Channel Estimation and Detection for Multibeam Satellite Communications Helmi Chaouech#1, Ridha Bouallegue*2 #,*
6’Tel Research Unit, Sup’Com, University 7th November at Carthage City of Communication Technologies, Raoued Road, Km 3.5, 2083 El Ghazala, Ariana, Tunisia 1 2
[email protected] [email protected]
Abstract— In this paper, a channel estimation method and a detection technique for multibeam communications systems are developed. The channel estimation uses the output of a beam former to determinate the channels parameters for each active user in the system. The detection technique assures the determination of QPSK symbols after compensation of channel effects. An antenna array is considered at the receiver with a null steering beam former. Mathematical presentations of the transmission model and channel estimation and detection algorithms detail the developed techniques. In order to evaluate the performance of channel estimation and detection methods, we have simulated an FDMA multibeam system under an AWGN environment. Simulation results show the good performance and the robustness of these techniques with equal power signals. Keywords— Beam forming, null steering, channel estimation, multiuser detection, antenna array.
I. INTRODUCTION The scarcity of radio spectrum resource requires wireless communication systems to reuse the frequency bands. However, when more than one transmitter operates in one frequency-division channel, they will interfere with each other. The so called co-channel interference (CCI) due to the crosscorrelation between users’ different channels has become one of the major causes of degradation in wireless system performance. Satellite communications constitute a good solution to overcome the problem of network coverage, especially for rural and isolated zones. Multibeam technology is one of important alternatives adopted in satellite communications. Its main advantages are high antenna gain, which leads to link improvement, and frequency reuse which allows the capacity system increasing. Channel estimation is an important task especially in wireless communication where the channel is unknown. This operation assures the determination of channel parameters, and then, the effects produced by this channel can be compensated by equalization operation. Some channel estimation methods examples for wireless systems are presented in [3], [8]. Detection techniques, particularly, those which are based on multiple interference cancellation, extract users’ original data with very low Bit Error Ratio (BER). Some of multiuser
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detection techniques with multiple access interference suppression can be found in [6], [7]. Detection techniques combined with forward error (FEC) coding show very good results especially for high noised environment and/or high signals cross-correlations or co-channel interference [2], [4]. In this work, we have developed a channel estimation method and a detection technique for satellite multibeam communications. The channel estimation, which operates at the output of a null steering beam former and uses an aided sequence of symbols, permits the determination of amplitudes and phases of the users’ signals. The detection technique assures the determination of each user data after compensation of channels effects with use of the parameters feed by the channel estimator. The channel model considered is an AWGN channel model, as it presents an appropriate model for satellite link, particularly for fixed services such as digital television. Some of link characteristics adopted here, such as QPSK modulation, carrier frequency and FDMA access are inspired from DVB RCS system [5]. In Section II, we have presented the signal model for multibeam communications and detailed the null steering beam former as it will be considered in this work. In Section III, we have developed the channel estimation technique and specified its mathematical presentation. In Section IV, we have presented the detection algorithm. In Section V, we have evaluated the performance of channel estimation and detection algorithms with showing and analyzing the simulation results. Finally, in Section VI, some conclusions are drawn from this work. II. MULTI BEAM SYSTEM A. Signal Model We consider the uplink of a satellite multibeam communications system with K active users. The sharing of physical resource is done by a frequency division multiple access (FDMA). Due to frequency reuse possibility, we considered that the K signals or beams are co-frequency, i.e. they share the same carrier with frequency f 0 . Each user signal consists of transmitting N bits where the m firsts are served as a training sequence used in channel estimation purpose. After QPSK mapping, the signal of the kth user is given by:
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y k (t ) = Wk x(t )
N −1
rk (t ) = Ak e jΦ k ∑ d k(i ) g (t − iT )
(1)
i =0
Where: Ak , Φ k , g (t ) and T denote respectively the signal amplitude , the signal carrier phase, the emitter filter response (i ) and the symbol duration. d k ; k = 1..K , i = 0..N − 1 take their values into {±1 ± j}. that
Where:
At the receiver, the antenna array is formed of Q omnidirectional elements. The distance between two adjacent elements are the same and is equal to α . The signal received by the qth radiating component is given by:
xq (t ) = ∑ rk (t )e
j 2Πf0τ kq
+ nq (t )
(2)
k =1
τ kq =
Where:
α c
(q − 1) cos Θ k
(3)
With, c and Θk denote respectively, the speed of propagation of the plane wave front (the carrier of the signal) and the angle between the direction of the kth signal and the antenna array axe (see Fig. 1).
