Chapter 4 Preamble-Assisted Estimation for I/Q Mismatch 69
4.4 Transmitter IQ-M Estimation
An OFDM system in the presence of IQ-M and CFO is depicted in Figure 4-13. Let ( )
x n be the transmitted baseband signal before being distorted by IQ-M. Here we consider the system with constant transmitter (TX) and receiver (RX) IQ-M. The distorted baseband signal is given by
( ) tx ( ) tx ( )
x n =ξ x n +σ x n∗ (4.47)
The TX IQ-M parameters, ξ and σ , are expressed as
Modulation De-Mapper
Analog IQ-M & CFO
2 s 2 s
j fnT j fnT
rxre rxr e
y =α πΔ +β ∗ − πΔ Figure 4-13. An OFDM system with transceiver IQ-M and CFO.
( )
front-end. The received baseband (digital) signal with sampling period T can then be s expressed as(2 )
(
(2 ))
*( ) rx ( ) j fnTs rx ( ) j fnTs ( )
y n =α r n e πΔ +β r n e πΔ +w n (4.49)
where ( )r n and ( )w n denote the representations of the received signal and additive white Gaussian noise (AWGN), respectively. fΔ denotes the frequency offset. α rx and β are defined in (4.2). The received signal can also be expressed as rx
( ) ( ) ( )
r n =h n ⊗x n (4.50)
where ( )h n stands for the representation of channel response, and ⊗ means convolution operations. The received signal can thus be regarded as a gain, α , from rx
the original signal added to the conjugate multiplied by a sigma value, β . If neither rx gain nor phase error exists, ξ or tx α remains at unity, and rx σ or tx β decreases to rx zero. Note that the phase rotation is inversed in the direction between original signals and their conjugate if the CFO is present. This means that conventional methods, simply multiplied the data by an exponential term, has to be modified in accordance with IQ-M.
4.4.2 The Proposed Method
In order to simplify the notation, noise distribution is ignored. With the estimated CFO value, the RX IQ-M parameters can be calculated by following equation
( ) ( )
where N denotes the data samples of a long training symbol. A better estimate of l
rx rx
(2 ) 2 (2 )
From (4.53), it is apparent that the exponential term could be removed by CFO compensation, and the RX IQ-M compensation gain, κ , could be balanced by channel equalization. After CFO compensation, the received signal is demodulated using an FFT as stands for CFR. It is worth noticing that CFO and RX IQ-M parameters are estimated in time domain (pre-FFT), while TX IQ-M parameter is extracted in frequency domain (post-FFT). With mathematic derivations, one pair of sub-carriers could be arrayed in a matrix form as follows:
11, 12, problem is how to estimate the overall distortion matrix, Φk. Because the coherence bandwidth of the channel is much larger than the inter-carrier spacing, the variation between two consecutive sub-carriers could be small. It implies that Φ ≈ Φk k +1. Therefore, long preambles are used to calculate the distortion matrixes. For instance, if X and k X−k are all 1, (4.56) can be rewritten as
From (4.57) and (4.58), the distortion matrix is estimated by
11,
Since distortion matrices are estimated from (4.59), the desired signal can then be recovered. Generally, TX IQ-M could be solved by calibration with carefully designed analog hardware [63]. In order to release the front-end specification, an all-digital estimation method is developed. Recalling from (4.44), a similar approach can be applied at transmitter. The transmitted signal can be pre-compensated according to
( ) ( ) tx ( )
Inserting (4.60) into (4.47) yields
2
Equation (4.61) indicates that the transmitter can compensate for TX IQ-M by the pre-compensation scheme. The issue now is how to extract TX IQ-M parameters exactly. From (4.56), the matrix, Φ , is expressed as k
It is readily shown that
12, 21,
In order to analyze the sensitivity of noise, a multivariable first order Taylor series3 of (4.63) is expressed as
12, 12,
which is proportional to 1 |φ11,k |2 . By weighting the component inversely proportional to the variance, a better estimate of σ ξtx tx could be obtained
where N is the data carriers of an OFDM symbol. While TX IQ-M parameters are estimated at receiver, it can be fed back to transmitter (Figure 4-14). This technique may consume link capacity and utilization of packet field. Moreover, the proposed IQ-M compensation method adopts the existing packet format defined in current standards, while the previous literature employs user-defined training symbols [54], [48].
