical results show that MIMO systems can offer significant capacity gain over traditional SISO channels. This increase in capacity is enabled by the fact that in rich scattering environments, the signals from each transmitter appear highly uncorrelated at each of the receive antennas, i.e., the signals corresponding to each of the individual transmit antennas have attained different spatial signatures. The receiver exploits these differences in spatial signatures to separate these signals.
MIMO
Figure 2-2. Block diagram of the MIMO system.
Figure 2-2 shows the block diagram of the MIMO system with M transmit antennas and N receive antennas. The input-output relationship of this system is expressed as
where h is the complex gain from the jth transmit antenna to the ith receiver antenna. ij If the channel matrix is known at the receiver, the capacity equation of the MIMO
channel is given by [13]
where I denotes the identity matrix, the superscript H indicates the conjugate transpose, and P is the per-receive antenna SNR. In order to gain insight on the capacity, (2.4) can be expressed as [13]
min{ , } capacity is equal to the richness of the channel plus a term depending on the power level.
2.1.3 Space-Time Processing
In order to improve the reliability for MIMO communication, space-time coding techniques are developed. A pioneering work in the area of space-time coding for MIMO channels has been carried out by Tarokh et al. in [14]-[15]. However, the coding scheme in [14]-[15] requires high decoding complexity. Afterward, Alamouti developed the most famous space-time block coding (STBC) scheme for two transmit and multiple receive antennas [16]. The complexity of the maximum likelihood decoder for Alamouti’s code is very low. Figure 2-3 shows the block diagram of the 2 2× MIMO system with Alamouti’s code. The encoding rule of Alamouti’s scheme is
h1
Figure 2-3. Block diagram of the 2 2× MIMO system with Alamouti’s scheme.
1 2 slot, antenna one transmits c and antenna two transmits 1 c . In the next time slot, 2 antenna one transmits −c2∗ and antenna two transmits c1∗. The columns of the matrix represent time slots and the rows denote transmit antennas. Since two time slots are required to transmit two symbols, the code rate for Alamouti’s scheme is equal to one.
Assuming that the channel coefficients are constant in both consecutive symbol periods, the symbols received by antenna one over two consecutive time slots are given by
1 1 2 1 1
Assuming that the receiver has knowledge of the channel coefficients, the decision statistics are given by
( )
1 1 2 1 1Adding all the decision statistics from all N receive antennas, the estimated symbols will be a scale version. In order to estimate the symbols, we can scale the decision statistics.
This result presented above can be directly extended to other STBC codes.
1,1
Figure 2-4. Space-time block code in the MIMO-OFDM system.
Figure 2-4 shows the STBC scheme applied to a MIMO-OFDM system. In MIMO-OFDM systems, STBC is used independently to each sub-carrier [17]. For the convenience of explanation, two transmit antennas and one receive antenna are considered. Let r denote the kth received sub-carrier at the ith symbol duration. The i k, received data over two consecutive symbol periods at receiver one are expressed as
1, 1, 1, 2, 2, 1,
where h is the channel frequency response for the kth sub-carrier from the ith i k, transmit antenna to the receiver and w is the noise term. The received data are then i k, rewritten in matrix form as
1, 1, 2, 1, 1, symbols can be decoded by the STBC decoder with the estimated channel state information (CSI). The data are then equalized by the following equation.
ˆk = k−1 k
X H R (2.11)
In contract with STBC scheme, spatial-division multiplexing (SDM) technique is used to achieve higher throughput [18]. With SDM, multiple transmit antennas transmit independent data streams, which can be individually recovered in the receiver.
An applicable method is required to separate each transmitted stream form other transmitted streams (interference cancellation). Many approaches, such as zero-forcing (ZF), minimum mean square error (MMSE), and maximum likelihood (ML) detectors, are known for the detection of SDM signals. However, the computation complexity of performing a full search for ML detection is too high to be suitable for practical applications. In order to reduce the complexity, various MIMO detection methods, such as sphere decoding technique [19] or K-best algorithm [20], have been proposed.
Different detection methods have different criteria, and therefore it is preferred to adopt a reduced-complexity data detection scheme for MIMO systems.
2.1.4 MIMO-OFDM Systems
OFDM has been shown to be an effective technique to combat multipath fading in wireless channels [21]-[23]. It has been used in various wireless communication systems such as wireless local area network (WLAN) and wireless metropolitan area network (WMAN). OFDM is a multi-carrier technique that operates with specific orthogonality constraints between the sub-carrier. OFDM is attractive since it admits relatively easy solutions to some difficult challenges that are encountered when using single-carrier modulation schemes on wireless channels. Due to the demand for high speed wireless applications and limited radio frequency (RF) signal bandwidth, OFDM is being considered in the standard that considers MIMO systems, where multiple antennas are used for the purpose of spatial multiplexing or to provide increased spatial diversity.
