Chapter 5 Adaptive Channel Estimation 105
5.5 Architecture and Implementation
5.5.2 Implementation Results
In the MATLAB platform, an overall system (transmitter, inner and outer receiver) is constructed to evaluate the performance. In this chip, the Viterbi decoder is not implemented (limited by chip area). For rapid verification, a 2 2× software-defined radio (SDR), as displayed in Figure 5-13, is constructed. TABLE 5-2 lists the experimental parameters in the software-defined radio. The carrier frequency of each transmit antenna is 2.4 GHz. At the transmitter part, the transmitted data are produced by the MATLAB module and then these data are stored in memory. The proposed method is mapped onto the field programmable gate array (FPGA) chips (Xilinx Virtex-II) with on-board 14-bit digital-to-analog converters (DACs). The signals are then transmitted using an in-house RF front-end. Because it is essential to make MIMO transmissions coherent at all DACs and antennas, there is an additional DAC module as a hardware trigger of TX, namely “Sync” in Figure 5-13, to control four DACs coherently. After down-converting the RF signals to baseband at the receiver, analog signals are fed into 14-bit analog-to-digital converters (ADCs). The proposed algorithm then processes the down-converted signals. The hardware-description language (HDL) can be generated as soon as the architecture with a fixed-point evaluation has been created. After performance assessment and HDL validation, the 4 4× MIMO-OFDM modem (Figure 5-1) is implemented by Taiwan Semiconductor Manufacturing Company (TSMC) 0.13-μm one-poly eight-metal layer (1P8M) CMOS library. TABLE 5-3 presents the synthesized results. Based on synthesis, automatic place and route (APR) can be carried out by SOC encounter (Cadence). Layout versus schematic (LVS) and design rule checking (DRC) must be performed to assess the APR result. Finally, post-layout simulations are performed to verify the clocking, timing, and power of the proposed design. The proposed design passes the SS model (supply voltage:
1.08V) and temperature 125DC corner simulation. The received data from SDR platform is applied to the chip testing, which is performed to verify the full functionality of the chip using Agilent 93000 SOC Test System. The modem area is 4.1 4.1× mm , 2 and the area of the proposed FD-CE is 3 3.1× mm (Figure 5-14). The memory 2 requirement for the proposed FD-CE is 50 K bits. Since one adaptive procedure requires 24.6 μs to measure 4 OFDM symbols (208 carriers), the efficient throughput is 50 Mbps with a 64-QAM modulation at 20 MHz. If we use all carriers ( 64 4× =256) of four OFDM symbols to compute the data rate, the data rate is 62.4 Mbps. The chip area with I/O pads and a power ring is 4.6 4.6× mm . At 1.2V supply voltage, the power 2 consumption is about 62.8 mW. TABLE 5-4 lists chip summary of the 4 4× MIMO-OFDM modem.
Figure 5-13. Software-defined radio platform.
TABLE 5-2. Experimental Parameters.
Parameters Value RF carrier frequency 2.4 GHz
RF power level －40 dBm
ADC/DAC resolution 14 bits
(I)FFT 64 points
TABLE 5-3. Synthesized Results (Gate Count).
# of RX Module Gates Channel estimation 10,976
Matrix inverter (MI) 142,412 Matrix multiplier (MM) 105,224
De-mapper 1,206 Others (control unit & buffers) 214,482
1 RX
Total 474,300
4 RX Total 1,901,644
TABLE 5-4. Chip Summary of The 4 4× MIMO-OFDM Modem.
System 4 4× MIMO OFDM with STBC Modulation BPSK, QPSK, 16QAM, 64QAM Technology 0.13-μm 1P8M CMOS
Package 160 CQFP
4.6 mm
Figure 5-14. Chip microphotograph of the 4 4× MIMO-OFDM modem.