3For a function that depends on two variables, x and y , the Taylor series to first order about the point ( , )a b is written as
P/S
IFFT Analog
IQ-M
TX IQ-M Parameter From RX
x Digital TX IQ-M Pre- xc x
Digital RX IQ-M Compensation
Feedback Link to TX TX IQ-M Parameter
Figure 4-14. Block diagram representation of the proposed method. (a) Transmitter part with pre-compensation scheme. (b) Receiver part with joint compensation scheme.
4.5 Summary
This chapter develops preamble-assisted methods for combating IQ-M with CFO in direct-conversion OFDM receivers. The IQ-M with CFO can be estimated by taking advantage of the relationship between desired sub-carriers and image sub-carriers. Both simulation and experiment results indicate that the proposed method can meet system requirements to prevent from an obvious performance loss under the condition of IQ-M.
Furthermore, this method is compatible with current standards because it does not
Chapter 5
Adaptive Channel Estimation
This chapter presents an adaptive frequency-domain channel estimator (FD-CE) for equalization of space-time block code (STBC) multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems in time-varying frequency-selective fading. The proposed adaptive FD-CE ensures the channel estimation accuracy in each set of four MIMO-OFDM symbols. Performance evaluation shows that the proposed method achieved a 10% packet error rate of 64-QAM modulation at 29.5 dB SNR under 120 km/hr (Doppler shift is 266 Hz) in 4 4× MIMO-OFDM systems. To decrease complexity, the rich feature of Alamouti-like matrix is exploited to derive an efficient VLSI solution. Finally, this adaptive FD-CE using an in-house 0.13-μm CMOS library occupies an area of 3 3.1× mm , and the 2
4 4× MIMO-OFDM modem consumes about 62.8 mW at 1.2V supply voltage.
MIMO-OFDM systems offer reliable communications with bandwidth efficiency and high throughput rate. Space-time block code (STBC) has recently been integrated into MIMO-OFDM systems. The combination of MIMO transmission, OFDM
technology, and the STBC scheme comprises a promising solution for next-generation wireless communications [64]-[65]. The MIMO-OFDM systems, however, require additional complex considerations in signal processing, as compared with single-input single-output (SISO) systems. Recently, the request for wireless communication under mobile conditions is increased. For instance, very high throughput (VHT) study group wants to go beyond the IEEE 802.11n standard. This study group thinks that MIMO-OFDM technology will be a potential solution to increase the data rate. In addition, VHT group also considers to support for moderate mobility or equivalently, improving outdoor operations. VHT study group hopes to not only supply data rate above 1 Gbits/s but also cooperate with metropolitan area network (MAN) network.
The ability of fast channel tracking is therefore needed to achieve high performance receivers. Portable applications, such as ultra mobile PCs, personal digital assistants (PDAs) and smart phones, are often used in mobile (time-varying) environments. The accuracy of channel state information (CSI) is critical to ensure the required performance in mobile applications. For successful transmissions, obtaining accurate CSI as soon as possible is extremely important. Advanced military wireless communications and vehicular ad hoc network (VANET) technology (IEEE 802.11p) are other practical applications which will adopt MIMO transmission and STBC. For example, remote controlled vehicles can access the street and battlefield information from the control center or communicate with other moving vehicles. Robust communications in such environments are very important.
Many studies have investigated MIMO detection, and developed and implemented equalization algorithms [66]-[71]. A scalable STBC decoder [66], supporting 2 2× , 8 3× and 8 4× STBCs, was implemented using a low-computational symmetrical approach. A 2 2× MIMO-OFDM detector [67] was developed to offer two modes of space-frequency block code and space division multiplexed OFDM. A vertical-bell
laboratory layered space-time (V-BLAST) detector [68] was based on the square-root algorithm for 4 4× MIMO-OFDM systems. These systems are developed for low mobility. For time-varying environments, Akhtman and Hanzo [69] proposed a decision-directed channel estimation scheme utilizing pilot tones. Song and Lim [70]
presented a channel estimation based on particular pilot formats. The channel correlation function [71] was also proposed to exploit the time-varying effects. However, most methods require high complexity and specific pilot for-mats.
