Uplink Channel Estimation and DSP Implementation
4.1 Channel Estimation Techniques
Channel estimators in OFDMA system usually need pilot information as reference. A fading channel requires constant tracking, so pilot information has to be transmitted continuously.
In general, the fading channel can be viewed as a two-dimensional (2-D) signal (time and frequency), whose values are sampled at pilot positions.
We consider three topics in this section, which are channel estimation at pilot subcar-riers, interploation schemes and time-domain improvement methods. More specifically we use the least-squares (LS) technique to estimate the channel response at pilots, use linear interpolation to estimate the frequency response at nonpilot subcarriers in the frequency
domain, and consider two ways of time-domain improvement including simple average and exponential average. These are discussed seperately in the following subsections.
4.1.1 The Least-Squares (LS) Estimator
Based on the priori known data, we can estimate the channel information on pilot carriers roughly by the least-squares (LS) estimator. An LS estimator minimizes the squared error [13]
||Y − ˆHLSX||2 (4.1)
where Y is the received signal and X is a priori known pilots, both in the frequency domain and both being N × 1 vectors where N is the FFT size. ˆHLS is an N × N matrix whose
Therefore, (4.1) can be rewritten as
[Y (m) − ˆHLS(m)X(m)]2, for all m = mi. (4.3)
Then the estimate of pilot signals, based on only one observed OFDMA symbol, is given by HˆLS(m) = Y (m)
X(m) = X(m)H(m) + N(m)
X(m) = H(m) + N(m)
X(m) (4.4)
where N(m) is the complex white Gaussian noise on subcarrier m. We collect HLS(m) into Hˆp,LS, an Np× 1 vector where Np is the total number of pilots, as
The LS estimator is a simplest channel estimator one can think of.
4.1.2 Linear Interpolation
After obtaining the channel response estimate at the pilot subcarriers, we use interpolation to obtain the response at the rest of the subcarriers. Linear interpolation is a commonly considered scheme due to its low complexity. It does the interpolation between two known data. That is, we use the channel information at two pilot subcarriers obtained by the LS estimator to estimate the channel frequency response information at the data subcarri-ers between them. We also use linear extrapolation to estimate the response as the data subcarriers beyond the outermost pilot subcarriers.
The channel estimatw at data subcarrier k, mL < k < (m + 1)L , using linear interpola-tion is given by [14]
He(k) = He(m + l) = (Hp(m + 1) − Hp(m))l
L + Hp(m) (4.6)
where Hp(k), k = 0, 1, · · · , Np, are the channel frequency responses at pilot subcarriers, L is the pilot subcarriers spacing, and 0 ≤ l < L.
4.1.3 Time Averaging
We also consider processing the channel information along the time axis to get better estima-tion. Averaging several channel responses over a period of time should mitigate the influence of noise. Coherence time is a statistical measure of the time duration over which the channel impulse response is essentially invariant. It quantifies the similarity of the channel response at different times. The channel can be considered slowly varying if the coherence time is greater than the OFDMA symbol period. The channel may even be assumed to be static over one or several reciprocal Doppler spread intervals.
For example, assume the SS moves at a speed of 60 km/h. The maximum Dopper shift
with a center frequency 3.5 GHz can be calculated as fm = v
λ = 194.44 Hz. (4.7)
The corresponding coherence time is approximately [15]
Tc ≈ 9
16πfm = 920.83 µs. (4.8)
Consider an OFDMA system of bandwidth 20 MHz, and using 2048-FFT and 256-point cyclic prefix. The symbol period is
(2048 + 256)
¡b28258000·20Mc × 8000¢ = 102.86 µs. (4.9) Hence, the channel response over b920.83102.86c = 8 symbols can be regarded static. Thus we may use simple averaging over 3 symbols to reduce noise effect as
Havg(k) = H0interp(k) + H−1interp(k) + H−2interp(k)
3 (4.10)
where Hninterp(k) is the interpolated channel response at the previous nth symbol time.
If the channel remains static, over a longer time period, we may use more symbols in the averaging to reduce the noise effect more effectively. But then the storage requirement and the computational complexity both increase, a simple way to take more (or less) symbols into the average effectively and yet without the storage and complexity penalty is exponential averaging:
˜hexpn (f ) =
½ w · ˜hexpn−1(f ) + (1 − w) · ˜hinterpn (f ), n > 1,
˜hinterpn (f ), n = 1, (4.11)
where ˜hexpn (f ) is the estimated channel after exponential averaging at nth symbol time,
˜hinterpn (f ) is the channel response by using only the interpolation discussed before at the nth symbol time, and w is the exponential factor.
Exponential averaging may yield better performance than simple moving average when the channel is very static, but its performance may degrade more significantly than that of
Figure 4.1: Tile structure.
moving average in fading channels. We will compare the performance at different values of w and in different conditions later.
4.1.4 Application to IEEE 802.16e OFDMA Uplink
As described before in chapter 2, uplink transmission uses tile structure to transmit pilot and data information. Fig 4.1 shows an example of tile transmission. Within a tile, we first estimate the channel response at each pilot position. Second, we interpolate the frequency response at data subcarriers in symbol 1 and 3 by the estimated pilot. Last, we get the frequency response of symbol 2 by time averaging the channel response estimates of symbols 1 and 3.
We give the detail steps for channel estimation as follows:
• Estimate the channel response at each pilot location by using the LS technique.
• Use the linear interpolation scheme to get the data subcarrier response in symbols 1 and 3 from the estimated values at pilot locations.
• Estimate the channel response at middle symbol that contains no pilots in a tile by
Table 4.1: OFDMA Uplink Parameters
Parameters Values
Bandwidth 20 MHz
Central frequency 3.5 GHz
Nused 1681
Sampling factor n 28/25
G 1/8
NF F T 2048
Sampling frequency 22.4 MHz Subcarrier spacing 10.94 kHz Useful symbol time 91.43 µs
CP time 11.43 µs
OFDMA symbol time 102.86 µs
Sampling time 44.65 ns
averaging the first and third symbols in the time domain as
H2est(f ) = H1interp(f ) + H3interp(f )
2 . (4.12)
Exponential averaging is an alternative.