Summary

In this chapter, the proposed STBC-OFDM system is presented, and the system specification and design targets are also discussed. A simple symbol boundary detection scheme, a carrier frequency recovery loop modified by the ping-pong algorithm and an accurate two-stage DFT-based channel estimation method are included in the proposed receiver. From the system simulation results, we have shown that the CFO detection modified by the ping-pong algorithm can effectively maintain the ICFO error probability of about 10^-3 in the weak region. The detail descriptions and simulation results of the proposed two-stage channel estimation will be given in Chapter 4. The performance of the proposed receiver meets the requirements of WMAN in an AWGN environment. Moreover, at υe of 120 km/hr, the coded BER of the proposed receiver for both QPSK and 16QAM modulations can be less than 10^-6. The simulation results show that the proposed STBC-OFDM system can meet our design targets and used for WMAN systems in fixed and mobile environments.

Chapter 4

A Robust Channel Estimator for STBC-OFDM Systems

4.1 Introduction

With multiple transmit antennas, STBC can provide transmit diversity gain to improve system performance in wireless communications. However, for STBC decoding, STBC-OFDM systems require accurate CSI, which is particularly difficult to obtain in mobile wireless channels. Therefore, high quality channel estimation with acceptable hardware complexity is a crucial challenge for realizing a successful STBC-OFDM system.

Blind channel estimation method has an advantage of bandwidth-saving since it estimate channel response merely depending on the received signals. However, it must record numerous data symbols to obtain reliable channel estimation, involves high computational complexity, and only applies to slowly time-varying channels. On the contrary, pilot-aided channel estimation method using known pilots can provide more precise estimation for applications in mobile wireless communication.

Various pilot-aided channel estimation methods have been proposed for OFDM systems. Among these methods, DFT-based channel estimation methods using either minimum mean square error (MMSE) criterion or maximum likelihood (ML) criterion have been studied for OFDM systems with preamble symbols [33]-[35], [51], [52].

Since no information on channel statistics or operating SNR is required in the ML

scheme, the ML scheme is simpler to implement than the MMSE scheme [33]-[35], [51]. Furthermore, when the number of pilots is sufficient, the two schemes have comparable performances [34]. For this reason, the DF DFT-based channel estimation method is adopted to use the decided data as pilots to track channel variations for providing sufficient tracking information. Recently, Ku and Huang [19], [31]

presented a DF DFT-based method derived from ML criterion and Newton’s method.

Moreover, they concluded that a refined two-stage channel estimation method [31] is more robust than the classical DF DFT-based method to apply in fast time-varying channels. Thus, the two-stage channel estimation method with an initialization stage and a tracking stage is adopted in this paper. Nevertheless, the two-stage channel estimation method has high computational complexity and is difficult to realize in hardware directly; hence, a novel architecture and an implementation method shall be proposed to reduce the implementation complexity.

In this chapter, a robust channel estimator for STBC-OFDM systems is proposed and applied in IEEE 802.16e baseband receiver. As compared with interpolation-based channel estimation methods which are commonly adopted in the pilot-aided channel estimator designs [53], [54], [65], and [66], our proposed channel estimator has significant performance improvements, especially when it is applied in outdoor mobile channels. This chapter is organized as follows. Section 4.2 introduces pilot-aided channel estimation methods. Section 4.3 briefly reviews the two-stage channel estimation method. Section 4.4 presents the proposed channel estimator. Then, the computational complexity of different channel estimation methods are given in Section 4.5. The simulation results are provided in Section 4.6. Finally, the conclusions of this chapter are drawn in Section 4.7.

Notation: By convention, boldface letters are used for sets, vectors, and matrices.

The superscript (.)^* stands for complex conjugate. The notation sign(.) takes the sign of (.). The notations Re(.) and Im(.) stand for the real part and the imaginary part of (.).

The notation {…} denotes the contain elements of a set or a vector.