Figure 2-5 displays the block diagram of the 4 4× MIMO-OFDM system. In the MIMO-OFDM system, the incoming bit stream is first encoded by the one-dimensional encoder (FEC encoder), and then the encoded bits are mapped onto three dimensions (time, frequency, and space) by the space-time coding. The receiver uses the preambles to complete the synchronization, and transforms the signal from time to frequency domain. Spatial streams are then demodulated to bit-level streams, which are de-interleaved and merged into a data stream. Finally, the data stream is decoded by the forward error correction decoder.
Although OFDM is robust against the multi-path propagation, it is very sensitive to the non-ideal front-end effects that destroy the orthogonality between sub-carriers.
For example, OFDM is vulnerable to non-linearity, timing offset and frequency offset [21]. Hence, MIMO-OFDM systems also inherit these disadvantages of the OFDM modulation. In the following section, the non-ideal front-end effects will be discussed.
...
2.2 Non-Ideal Front-End Effects
The receiver architecture adopted in this work is based on the direct-conversion architecture. A block diagram of the direct-conversion receiver is shown in Figure 2-6.
The direct-conversion receiver converts the carrier of the desired channel to the zero frequency immediately in the first mixers [24]-[26]. Hence, the direct-conversion is often called also as a zero-intermediate frequency (IF) receiver. Since the direct-conversion receiver has no IF, the evident benefit of the this architecture is low hardware cost.
However, the direct-conversion receivers are sensitive to several non-ideal effects caused in the front-end. These non-idealities will be covered in the following subsections.
In this work, the MIMO-OFDM system shares the local oscillator (LO) and the sampling clock. In this way, the synchronization error is common to all receive branches, resulting in a simplified implementation.
Baseband
Figure 2-6. Direct-conversion receiver.
2.2.1 Effects of Carrier Frequency Offset
Basically, the band-pass signal yRF( )t at carrier frequency f can be expressed as c
where ( )r t is the complex baseband signal and the initial phase of the carrier is neglected. Re ( ){r t } and Im ( ){r t } denote the in-phase component and the quadrature component of ( )r t , respectively. Based on the direct-conversion receiver, the down-converted signal is expressed as
( )
Figure 2-7. (a) I/Q demodulation. (b) Signal spectrum.
After passing through the low-pass filters (LPFs), the complex baseband signal ( )r t is regenerated. The process (I/Q demodulation) in the spectrum domain is shown in Figure 2-7.
In practice, OFDM is sensitive to carrier frequency offset (CFO) due to the mismatch of LOs between the transmitter and the receiver. The presence of CFO introduces inter-carrier interference (ICI), which can degrade the system performance significantly. When the system suffers from CFO fΔ , the received signal after baseband processing is given by [27]
{ } { }
where ( )w t denotes the representations of the additive white Gaussian noise (AWGN).
From (2.14), the CFO effect results in phase shift in the time domain. The behavior of CFO in the spectrum domain is shown in Figure 2-8. It is clear that the spectrum is shifted with a frequency Δ . After digitizing the signal and passing through the FFT f block, the frequency domain data is given by (see Appendix A for details) [28]
c f
Δf Down Conversion
Figure 2-8. The behavior of the CFO in the spectrum domain.
{ } channel frequency response, respectively. The frequency offset fΔ is normalized to sub-channel bandwidth, and the relative frequency offset is shown as ε . In (2.15), the first term of the right hand side is the decayed original signal transmitted in the kth sub-carrier, and the second term denotes the inter-carrier interference (ICI) from others.
All sub-carriers in an OFDM symbol are orthogonal if they all have a different integer number of cycles within the FFT interval. If there is CFO, the number of cycles in the FFT interval will not be an integer. When the LOs between the transmitter and the receiver are not aligned, CFO occurs and the frequency spectrum is not sampled at the optimum peaks of the sinc functions. The property is shown in Figure 2-9. In Figure 2-9, the received data on each sub-carrier is not the original transmitted data when there is CFO. The effect of frequency offset on a QPSK constellation is depicted in Figure 2-10.
With 5 ppm CFO value, the constellation points have rotated over the decision boundaries after 10 OFDM symbols. Since the phase rotation is increasing with time, it has to be compensated even for a small CFO.
-5 -4 -3 -2 -1 0 1 2 3 4 5 -0.4
-0.2 0 0.2 0.4 0.6 0.8
1 ε
Figure 2-9. The received sub-carriers in the presence of CFO.
Another reason causing CFO is the Doppler shift of the RF carrier. As the result of the relative motion between the transmitter and the receiver, each multipath wave is subject to a frequency shift. The frequency shift of the received signal caused by the relative motion is called the Doppler shift, which is proportional to the speed of the mobile unit. When a signal with carrier frequency f is transmitted and the received c signal comes at an incident angle θ with respect to the direction of the vehicle motion, the Doppler shift f of the received signal is given by [29] D
cos( )
D
f v
c θ
= (2.16)
practical conditions, the Doppler effect adds some hundreds of Hz in frequency
Figure 2-10. QPSK constellation in the case of the AWGN channel. (a) CFO: 0 ppm.