5.6 Summary
This chapter presents an adaptive FD-CE that measures channel variations and prevents performance loss in time-varying frequency-selective fading. Without both specific formats and scattered pilots, all data carriers can be utilized to ensure accurate estimation of channel variations, namely, virtual pilots. Moreover, the proposed FD-CE utilizes the property of the Alamouti-like matrix to decrease the implementation costs of complex operators. Performance evaluations indicate that the proposed FD-CE can
be widely applied in time-varying environments. Consequently, the 4 4× MIMO-OFDM modem implemented using an in-house 0.13-μm 1P8M CMOS library occupies an area of 4.6 4.6× mm and consumes about 62.8 mW at 1.2V supply 2 voltage.
Chapter 6
Digital Beamforming
This chapter presents the digital beamforming for wireless communication systems. In communications, beamforming is used to point an antenna at the signal source to reduce interference and improve signal quality. Digital beamforming is a marriage between antenna and digital technology. In digital beamforming, the operations of phase shifting and amplitude scaling for each antenna element, and summation for receiving, are performed digitally to form the desired output. The process of digital beamforming is carried out by a digital signal processor. It is the digital signal processing capability which makes the system smart.
The rest of this chapter is organized as follows. Section 6.1 introduces the basics of digital beamforming. Section 6.2 then describes the angle-of-arrival estimation. Next, adaptive beamforming technology is presented in Section 6.3. Section 6.4 describes the digital beamforming in multiple-input multiple-output (MIMO) transmissions.
Conclusions are finally drawn in Section 6.5.
6.1 The Basics of Digital Beamforming
A generic digital beamforming system is shown in Figure 6-1. This beamforming system consists of three major components: the antenna array, the beamforming unit, and the signal processing unit [77]-[78]. At the receiver part, the system consists of down-conversion chains and analog-to-digital conversion. Based on the received signal, the signal processing unit calculates the complex weights which the received signal from each antenna is multiplied with. These complex weights are adjusted until the array output matches the desired signal. These weights can also determine the array factor.
Transmit Beamformer Receive
Beamformer
Smart Algorithm
Signal Modulator Signal
Demodulator
Baseband Processing
Antenna Array
Figure 6-1. A generic digital beamforming system.
In antenna field, the principle of pattern multiplication states that the radiation pattern of an array is the product of the element pattern and the array factor. In this work, we focus on the determination of the array factor. Digital beamforming is driven by digital
processing to produce different types of beams. The procedure used for modifying the beam pattern to enhance the reception of a desired signal is illustrated by the following example. Figure 6-2 shows a two-element array for interference suppression. The most fundamental and simplest array to analyze is the two-element array. In this example, we consider a uniform linear array consisting of two identical omnidirectional antenna with λ/2 spacing, where λ denotes the wavelength corresponding to the carrier frequency.
π/ 6 ( ) j2ft
S t =Ae π ( ) j2ft
I t =Ne π
w1
w2
y
1 2
Figure 6-2. Two-element array for interference suppression.
The desired signal, S t , arrives from the boresight direction, and the interference ( ) signal, I t , arrives from the angle / 6( ) π radians. The signal from each antenna is multiplied by a complex weight, and the weighted signals are summed to form the array output. The criterion which is applied to enhancing the desired signal and minimizing the interference signal is based on maximizing the signal-to-interference ratio (SIR) [78]-[79]. The array output due to the desired signal is
2
1 2
( ) j ft( )
y tS =Ae π w +w (6.1)
For ( )y tS to be equal to ( )S t , it is necessary that
The interference signal arrives at antenna 2 with a phase lead with respect to antenna 1 of value /2π . The array output due to the interference signal is
For the interference to be zero, it is necessary that
1 2
From (6.2) and (6.4), the necessary weights can be calculated to be
1
Figure 6-3(a) shows the array factor for a two-element antenna array without any weighting in the pattern forming network. Figure 6-3(b) shows the array factor for a two-element antenna array when the weights of (6.5) are applied in the pattern forming network. It is clear that now a null is placed exactly at an azimuth of 30D, the direction of the interference signal. In fact, one can change the weighting vector to point the
beam in any wanted direction. Therefore, the flexibility of digital beamforming allows the implementation of adaptive beamforming.
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Figure 6-3. (a) Array factor for a non-weighted two-element array. (b) Array factor for a weighted two-element array.