4.2 Pilot-aided Channel Estimation Methods

Pilot assisted channel estimation provides promising performance since it inserts known pilots periodically both in the time and frequency axes to track the time variations and frequency selectivity of the channel. Two types of pilot patterns, block type and comb type are widely adopted in various standards or literatures [55]-[59], while other two-dimension pilot patterns are discussed in [60], [61]. Comb-type pilot patterns and the time- and frequency-domain scattered pilot patterns usually perform better than the block-type pilot patterns in fast fading channels. Since block-type pilot patterns use all the subcarriers of one OFDM symbol as pilots, the insertion interval of the OFDM pilot symbols must be much less than the coherent time. Therefore, block-type pilot patterns are only suitable for slow fading channels. In order to apply in wireless mobile environments, we focus on comb-type pilot-aided channel estimation methods. Various comb-type pilot-aided channel estimation methods have been proposed for OFDM systems. Among these methods, there are two major categories of (a) interpolation-based channel estimation method and (b) DFT-based channel estimation method. These two kinds of comb-type pilot-aided channel estimation methods are briefly introduced in the following subsections.

4.2.1 Interpolation-based Channel Estimation

The channel complex gains at pilot subcarriers can be easily obtained from the received signals and known pilots, and the interpolation-based channel estimation methods are then applied to estimate the channel frequency responses at data subcarriers. Interpolation-based channel estimation methods cooperating with different pilot patterns have been extensively studied in the literatures [53], [54], [65], [66]. For the comb-type pilot-aided OFDM system, the NPilot pilot subcarriers XP[m], m=0,…,NPilot-1, are uniformly inserted into an OFDM symbol X[k], k=0,…,N-1, where N is the total subcarrier number. The interval of pilot subcarriers is L=N/NPilot, where L is an integer. In the following, we will introduce several conventional polynomial interpolation-based channel estimation methods.

At the data subcarrier k, mL ≤ k < (m+1)L, the estimated channel response M[k]

using a piecewise linear interpolation method is given by [53]

[ ] [ ]

where MP[m], m=0,…,NPilot-1, is the estimated channel response at pilot subcarriers.

The estimated channel responses using higher-order interpolation methods may have more accurate fitting than that using the linear interpolation method. However, the computational complexity also grows as the order increases. A piecewise second-order interpolation method adopted in [62] is expressed as

[ ] [ ]

The coefficients of the cubic interpolation method adopted in [65] is given by

[ ] [ ]

Since OFDM signal is a two-dimensional function of time and frequency, pilots can be scattered in both time and/or frequency axes of an OFDM frame. Therefore, the channel frequency responses at data subcarriers can be performed by two-dimensional (2-D) interpolation-based channel estimation methods which are widely used to further improve the estimation performance. The 2-D interpolation-based channel estimation can be performed by cascading two one-dimensional interpolation-based channel estimations. Nevertheless, the conventional 2-D interpolation-based methods need huge amount of storage for implementation of the non-causal property in the time-domain interpolation. Lin and Lee [54] have effectively presented 3 kinds of the predictive algorithms to save the storage requirement in time-domain interpolation.

The interpolation-based channel estimation methods are often used in the condition that the frequency-domain channel response is oversampled by the pilot subcarriers. The number of pilot subcarriers must be larger than the normalized maximum excess delay [66]. If the normalized maximum excess delay is close to the number of pilot subcarriers, then the performance of interpolated channel response is seriously degraded. Hence, based on the limited pilot subcarriers, using the interpolation-based methods to estimate channel responses is a challenge in outdoor mobile channels. Because the coherent bandwidth becomes small, the interpolation-based method becomes more difficult to recover channel variations.

4.2.2 DFT-based Channel Estimation

The DFT-based channel estimation method obtains the time-domain CIR by inverse DFT (IDFT) transforming the frequency-domain channel response at pilot subcarriers and effectively improves the performance by suppressing time-domain noise and aliasing effect. Many DFT-based methods derived from ML scheme have been studied for OFDM systems with preambles [33]-[35], [51], [52]. In order to further improve the estimated performance, the DF DFT-based channel estimation methods employ decided data subcarriers as pilot subcarriers to track channel variations for saving transmission bandwidth and providing sufficient tracking information [33], [35], [51].