To increase throughput, the number of pilots in MIMO-OFDM systems must be significantly smaller than that of data carriers. The objective of this study is to derive an adaptive frequency-domain channel estimator (FD-CE) for frequency-domain equalization without scattered pilots and specific pilot formats in MIMO-OFDM WLAN applications over time-varying fading. Conversely, non-pilot-based channel estimator is built to provide acceptable performance. In the proposed FD-CE, all data carriers are applied to measure channel variations, namely, virtual pilots. Consequently, the system with 64 quadrature amplitude modulation (QAM) can achieve a 10% packet error rate at 29.5 dB signal-to-noise ratio (SNR) at 120 km/hr (Doppler shift is 266 Hz).
Furthermore, the adaptive FD-CE utilizes the rich property of an Alamouti-like matrix to derive an efficient architecture for VLSI implementation. By using an in-house 0.13-μm CMOS library, the chip area of the 4 4× MIMO-OFDM modem is 4.6 4.6×
mm and power consumption is 62.8 mW at 1.2V supply voltage. 2
This chapter is organized as follows. Section 5.1 introduces the MIMO-OFDM modem specifications and presents the problem statement. Section 5.2 introduces the STBC scheme. Section 5.3 describes the mathematical derivations for the proposed adaptive FD-CE. Next, Section 5.4 summarizes the simulation results. Section 5.5 then presents the proposed architecture and implementation results. Conclusions are finally drawn in Section 5.6.
5.1 System Description and Problem Statement 5.1.1 Modem Specification
Figure 5-1 presents a block diagram of the 4 4× MIMO-OFDM modem. First, source data is scrambled and then encoded by the convolutional encoder. The encoded bit stream is punctured to the required data rate. According to the number of transmit antennas, the punctured bit stream is parsed into spatial streams. To prevent a burst error, the interleaver changes the bit order for each spatial stream. The interleaved sequence is modulated by the BPSK, QPSK, 16-QAM, or 64-QAM scheme. The STBC encoder is then applied to encode the modulated OFDM (with 64-point IFFT) symbols.
Each OFDM symbol has 64 sub-carriers, 52 of which are data carriers and 12 are pilots and null carriers. The time-domain signal is preceded by the guard interval containing the last 16 samples of the OFDM symbol. After all, signal is then transmitted by RF modules.
The receiver synchronizes the received signals to recognize the OFDM symbols.
After fast Fourier transform (FFT), the OFDM symbols are decoded by the STBC decoder with the proposed method. Spatial streams are demodulated to bit-level streams, which are then de-interleaved and merged into a single data stream. Finally, the data stream is decoded by the forward error correction (FEC) block, which has a de-puncturer, Viterbi decoder and de-scrambler.
Puncturer Spatial Parse
De-scrambler De-puncturer Spatial Merge
Scrambler Convolutional Encoder
Viterbi Decoder
Figure 5-1. Block diagram of the 4 4× STBC MIMO-OFDM modem.
5.1.2 Problem Statement
In time-varying fading, the system must measure channel variations to prevent the equalized degradation. It is known that pilot tones can be applied to extract the channel variations. Getting accurate CSI, the system must increase the number of pilot tones, but it also reduces the data rate. The possible solution is to use the scattered pilots to balance the accurate CSI and data rate. The 2-D methods [72]-[73] have been developed for SISO-OFDM applications. However, most WLANs do not include any scattered pilot, and the number of pilots is also much smaller than that of data carriers (e.g., IEEE 802.11 a/g/n and HiperLAN). Due to above limitations, all data carriers should be adopted to ensure accurate estimation of channel variations, namely, virtual pilots.
For VLSI implementation, the hardware complexity of MIMO designs increases greatly; thus, low-complexity architectures are preferred for MIMO-OFDM modems.
For example, the coordinate rotation digital computer (CORDIC) algorithm, which is widely used in vector rotation, can be applied for MIMO detection (e.g., QR decomposition [74]-[75]). Although the CORDIC algorithm is advantageous during implementation, the computing latency caused by CORDIC iterations is too long to be
suitable for MIMO-OFDM WLAN applications over time-varying fading. In order to acquire a win-win scenario for latency and throughput, the proposed FD-CE capitalizes on the rich property of an Alamouti-like matrix for an efficient solution.
