Chapter 3 Channel Estimation Techniques for IEEE 802.16e Downlink and
3.1 Channel Estimation Techniques for 802.16e Downlink
In this chapter, we introduce three algorithms of channel estimation for IEEE 802.16e OFDMA transmission system and evaluate the performance of each channel estimation method mainly by the bit error rate (BER) and the mean square error (MSE).
This chapter is organized as follows. In section 3.1, we present the algorithms of channel estimation. In section 3.2, we introduce our simulation environment. In section 3.3, we show floating-point simulation figures of all algorithms. In section 3.4, we show performance tables and fixed-point simulation figures which implement in DSP.
Section 3.5 is the WiMAX system integration on the DSP platform.
3.1 Channel Estimation Techniques for 802.16e Downlink
In IEEE 802.16e OFDMA-PHY downlink PUSC, the sub-carriers are divided into many clusters containing 14 adjunct sub-carriers each. Fig 3.1 depicts this cluster structure and the position of pilot sub-carriers in each cluster for even or odd symbol.
According to the pilot arrangement, we adopt three different techniques to estimate
channels and discuss in following sections.
Fig. 3.1 Cluster structure [9].
3.1.1 Channel estimation with linear interpolation (LI)
The received signal yk (with cyclic prefix removed) can be expressed as
1
wk represents the additive white Gaussian noise and N is FFT size. Taking an FFT of y , we obtain the received signal in frequency domain: k
1
When m ≠ i, Hi m, represents the effect of X onm Yi. So we can see clearly here how ICI is introduced by the time-varying channel. In the following, we just use linear interpolation techniques to estimateH . i i,
Fig. 3.2 Pilot distribution in successive clusters [9].
We ignore Hi m, (m ≠ i) in (3.3), then estimate H . This can be done by i i,
Step 1) Estimating H at pilot positioni i,
i
n, which means to obtain all the frequency responses at the black sub-carriers in each cluster shown in Fig. 3.2, could be written asˆ
, nwhere the superscript l represents the symbol index.
Step 2) Interpolating between symbols, we obtain all frequency responses at the brown sub-carriers in different clusters shown in Fig. 3.2.
The ˆ ,
n n
l
Hi i will be obtained by linear interpolation as follows:
(
1 1)
Step 3) When completing Step 2, we can regard pilot arrangement asequal-spaced distribution. In order to obtain all the frequency responses at the white sub-carriers in different clusters shown in Fig.
3.2, we do linear interpolation once again as follows
1 1 range values which are on the edge of clusters.
Step 4) This is the final step to estimate the transmitted frequency data as follows: For the above steps, we know how to use linear interpolation with pilots. If we use preamble to estimate channel frequency response, our equation is similar to (3.6) because of preamble structure (see Fig. 1.11). Simulation results are shown and discussed in the back section.
3.1.2 Channel Estimation with circular interpolation (CI)
Circular interpolation [14] is the ability to interpolate values around a circular trajectory. We treat all complex values as the form of
r × e
jθ, which r is the radius and θ is the phase in complex plane. In the section, we do linear interpolation in the radius and phase, but we get the complex values which aren’t interpolated linearly in real and imaginary part. Therefore, the algorithm which is discussed in section 3.1.1 can be employed here and repeat all steps in the phase and radius. Simulation resultsare shown and discussed in the back section.
3.1.3 Least-Square (LS) Estimator with time-domain linear interpolation
The algorithm of least-squares channel estimation mainly estimates time-varying channels. In a time-varying environment, it amounts to estimating N channelsh : [k = hk,0, ,… hk L, −1] ,0T ≤ ≤ −k N 1; in other words, we need to estimate
N×L parameters. We assume that there is not significant variation between channels
h
0 and hN-1. In order to reduce complexity, we only estimate2 L× parameters which are h0 and hN-1 channels. Interpolating between channelsh
0 and hN-1, we obtain the remaining channels by linear interpolation. Based on [10], we use P pilot tones to estimate channelsh
0 and hN-1 by least-squares method, but P must be chosen such that P≥2L. Revisiting (3.3) for a pilot tone p, then the received toneY
p would be, , ,
noise
p p p p p q q n p n
q pilot n not pilot
q p
0 1
The number am r, is the linear interpolation coefficients between channels
h
0and hN-1. For the above description, the pilot-based channel estimation can be achieved by
Step 1) Revisiting (3.9), we can express the received tone
Y
p as,
Step 2) Form the P × 2L system of linear equations
(1), (1)
Step 3) Obtain
h
as the least squares solution of the aforementioned system of linear equations (3.14).For the above steps, we know how to estimate channels with least-squares method.
Simulation results are shown and discussed in the back section.
3.1.4 ICI Cancellation by Equalization of Time-Varying Channels
For mobile applications, channel variations within an OFDM block period destroy the orthogonality between sub-carriers; the effect, known as Inter-carrier Interference (ICI), will degrade the system performance. In [11], we use a block MMSE equalizer to cancel out the ICI. The received signal Y could be expressed by
Y= ΛX + noise (3.15) where Y is the N × 1 received vector, X is the N × 1 transmitted vector, and Λ is the N
× N frequency-domain channel matrix as below
0,0 1,0 1,0
All elements of Λ channel matrix could be estimated by LS channel estimation, which had introduced in section 3.1.2. Linear block MMSE equalization could be expressed by
(
1)
1ˆX
MMSE= Λ ΛΛ +
H Hγ
−I
N −Y
(3.17) where γ is the signal-to-noise ration (SNR), IN is the N-dimension identity matrix, and the superscript H represents the conjugate and transposed matrix. The transmitted signal X could be recovered by (3.17). In fact, we are unable to estimate time-varying channel matrix accurately so that the effect of ICI cancellation is not good. Simulation results are shown and discussed in the following sections.3.1.5 Computational Complexity Analysis
Table 3.1 is the computational complexity analysis of all algorithms. Note that Nused is the number of all data sub-carriers and N is the FFT size and Np is the number of all pilots and L is the number of all channel taps. The computational complexity of phase and amplitude is calculated by CORDIC algorithms [13] and quantified by 14-bit. And the matrix inversion in (3.17) requiresO N
( )
3 flops.Table 3.1 Computational Complexity
Algorithm Complexity Comments
Linear interpolation 2×Nused multiplications