A classical DF DFT-based channel estimation method can be decomposed to

four parts which include an least square (LS) estimator, an IDFT matrix, a weighting matrix, and a DFT matrix as shown in Fig. 4.1 [33]-[35], [52]. The LS estimator uses the decision data symbols and pilots to calculate the LS estimates which are the contaminated channel frequency response. After the IDFT processing, the LS estimates are transformed to time domain, and a weighting matrix is used to reduce noise and aliasing effect in time domain. Some of the weighting methods are to directly cut off the path gains of CIR below a threshold or keep only significant paths of the CIR. Other methods are to give the weighting of each path of CIR, and the weighting matrix can be derived form the ML or MMSE criterion [33], [52]. Finally, the weighted CIR is transformed back to frequency domain by DFT processing.

Based on the architectures of the transmitter and receiver in the proposed the STBC-OFDM system, the channel frequency response between the first / second transmit antenna and the receive antenna is denoted as H⁽¹⁾[k] / H⁽²⁾[k], respectively.

Within a time slot (two OFDM symbols), after the received signals have passed through the guard interval removal and the N-point FFT, the two successive received OFDM symbols, R[1,k] and R[2,k], are given by

(1) (2)

[1, ] [ ] _F[ ] [ ] _S[ ] [1, ]

R k =H k X k +H k X k +Z k (4.6)

( )^* ( )^*

(1) (2)

[2, ] [ ] _S[ ] [ ] _F[ ] [2, ]

R k = -H k X k +H k X k +Z k (4.7) Fig. 4.1 Block diagram of a classic DF DFT-based channel estimation method.

for kÎ ÈQ J , where Q and J denote the sets of data and pilot subcarrier indices, respectively, XF[k] and XS[k] are two transmitted OFDM symbols within a time slot, and Z[1,k] and Z[2,k] are the uncorrelated additive white Gaussian noise (AWGN) antenna, and Θ is a subset of Q used to track channel variations. Moreover, at the k-th subcarrier, the ^Xˆn

[ ]

^{k =}

{

^{Xˆn( )i}

[ ]

^{t k, : t=0,1}

}

is the re-encoded STBC matrix with decision symbols

{

^{X kˆF}

[ ]

^{, X kˆS}

[ ] }

as its elements obtained by applying the previously estimated channel frequency response to decode the received signal.

[ ]

^{k =}

{

^{R t k}

[ ]

^{, : t=0,1}

}

the energy normalized factor. Then, the LS estimate is improved by using a truncated DFT matrix F_DFT^{( )i} as follows:

frequency response vector. The truncated DFT matrix F_DFT^{( )i} is given by

In the DFT-based channel estimation methods, most mobile wireless channels are characterized by CIR consisting of a few dominant paths. These path delays usually change slowly in time, but the path gains may vary relatively fast. In this section, the refined two-stage channel estimation method [31] will be briefly reviewed.

An initialization stage uses a MPIC-based decorrelation method to identify the significant paths of CIR in the beginning of each frame. However, the CIR estimated by the preamble can not be directly applied in the following data bursts since the receiver is mobile. Thus, a tracking stage is then used to track the path gains with known CIR positions. The details are described in following subsections.

4.3.1 Initialization Stage

The preamble, which is the known sequence, is the first symbol of each downlink transmission frame. The significant paths can be estimated by matching the preamble;

however, the preamble does not have ideal auto-correlation due to the use of either guard band or non-equally spaced pilots in most wireless standards. The MPIC-based decorrelation is used to estimate CIR path-by-path and cancel out the known multipath interference. The flowchart of the MPIC-based decorrelation is shown in Fig. 4.2. The channel estimation for each transceiver antenna pair can be

independently performed because the preambles transmitted from different antennas do not interfere with each other. First, two parameters NP and WB are defined as a presumptive path number of a channel and an observation window set, respectively.