5.2 STBC Decoder and Equalization
Figure 5-2 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, four transmit antennas and one receive antenna are considered. To provide the full rate of 1 (4 symbol periods transmit 4 symbols), the following code matrix is chosen
1 2 3 4
Let r denote the kth received sub-carrier at the ith symbol duration. The received i k, data over four consecutive symbol periods at receiver one is expressed as
1, 1, 1, 2, 2, 3, 3, 4, 4, 1,
1,1
Figure 5-2. Space-time block code in the 4 4× MIMO-OFDM system.
where h is the channel frequency response for the kth sub-carrier from the ith i k, transmit antenna to the receiver and n is the noise term. The received data is then i k, rewritten in matrix form as
1, 2, 3, 4, sub-matrices in H are Alamouti-like matrices. The basic 2 2k × Alamouti matrix is defined as [16]
1 2
where , 1,2c i =i terms represent the transmitted complex data on the sub-carrier.
The received symbols can be decoded by the STBC decoder with the estimated CSI.
The data is equalized by the following equation.
ˆk = k−1 k
X H R (5.5)
where H can be inverted blockwise using the following inversion formula [76] k
1 1 1 1 1 1
5.3 The Proposed Method
5.3.1 Adaptive Frequency-Domain Channel Estimator
Figure 5-3 shows the sub-carrier frequency allocation. Each OFDM symbol employs 64 sub-carriers, 52 are data carriers while the rest are used for pilots and null carries. Four pilots are put in sub-carriers 21, 7, -7 and -21. In general, pilot tones are employed to estimate channel variations in flat-fading channels. In fast-fading channels, it is not
injecting additional pilots, accuracy channel variations between consecutive OFDM symbols can be estimated; however, this approach can reduce the data rate. Therefore, the proposed method uses four OFDM symbols (total = 208 data carriers + 16 pilots) every time to calculate channel variations without injecting additional pilots. In addition, the proposed method is compatible with the current standard because it does not require special pilot patterns.
Figure 5-3. Sub-carrier frequency allocation.
Figure 5-4 shows a block diagram of the adaptive FD-CE-based frequency-domain equalizer. First, training symbols are employed to estimate channel frequency response (CFR). The decoded symbols are adopted to extract channel variations. Due to time-varying effects, CSI is not consistent within the entire packet. In an adaptive procedure, the estimated CFR is assumed to be Hk′ , which is defined as
k k k
Therefore, received data are written as
Rk Xk′ +Xk +Hk
Figure 5-4. Block diagram of the adaptive frequency-domain equalizer.
k k k k symbol contains a residual term that causes a decision error, as shown in (5.10). The relationship between X and k Xkk′ can be interpreted geometrically in the complex plane (Figure 5-5). The difference between ideal code sets and received symbols is used to extract channel variations. The residual term is expressed as
1
x
Figure 5-5. Relationship between decided symbol and decoded symbol.
1, 2, 3, 4, 1,
TABLE 5-1 summarizes the operations of the adaptive FD-CE. The adaptive FD-CE is applied to every four OFDM symbols for 208 tones. Notably, H is multiplied by the k−1 received OFDM symbols. The decoded symbols Xkk′ are employed to calculate residual term +Xk. To acquire +Rk, channel matrix H is multiplied by the stored distance k vector +Xk. After calculating channel variations, Hk′ is updated by (5.7).
TABLE 5-1. Operation of the Adaptive FD-CE.
Step Operation 1 Estimate the channel state information 2 Xk′ =H R k−1 k
3 Calculate the residual term +Xk 4 +Rk =Hk+Xk
5 Calculate the channel variation 6 Update the channel matrix Hk′
The 4 4× code matrix, as defined in (5.1), can be applied to four transmit antennas and any number of receive antennas. In the above derivation, the receiver takes advantage of the orthogonality of code matrix to find a decision statistic. If the receive antenna number is greater than one, we can add all the statistics from all receive antennas. In multiple receive antennas, the additional computational cost includes STBC decoding and scale operations. For instance, the statistics from four receive antennas are given by
where the subscript i represents the ith receive antenna. It is clear that the estimated symbols will be a scale version. To estimate the symbols that were sent, we can scale the
decision statistics. This result presented above can be directly extended to other STBC codes.