6.2 Angle-of-Arrival Estimation
If several transmitters are operating simultaneously, each transmitter can create many multipath components at the receiver. Therefore, it is important for a receive array to be able to estimate the angles of arrival in order to resolve which emitters are present and what are their possible angular locations. This information can be used to eliminate or combine signals. Angle-of-arrival (AOA) estimation is also known as spectral estimation, direction-of-arrival (DOA) estimation. The goal of AOA estimation techniques is to define a function that gives an indication of the angles of arrival. This function is traditionally called the pseudospectrum. There are several approaches to defining the pseudospectrum via beamforming, the array correlation matrix, eigenanalysis, linear prediction, minimum variance, maximum likelihood, minimum-norm, and MUSIC [80]-[84]. In this section, we will discuss Capon and MUSIC pseudospectrum solutions.
θ1 w1
Figure 6-4. M-element array with arriving signals.
Many of the AOA algorithms rely on the array correlation matrix [78]. Figure 6-4 shows D signals arriving from D directions. These signals are received by an M-element array with M complex weights. Time is represented by the kth time sample. Each received signal includes AWGN. Let ( )a θ denote the array vector for an M-element linear array
where d denotes the element spacing. The vector ( )a θ is a Vandermonde vector because it is in the form [1 z ... zM−1]T. Thus, the array output y is given in the
where the superscript H denotes Hermitian matrix operation and
1 2
Thus, the array correlation matrix R is xx
E
The array correlation matrix Rxx and the source correlation matrix R are ss calculated by the expected value of the respective absolute values squared.
6.2.1 Capon AOA Estimate
The Capon AOA estimate is also known as the minimum variance distortionless response. The Capon AOA estimate is a maximum likelihood estimate of the power arriving from one direction while all other sources are considered as interference. In this method, the array output power is minimized with the constraint that the gain in the desired direction ( )a θ remains unity. This constrained quadratic problem can be expressed as
min H xx subject to H ( )θ =1
w w R w w a (6.11)
Solving this constraint optimization problem, the array weights are given by [81]
1
Substituting the weights of (6.12) into the array of Figure 6-4, the pseudospectrum is then given by
The estimate of the desired direction of arrival is the angle θ that corresponds to the peak value in the pseudospectrum.
5D
Figure 6-5. M-element array with two arriving signals.
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Figure 6-6. Capon pseudospectrum.
Figure 6-5 shows an M-element array with / 2λ element spacing. The signals are assumed to be uncorrelated and equal amplitude. The arrival angles are ±5D and the AWGN variance is 0.1. From the information, the following parameters are obtained [78] we can plot the pseudospectrum as shown in Figure 6-6. It is clear that the two sources are not resolvable if a two-element antenna array is used. However, the Capon AOA
estimate can resolve these two sources if a six-element antenna array is used. The reason is that the ability to resolve angles is limited by the array half-power beamwidth. In order to increase the resolution, a larger array is thus required.
6.2.2 MUSIC AOA Estimate
MUSIC is an acronym which stands for multiple signal classification. The MUSIC algorithm was developed by Schmidt [85] by noting that the desired signal array response is orthogonal to the noise subspace. The signal and noise subspaces are first identified using decomposition of the array correlation matrix. The eigenvalues and eigenvectors of R can be calculated. We then produce D signal eigenvectors and xx (M −D) noise eigenvectors. The eigenvalues and eigenvectors are sorted from the least to the greatest. The M×(M −D) dimensional subspace spanned by the noise eigenvectors is then given by
1 2 ...
N = ⎢⎡⎣ M D− ⎤⎥⎦
E e e e (6.15)
Once the subspaces are determined, the MUSIC pseudospectrum is given by [85]
( ) ( )
( ) ( ) ( )
H
MUSIC H H
N N
P θ θ θ
θ θ
= a a
a E E a (6.16)
Because the desired array response vectors A are orthogonal to the noise subspace, the peaks in the MUSIC spatial spectrum represent the AOA estimates for the desired signals. One can show that the Euclidean distance aH( )θ E E aN HN ( )θ =0 for each arrival
angle. Placing this distance expression in the denominator creates sharp peaks at the angles of arrival.