Second, the cyclic cross-correlation CRP[τ] between the received and transmitted preambles as well as the normalized cyclic auto-correlation CPP[τ] of the transmitted preamble are calculated. The indices l and κ which stand for a path counting variable and the number of the legal paths found by the MPIC-based decorrelation are initialized to zero. Third, the process is started by picking only one path whose time

Fig. 4.2 Flowchart of MPIC-based decorrelation method.

delay τl yields the largest value in CRP[τl], for τlÎWB. If the path delay τl is larger than the length of CP, this path is treated as an illegal path and discarded by setting CRP[τl]=0. Otherwise, this path is recorded as the κ-th legal path with a time delay τκ=τl and a complex path gain μκ=CRP[τl]. Then, the interference associated with this legal path is canceled from CRP[τ] to obtain a refined cross-correlation function:

0 1

[ ] [ ] [ ], \{ ,..., }.

RP RP PP B l

C t =C t -m_kC t t- _k tÎ W t t _- (4.13)

Meanwhile, κ is increased by one. The value of l is also increased by one at the end of each iteration, and the iterative process is continued until l reaches the presumed value of NP.

4.3.2 Tracking Stage

After the initialization stage, we can obtain the information of the path numbers κ⁽ⁱ⁾, the multipath delays τl(i), the multipath complex gains μl(i), for lÎ{0,…, κ⁽ⁱ⁾-1}, and the corresponding channel frequency responses. Under the assumption that the multipath delays do not change over the duration of a frame, the DF DFT-based channel estimation method can be equivalently expressed in Newton’s method as [36]: difference between the previous estimated channel frequency response vector

( ) applying the previous estimated channel frequency responses to decode the received signal vector R[k]={R[t,k]: t=1,2}, where t is the symbol index within a time slot. The value C kˆ_n[ ] |= X kˆ_F[ ] |² +|X kˆ_S[ ] |² is the energy normalization factor. The IDFT

In the previous studies [33], [35], the pilots as well as the decided data symbols are simultaneously adopted to perform channel estimation at each tracking iteration.

From the viewpoint of optimization, since the pilots inserted in each OFDM symbol are much more reliable than the decided data symbols, they should play a dominant role in providing a global search direction at the first tracking iteration [31]. Thus, the first iteration of the channel tracking is modified as

( ) ( ) ( ) ( ) pilot subcarrier set J instead of the set Θ, and the value γ is an experimental constant of step size to have the best performance.

It is demonstrated in [31] that the two-stage channel estimation method has better performance than the classical DF DFT-based method, the STBC-based MMSE

method, and the Kalman filtering method for estimating channels in mobile environments, and its computational complexity is quite the same with these methods.

However, the high complexity problem still needs to be solved for hardware implementation. Hence, we propose a modified two-stage channel estimation method and its architecture for implementation.

4.4 Proposed Channel Estimator

The overall block diagram of the proposed channel estimator is shown in Fig. 4.3.

The initialization stage is decomposed to a preamble match, an IFFT, a straight MPIC (SMPIC)-based decorrelator, and an FFT. The tracking stage is decomposed to an STBC decoder, a demapper, an LS estimator, an IFFT, a path decorrelator, a Hessian matrix calculator and an FFT. Moreover, the IFFT and FFT are shared between the initialization stage and the tracking stage. These key blocks are described in the following subsections.

Fig. 4.3 Overall block diagram of the proposed channel estimator.

4.4.1 Initialization Stage: Preamble Match

In the initialization stage, the preamble match is first used to estimate the preliminary channel frequency responses M⁽ⁱ⁾[k] for i= 1,2 by matching the received signal with the preamble symbol P⁽ⁱ⁾[k] transmitted from the i-th antenna. Since the preambles transmitted from different antennas do not interfere with each other, M⁽ⁱ⁾[k]

can be independently performed by

where R[k] in the initialization stage is the first received OFDM symbol of a frame, and Z[k] is AWGN. Consequently, the preliminary channel frequency responses M⁽ⁱ⁾[k]

pass through IFFT to obtain the channel impulse responses.

4.4.2 Initialization Stage:

SMPIC-based Decorrelator

After IFFT operation, the CSIs are obtained in time domain m⁽ⁱ⁾[τ]. The MPIC-based decorrelation method estimates CIR path-by-path. It picks the maximum path of m⁽ⁱ⁾[τ] for τÎWB and cancels the maximum path interference to other paths. If the set WB has NB paths, the process must iterate NP times for finding the maximum path of these NB paths and canceling the maximum path interference to other (NB-1) paths. This method requires too many execution cycles and is unsuitable to directly implement in the proposed channel estimator.