5.3.2 Discussion
We provide the discussion with regard to the M× MIMO system for N M >2 and 2
N > . First, we describe the encoding and decoding operations of Alamouti scheme.
The Alamouti code is an STBC using M = transmit antennas and any number of 2 receive antennas (N >2) [Figure 5-6(a)]. The Alamouti code matrix is defined in (5.4).
Assuming that the channel coefficients are constant in both consecutive symbol periods, the signal received by antenna one is expressed as
1, 1, 2, 1, 1,
where the parameters are defined (5.2). Assuming that the receiver has knowledge of the channel coefficients, the decision statistics are given by
( )
1 1, 2, 1 1,There may be applications where multiple receive antennas are feasible. The Alamouti scheme can be applied for the system with multiple receive antennas. Adding all the decision statistics from all N receive antennas, the estimated symbols will be a scale version. To estimate the symbols, we can scale the decision statistics. This result
presented above can be directly extended to other STBC codes.
We discuss the case with M >2 transmit antennas subsequently. In general, the STBC code can be defined by a M× matrix C . The elements of the matrix C are p combinations of the symbols , c ii =1,...,k. The columns of the matrix represent time slots and the rows denote transmit antennas. Hence, p time slots are required to transmit k symbols (code rate R =k p/ , where R ≤ [15]). For M transmit antennas, 1 we are more interested in the minimum time slots (p ) needed to transmit a block. In summary, STBC systems transmit the same information stream via different transmit antennas to obtain transmit diversity. Despite the reduction in the data rate, the STBC
system take the advantage of transmit diversity to obtain a robust communications.
For instance, C is the STBC matrix with three transmit antennas [Figure 5-6(b)]. 3 The matrix C (code rate 3 R =3/ 4) is given below [17]
To decode the C , the receiver one constructs the decision statistics as follows: 3
4, 3, 3, 4, 3, 3,
where these parameters are defined in (5.2). Adding all the decision statistics from all receive antennas, the estimated symbols will be a scale version. We can scale the decision statistics to estimate the symbols. After the STBC decoding, the difference between ideal constellation points and the received symbols can be calculated directly, and then channel variations can be extracted. From (5.17), it is clear that the computational complexity is higher than Alamouti-like case adopted in this study. In system designs, we prefer to choose a feasible STBC matrix which can be decoded by simple liner processing. Alamouti-like matrix is one potential candidate for simple processing among various STBC codewords.
In addition, the complexity of channel estimation scheme also depends on the
MIMO detection method. To achieve higher throughput, spatial-division multiplexing (SDM) technique can be used. With SDM, multiple transmit antennas transmit independent data streams, which can be individually recovered at receiver. An applicable method is required to separate each transmitted stream form other transmitted streams (interference cancellation). Many approaches are known for the detection of SDM signals. For instance, zero-forcing (ZF), minimum mean square error (MMSE), and maximum likelihood (ML) detectors estimate the transmitted signals with the estimated channel state information. In general, ML detector provides improved performance over ZF, MMSE detectors. However, the computation complexity of performing a full search for ML detection is too high to be suitable for practical applications. To reduce the complexity, sphere decoding technique or K-best algorithm can be applied to the ML detector. In ZF detector, the detector finds the
MIMO detection method. To achieve higher throughput, spatial-division multiplexing (SDM) technique can be used. With SDM, multiple transmit antennas transmit independent data streams, which can be individually recovered at receiver. An applicable method is required to separate each transmitted stream form other transmitted streams (interference cancellation). Many approaches are known for the detection of SDM signals. For instance, zero-forcing (ZF), minimum mean square error (MMSE), and maximum likelihood (ML) detectors estimate the transmitted signals with the estimated channel state information. In general, ML detector provides improved performance over ZF, MMSE detectors. However, the computation complexity of performing a full search for ML detection is too high to be suitable for practical applications. To reduce the complexity, sphere decoding technique or K-best algorithm can be applied to the ML detector. In ZF detector, the detector finds the