And,
Each ground station is characterized by a steering vector S k which defines the orientation of the user signal toward the antenna array; it is given by:
[
1
Q
2
S k = e j 2 Πf0τ k , e j 2Πf0τ k ,…, e j 2 Πf0τ k
]
T
(4)
With, (.) denotes the transpose operator. If we regroup the K steering vector, we can obtain the Q × K following steering matrix:
Ω = [S1 , S 2 ,… , S K ]
[
y (t ) = Wx (t )
(5)
T
(8)
(9)
]
T T K
W = W1T ,W2T ,…,W
(10)
y (t ) = [ y1 (t ), y 2 (t ),…, y K (t )]
T
1. e.g. for the first user,
(11)
e1 = [1,0,…,0]
T
(12)
The Null Steering beam former allows the construction of a beam with unity response in the desired direction and nulls in interference directions [1]. For the kth beam, the vector of weights is given by [1]:
Wk = ekT Ω −1
(13)
Then the output of the Null Steering beam former for the kth beam can be expressed as follows:
y k (t ) = ekT Ω −1 x (t )
(14)
III. CHANNEL ESTIMATION This channel estimation technique operates at the output of the beam former. It permits the estimation of the amplitudes and phases of each user signal with use of a training sequence. We supposed that the K signals are synchronized and the directional angles of the sources are known by the receiver. In the rest of the paper, any value or a decision of the value z .
T
]
We define the column vectors e k , k = 1..K , whose all elements are zeros except the kth position element is equal to
nq (t ) is a background noise which is supposed a white Gaussian noise.
[
x(t ) = x1 (t ), x2 (t ),…, xQ (t )
Generalization of expression (7) for the K beams can be expressed by:
j denotes the imaginary unit, so
j 2 = −1 .
K
Where:
(7)
zˆ designs an estimation
After an optimal sampling at a cadence of a symbol duration, the samples at the output of the matched filter can be presented by: yk (i) / i = 1..N , where y k (i) =
yk (t ) t =iT .
Estimation of the kth signal amplitude is computed as follows:
B. Beam Forming m −1 The beam forming assures the construction of the K beams ˆ = 1 (15) A yk (i ) k or users’ signals from the Q signals at the outputs of antenna m 2 i =1 array elements (Fig. 1). Many beam formers are presented and analyzed in [1]. In this paragraph, we will present one of them, Where, . is the modulus operator of a complex number. it is the beam former used in this work, called the null steering beam former. The phase estimate of the kth signal is given by: A beam former is defined by its complexes weights vectors. 1 m−1 For a user k, the vector of the kth beam former is given by: ˆ (16) Φ = angle yk (i)e j angle( dk (i )) k Wk = w1k , wk2 ,…, wkQ (6) m i =0 The output of the beam former for the kth user signal is then Where angle (.) denotes the angle operator of a complex given by: number.
∑
[
∑
]
367
(
)
IV. DETECTION ALGORITHM The detection operation operates after channel estimation computation. It uses the parameters to compensate the effects of the channels, and then extract the original data of each user.
-The average phase estimation error of the system, which is is expressed for the kth user by:
The detection of the QPSK symbols consists of estimating the real and imaginary parts of these symbols. If we present the ith complex symbol of the kth user by:
In Fig. 2, we have evaluated the performance of the detector without near-far problem. The detection with channel estimation outperforms that without channel estimation, and it show good performance for high SNRs.
d k(i ) = a k(i ) + jbk(i )
ˆ PERk = Φ k − Φ k
(17)
(22)
The Fig. 3 shows the simulation results of the system under near-far problem. The detection quality is degraded. But, in high SNRs, the results with channel estimation are better that (18) those without.