(b) CFO: 5 ppm.
2.2.2 Effects of I/Q Mismatch
Figure 2-11. Direct-conversion receiver with I/Q mismatch.
Figure 2-11 depicts the block diagram of a direct-conversion architecture. I/Q mismatch (IQ-M) arises when the phase and gain differences between I and Q branches are not exactly 90 degree and 0 dB, respectively [26]. The mismatched LO output signals are modeled as
where ε and ϕ denote the constant amplitude and phase mismatch, respectively.
Multiplying the band-pass signal by the mismatched LO signals and passing through the LPFs, the baseband signal is expressed as [30]-[31]
{ } { } { }
the OFDM system, the received signal is further passed through the FFT block. After the FFT operation, the frequency-domain data can be expressed as
{ }
Equation (2.19) shows that IQ-M can cause the symbol at the sub-carrier k to be scaled by the complex factor α . Moreover, the complex conjugate of the symbol at sub-carrier –k multiplied by another complex factor β will be present. The desired sub-carrier k will include the unwanted interference related to the sub-carrier –k, implying that IQ-M can distort the accuracy of received signal. The effect of IQ-M on the 16-QAM constellation is depicted in Figure 2-12. As a result of the IQ-M, the constellation is distorted severely. It implies that IQ-M can limit the ability of the receiver to achieve better performance especially for high constellation size, e.g., 64-QAM constellation.
The image reject ratio (IRR) as a function of the mismatch is given by [32]
2 the gain error must be smaller than 0.3% and the phase error must be smaller than 0.1 degree. Another design choice is that the gain error must be smaller than 0.1% and the phase error must be smaller than 0.2 degree.
(a)
(b)
Figure 2-12. 16-QAM constellation. (a) Without I/Q mismatch. (b) Gain error: 1dB, Phase error: 10 degree.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 25
30 35 40 45 50 55 60 65 70
Phase error (deg.)
IRR (dB)
gain error:10%
gain error: 1%
gain error: 0.3%
gain error: 0.1%
0.3%, 0.1 deg.
0.1%, 0.2 deg.
Figure 2-13. Image suppression as a function of the I/Q mismatch.
This mismatch can occur at the transmitter, receiver or both. Moreover, due to the impairment in the analog components, the low-pass filters (LPFs) of I and Q channels are not identical. The mismatched LPFs result in frequency-dependent IQ-M.
Frequency-dependent IQ-M means that the imbalances can vary with frequency. This will be further discussed in Chapter 4.
2.2.3 Effects of Non-linearity
The power transfer function of a power amplifier is shown in Figure 2-14. In Figure 2-14, the 1 dB compression point is labeled as P1dB and is defined as the point at which a 1 dB increase in input power results in 1 dB decrease in the linear gain of the amplifier [26]. For low values of the input power, the output power grows approximately linear.
For intermediate values, the output power falls below that linear growth and it runs into a saturation as the input power grows higher. The dynamic range of amplifier, which also corresponds to the linear region of operation for an amplifier, is defined between the noise-limited region and the saturation region. In order to recognize the signal, saturation should be avoided as much as possible.
1 dB
Pin
Pout
Nonlinear amplifier P1dB
Figure 2-14. Power transfer function.
The actual saturation behavior is difficult to model. Common AM-AM (amplitude modulation/amplitude modulation) and AM-PM (amplitude modulation/phase modulation) models are the third-order model and the Saleh model [33]. These mathematical models are listed in TABLE 2-1. In TABLE 2-1, coefficients a , i α and i
Considering an OFDM complex baseband signal x t( )=a t e( ) j tφ( ) with amplitude ( )a t respectively. An example of distortion on a 64-QAM constellation due to AM-AM is displayed in Figure 2-16. In addition, non-linearity can cause spectral widening of the transmit signal resulting in unwanted out-of-band noise. At the transmitter part, the transmitted signal itself is degraded by nonlinearities, resulting in increased bit error rates in the receiver.
TABLE 2-1. AM-AM and AM-PM Models.
( ( )) Figure 2-15. AM-AM and AM-PM functional model.
Figure 2-16. The effect of AM-AM on a 64-QAM constellation.
2.2.4 DC Offset
Another important source for reduction of the dynamic range in the analog part is direct current (DC) offset. Static DC offset may be generated by bias mismatch in the baseband chain, but also generated from self-mixing of the RF signal with the LO due to imperfect LO–RF isolation on the same substrate [24]-[26]. In addition, dynamic DC offset can be introduced by mixing of close-in interference with the LO signal. In general, the OFDM system uses null DC. The reason is that the DC offset can be removed by applying a DC blocking filter since there is no information around DC.