In order to reduce the execution cycles, we propose an SMPIC-based decorrelation method to identify NP significant paths in a straightforward method, and the flowchart is shown in Fig. 4.4. First, the proposed scheme sorts the NB paths to find the first NTP paths with large m⁽ⁱ⁾[τ]. Second, the decorrelation is carried out from

the largest to the smallest one of these NTP sorted paths to cancel the path interference.

The decorrelation process starts at the first legal path which is the maximum sorted path. If κ denotes the iteration number, for 0 ≤ κ < NTP-1, the process of the κ-th sorted path delay, and CPP[τ] is the normalized cyclic auto-correlation of the preamble.

Finally, the decorrelated NTP paths are sorted again to pick up the first NP paths. For using a sorting network of fixed I/O size NP to sort an arbitrarily larger data set, the number of NTP is defined to be β·NP, and β is an integer which is searched to optimize the computational complexity and guarantee the acceptable performance. Here, the

r r k r k

Fig. 4.4 Flowchart of the proposed SMPIC-based decorrelation.

output SNR at the STBC decoder is used as a gauge of the system performance to determine the value of β and defined as

1 1 complexity of the original MPIC-based decorrelation method requires O(NPNBlog2NB) comparisons, O(NPNB) complex multiplications and O(NPNB) complex subtractions because it must repeat NP times of sorting and decorrelation of NB paths. However, the complexity of the SMPIC-based decorrelation method only requires O(NBlog2NB) comparisons, O(NTP2) complex multiplications and O(NTP2) complex subtractions.

Thus, the requirement of execution cycles can be effectively reduced by about O(NP) times.

After the SMPIC-based decorrelator, the significant paths have been identified and are then transformed to channel frequency responses by FFT for using as the reference in the tracking stage.

4.4.3 Tracking Stage: STBC Decoder and Demapper

In the tracking stage, from (4.14), the LS estimator is used to calculate the LS

estimations followed by calculating the vector δn

[ ]

^k = D^{ n^{( )i}

[ ]

^{k i:} =^{1, 2}} that can be must be determined first. Based on the latest estimated channel frequency responses, the STBC decoder and the symbol demapper are used to decode these two received symbols and can be formulated as

limited constant set; thus, these normalizations can be merged to one multiplication of λ, and the value of λ has also a limited constant set. Therefore, the possible multiplication values of λ can be pre-computed and stored in advance, and on-line computation can be saved to reduce implementation cost. The LS estimations can be expressed as different time slot. In IEEE 802.16e, each cluster contains 14 subcarriers, and there are 60 clusters in an OFDM symbol with 1024 subcarriers. Each cluster has two pilot subcarriers, and the pilots are modulated by BPSK. If a pilot is transmitted on one pilot subcarrier from one antenna, the other antenna will not transmit a pilot on the same subcarrier to avoid the inter-antenna interference. The dimension of J is NJ. According to this allocation, if the pilot subcarrier index is kÎ =J

{

J J0, ,...,1 J_NJ_-1

}

, the LS estimations at the first iteration can be expressed as follows:

limited constant set; thus, these normalizations can be merged to one multiplication of λ, and the value of λ has also a limited constant set. Therefore, the possible multiplication values of λ can be pre-computed and stored in advance, and on-line computation can be saved to reduce implementation cost. The LS estimations can be expressed as different time slot. In IEEE 802.16e, each cluster contains 14 subcarriers, and there are 60 clusters in an OFDM symbol with 1024 subcarriers. Each cluster has two pilot subcarriers, and the pilots are modulated by BPSK. If a pilot is transmitted on one pilot subcarrier from one antenna, the other antenna will not transmit a pilot on the same subcarrier to avoid the inter-antenna interference. The dimension of J is NJ. According to this allocation, if the pilot subcarrier index is kÎ =J

{

J J0, ,...,1 J_NJ_-1

}

, the LS estimations at the first iteration can be expressed as follows:

在文檔中 適用於高速行動之無線都會區域網路之基頻接收機設計 (頁 77-0)