Then, the detection operations are done as follows:
( ( )) = sign(imag (y (i)e )) ˆ
aˆ k(i ) = sign real y k (i)e − jΦk
In Fig. 4, the effect of near-far problem on amplitude (19) estimation is dealt. Signals with different amplitudes are k estimated, with the following amplitudes ratios; A4/A1=8, A3/A1=5, A2/A1=3. The estimation quality depends on the Where, real (.) and imag (.) denote respectively the real and signal power. This result shows the sensitivity of the amplitude imaginary parts of a complex number. estimation against the near-far problem. Although this effect, the amplitude estimation error of the system becomes (i ) Finally, the estimation of a symbol d k is then given by: acceptable for low noised environment. When, the signals are of the same powers, the amplitude estimation show good dˆk(i ) = aˆ k(i ) + jbˆk(i ) (20) performance.
bˆk(i )
And,
ˆk − jΦ
V. SIMULATIONS RESULTS In this paragraph, we have evaluated the performance of the channel estimation and detection techniques through computer simulation. The parameters of simulation are taken as follows: Q = 4, K = 4, f 0 = 30GHz, N = 1000, m = 100. In order to evaluate the detection and channel estimation performance, the following quantities are computed and presented: -The average bit error ratio of the system BER. -The normalized average error of amplitude estimation in the system. It is defined for the kth user by:
AERk =
Signal k source
Ak − Aˆ k
(21)
Ak
Θk )
The same analyses as above can be done for the phase estimation related to Fig. 5. Moreover, although it sensitivity to near-far problem, the phase estimation shows very good performance with and without that problem. This result can be interpreted by the white character of the noise as it is considered a complex noise with real and imaginary parts of the same power. In fact, equal increment of real and imaginary values of QPSK symbols leads to augmentation of their modulus while their angles remain constant. The near far effect considered in the simulations is quite severe since the ratio between the power of the strongest signal and that of the weakest one is 82. This is done for comparison purposes with the results obtained for equal powers signals. Generally, in satellite communications, the near-far effect is not high. Thus, the channel estimation and detection performances will be more improved with near signals powers.
x1 (t )
x 2 (t )
)
Beam Forming
y k (t )
Channel Estimation
xQ (t ) ) Fig. 1 Receiver architecture
368
{Aˆ , Φˆ } k
k
Data Detection
dˆ k
0
10
0
10
Without near-far problem With near-far problem
P has e E stim ation E rror
Detection With Chan. Est. Detection Without Chan. Est.
-1
BER
10
-2
-1
10
-2
10
10
-3
10 -3
10
0
2
4
6
8 10 SNR (db)
12
14
16
18
0
2
4
6
8 10 SNR (db)
12
14
16
18
Fig. 5 Phase estimation performance against the near-far problem
Fig. 2 Evaluation of the detection with channel estimation and without nearfar problem 0
10
Detection With Chan. Est. Detection Without Chan. Est.
-1
BER
10
-2
10
VI. CONCLUSIONS In this paper, we have developed a channel estimation and a detection techniques for multibeam communications. The channel estimation operates at the output of a beam former assuring the determination of channels parameters, which are fed to the detector in order to determinate the data of each user. Detection technique shows good performance especially when there is a control power. Amplitudes estimation is sensitive of the near-far problem, but it shows good results when the signals are of equal powers. Phase estimation performs well even with near-far effect although a light degradation. As a future work, it is interesting to deal with the near–far problem at the channel estimation technique. REFERENCES
-3
10
0
2
4
6
8 10 SNR (db)
12
14
16
18
[1]
Fig. 3 Evaluation of the detection with channel estimation under near-far problem [2]
0
10
Amplitude Estimation Error
[3] -1
10
[4]
[5]
-2
10
[6] Without near-far problem With near-far problem
-3
10
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8 10 SNR (db)
12
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[7] [8]
Fig. 4 Amplitude estimation performance against the near-far problem
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