Assume that there is a 6-element antenna array with λ/2 element spacing. The signals are assumed to be uncorrelated and equal amplitude. The arrival angles are
±5D and the AWGN variance is 0.1. From the information, the following parameters are obtained [78]
1 2 3 4
The subspace created by four noise eigenvectors is given by
0.017 0.66 0.076 0.092 0.33 0.47 0.29 0.53 0.032 0.24 0.82 0.19 0.14 0.23 0.48 0.69 0.68 0.2 0.055 0.45 0.64 0.42 0.03 0.041
N
Applying this information to (6.16), we can plot the pseudospectrum as shown in Figure 6-7. From Figure 6-7, it is clear that MUSIC AOA estimate has better resolution than Capon AOA estimate. The price of increased resolution comes at the cost of greater computational complexity.
-30 -20 -10 0 10 20 30 -30
-25 -20 -15 -10 -5 0 5 10
Angle
|P(θ)|
Figure 6-7. MUSIC pseudospectrum.
6.3 Array Factor Calculation
In previous sections, the fixed weight beamforming is presented. The fixed beamforming approaches are applied to fixed arrival angle emitters. If the arrival angles don’t change with time, the optimum array weights won’t need to be adjusted. However, in mobile wireless communications, the desired arrival angles can change with time. The receiver must allow for the continuous adaptation to an ever-changing environment.
θ1
Figure 6-8. Five-element antenna array.
Let assume a five-element antenna array with one desired signal and two unwanted interferences, as shown in Figure 6-8. The element spacing is /2λ . The array vector is given by
2 sin sin sin 2 sin
( )θ = ⎢⎡⎣e−j π θ e−jπ θ 1 ejπ θ ej π θ⎤⎥⎦T
a (6.19)
Therefore, the total array output is given as
1 1 1 1
In matrix form, (6.20) can be written as
1 2
For the interference to be zero, it is necessary that
1
Therefore the required complex weight is [86]-[87]
1 ( ) 1
H = ⋅ H H +η −
w u A AA I (6.23)
where I denotes the identity matrix and η is a particular number. If the matrix inversion is singular, the particular number can be used to calculate a approximate solution. As an example, the desired signal is arriving from θ =D 0D while θ = −1 15D and θ =2 25D. If the particular number is 0.001, the necessary weights are calculated to be
If the desired signal is arriving from θ =D 30D while θ = −1 35D and θ =2 60D, the necessary weights are calculated to be
0.19
The corresponding array factor is plotted in Figure 6-9. In order to make it better, a possible scheme is to make the choices of the weighting vectors adaptive. In adaptive processing, there are many existing adaptive algorithms, such as least mean-square algorithm, recursive least-square algorithm, etc. Different adaptive algorithms result in different convergence speed and computational complexity [88].
In previous discussion, we have showed that how to calculate the complex weight, w . However, the computational complexity could be very high if the number of i
antennas is increased. In fact, there are some simple weight functions. A two-element uniform linear array and a four-element uniform linear array with /2λ element spacing are considered as examples. The weight vectors for the two-element uniform linear array and the four-element uniform liner array are shown in TABLE 6-1 and TABLE 6-2, respectively. The corresponding array factors are shown in Figure 6-10 and Figure 6-11, respectively. Note that the plots have been normalized so that the peak of the radiation pattern is equal to one.
-80 -60 -40 -20 0 20 40 60 80
TABLE 6-1. Weight Vectors for the Two-Element Array.
TABLE 6-2. Weight Vectors for the Four-Element Array.
Antenna No.
Figure 6-10. Corresponding array factors. (a) Weight vector = [+1+1]. (b) Weight vector = [+1− ]. 1
0.5
From TABLE 6-1, the case 1 gives uniform weighting to the array. The resulting pattern is shown in Figure 6-10(a). Other cases for the two-element uniform linear array and the four-element uniform linear array are shown in Figure 6-10 and Figure 6-11, respectively. In order to reduce the computational complexity, the simple weight functions could be applied in some conditions. Sidelobes could be controlled to some
extent by employing weight functions. These weight functions are observed in terms of mainlobe beamwidth, mainlobe angle, and sidelobe level.
6.4 Digital Beamforming in MIMO Transmission
In previous section, we have assumed that there is only one signal of interest. It has been shown that the signals from each antenna element are multiplied by a complex weight and summed to form the array output. In fact, there are more than one signals of interest in MIMO WLAN. In addition, the channel status in MIMO WLAM is complex. Under this condition, it is difficult to find a unique weight vector to form the desired output. transmitter transmits a different data stream. At the receiver part, the received signal is expressed as
1 11 1 12 2
where “ ⊗” denotes the convolution operator. From (6.26), it is difficult to find an
optimum weighting function to attain the desired output s t1( ) and s t 2( ) simultaneously. In practical applications, the channel status can also change with time.
Figure 6-13 shows the channel with angle-time pattern. Form Figure 6-13, the channel pattern could be time-varying and the arrival time of desired signals may also be different. In order to overcome this situation, a potential solution is to augment the simple linear combiner with space-time architecture shown in Figure 6-14. In Figure 6-14, each receiver antenna’s output is applied to a finite impulse filter. The filter outputs are summed to produce the desired signal. If there is no temporal filter, the space-time beamforming architecture is reduced to the linear combiner architecture.
The filter bank-based beamforming can accept the outputs of N antenna elements and coherently combine them to a desired output. In addition, the weighting functions could null out the undesired signals impinging on the array and it could equalize the effects of propagation on the received signals. In practice, however, such joint reduction is limited by the presence of noise and the lack of perfect synchronization.
Figure 6-13. Channel with angle-time pattern.
1( )
r t r ti( ) r tN( )
( ) y t
Figure 6-14. Space-time beamforming architecture.
6.5 Summary
This chapter presents the digital beamforming technology in wireless communication systems. Digital beamforming technology has numerous benefits in wireless communications. In wireless communications, digital beamforming can improve the signal-to-noise ratio and provide higher system capacity. Digital beamforming can be interpreted as linear filtering in the spatial domain. In mobile communications, digital beamforming technology has the potential for tracking the location of a particular mobile user. In addition, digital beamforming technology can also null multipath signals.
This can dramatically reduce fading in the received signal.
Chapter 7 Conclusion
The research on multi-input multi-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems is presented in this dissertation. We investigate the carrier frequency offset (CFO) estimation, I/Q mismatch (IQ-M) estimation, adaptive channel estimation, and digital beamforming.
7.1 Summary
In this work, a MIMO-OFDM communication system is implemented. For the frequency synchronization in the MIMO-OFDM system, a pseudo CFO (P-CFO) algorithm is developed to estimate the CFO value under the condition of IQ-M in direct-conversion OFDM receivers. The proposed synchronization algorithm is suitable for application-specific integrated circuit (ASIC) implementation. The proposed algorithm adopts three short training symbols to estimate the frequency offset from
4 4×
− ppm to 50 ppm under a 2.4 GHz carrier frequency with 2 dB gain error and 20 degree phase error in frequency-selective channels. Simulation results indicate that the average estimation error of the proposed P-CFO algorithm can fulfill many system requirements, preventing obvious performance loss under different IQ-M conditions.
The proposed design is implemented in a chip with +50
3.3 0.4 mm× 2 core area and 10 mW power dissipation at 54 Mbits/s data rate. Hence, the proposed algorithm can enhance the performance of wireless OFDM systems, enabling low-cost systems to be achieved.
Direct-conversion architecture is one potential candidate for simple integration among different architectures. However, direct-conversion receivers suffer from mismatch between the I and Q channels, e.g., IQ-M. In order to combat IQ-M with CFO in direct-conversion receivers, preamble-assisted methods are developed. IQ-M with CFO can be estimated by taking advantage of the relationship between desired sub-carriers and image sub-carriers. Moreover, the proposed IQ-M estimator can estimate not only constant IQ-M but also frequency-dependent IQ-M. 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, the proposed method is compatible with current wireless standards
Furthermore, the proposed method is compatible with current wireless standards