INTERFERENCE CANCELLATION FOR NARROWBAND MOBILE COMMUNICATION SYSTEMS Tao Wu, Christian Schlegel Electrical Engineering Department University of Utah Salt Lake City, UT 84112 PH: 801-581-5561, FAX: 801-581-5281
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[email protected], Abstract { A narrowband mobile communication systems is proposed in this paper. The interference cancellation is achieved by the projection receiver. Our study is concentrated on a dual-antenna system, including performance analysis and simulations. The e ects of delay, phase bias and frequency o set are considered. A blind receiver is also proposed and simulated for this system.
I. INTRODUCTION This paper proposes an interference canceling method for narrowband mobile communication systems using a projection operation approach. The projection receiver, originally developed for CDMA (Code-Division Multiple Access) systems to cancel the interference of other users, is applied to a narrowband system in conjunction with multiple receive antennas. We demonstrate that such a system can e ectively cancel a single co-channel interference (CCI) signal using dual receive antennas.
II. SYSTEM MODEL A dual-antenna narrowband transmission system is shown below [4]: s(t) b Encoder d Xmitter
i(t) s(t) i(t)
h(t)
y1
y2 h(t) Sampling
Projection ^b Receiver
Figure 1: System Model. A rate R=1/2 convolutional encoder is used in this system as the error control mechanism. d is the encoded sequence of user data b. s(t) = di p(t , iT )
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is the transmitted signal where di is the i-th coded symbol in the sequence d and p(t) is a square root raised cosine modulation pulse with rollo = 0:5 . T is the symbol interval. There is also an interfering signal i(t) which arrives at the receiver at a relative angle , a relative delay and a frequency o set f , but has otherwise identical system parameters. The receiver lter h(t) is a brickwall lowpass lter with cuto frequency T1 . Its output is sampled at the Nyquist rate T2 , which constitutes a sucient statistics. The receiver comprises the projection branch metric computer and a Viterbi decoder, see Figure 2. y is the received sampled sequence. Sampling the square root raised cosine signal and neglecting the tails, we obtain a length-limited sequence of samples for each symbol. The sampled waveforms are shifted versions of each other, and compose the columns of the matrix A, which are shifted by T=Ts where Ts = T2 is the sampling time.
AI , the matrix of the interference signal, is identical to A but with an additional delay of for the
waveform of interfering user. In the sequel we assume s(t) arrives at a 90 incident angle. In this case the received sampled signal vectors y 1 and y2 of the dual antenna system can be written as, y A f A ej n 1 I I 1 y2 = A d + f I AI ej(+) dI + n2 (1) where f I is a diagonal matrix with the ith element on the diagonal is exp(j 2f i Ts ). f is the frequency o set for the interfering user. d and dI are the data sequences of the desired and interfering users respectively, and n1 and n2 are sample Gaussian noise vectors. is the phase o set of the interfering signal at the rst antenna. For the second antenna, there is an additional phase di erence
Let A[i] be the sampled waveform of the desired user's signal during branch (2 symbols) interval i. By cutting o the tails of the sampled pulses outside the branch window to which they belong and assuming the length of the data sequence is K , we obtain 2 A[1] 3 6 77 A[2] A 664 75 ; (6) ... A[K ] which is a block diagonal matrix and A[i] is N 2, where N = 2TTs is the number of samples per branch. Also de ne A[i] = [A[i]; A[i]]T .
of the interfering signal with respect to the desired signal. The values of phase shifts are functions of the angle , the incident angle di erence between s(t) and i(t), antenna spacing L and frequency o set f (See Section IV). y
Linear Metric Generator
Λ( d[i])
Viterbi Decoder
^d[i]
Figure 2: The branch metric computer evaluates the metrics at each branch interval.
III. PROJECTION RECEIVER FOR NARROWBAND TRANSMISSION Interference Cancellation Using the Projection Receiver
Simplifying and reshuing the matrix AI in the same way, the projection matrix M can be written as a block diagonal matrix too. 2 M[1] 3 6 77 M[2] M = 664 75 ; (7) ... M[K ] where M[i] = I , AI [i](AI [i]T AI [i]),1AI [i]T .
Using the de nitions, y = [y1 ; y2 ]T , A = [A; A]T , AI = [f I AI ej ; f I AI ej+ ]T , and n = [n1 ; n2]T , equation (1) can be written as y = Ad + AI dI + n: (2)
We now evaluate (5) by processing a branch at a time, i.e., we evaluate (d[i]) = kM[i](y[i] , A[i]d[i])k2: (8) for all four hypothesis of d[i] (see Fig. 2).
The rst term on the right hand is the desired (constrained) data. The second term is the co-channel interference (CCI). Minimizing ky , AI dI k2 over dI yields the (conditional decorrelating) estimate [1] d^I = (ATI AI ),1ATI (y , Ad): (3)
The sequence metric (5) can now be computed sequentially by a sequential detector, e.g., the Viterbi algorithm.
IV. PERFORMANCE AND SIMULATIONS
Consequently, the sequence estimation for the data of the target user d is performed according to d^ = arg min kM(y , Ad)k2 (4)
In this section we study the e ect of delay, phase di erence and frequency shift of the interfering user on performance. We assume that we have already acquired these parameters. In the next section, a blind algorithm for this receiver is developed, which does not need to know these parameters explicitly.
d
where M = I , AI (ATI AI ),1 ATI is the projection matrix onto the nullspace of AI . The metric for each sequence d can be calculated as (d) = kM(y , Ad)k2 : (5)
Performance Analysis
The square root raised cosine pulse waveform is very bandwidth ecient [8] and popular in narrowband transmission systems. Since shifted copies of p(t) are orthogonal to each other, the columns of the matrix A are all orthogonal to each other and there is no ISI.
Considering the trellis corresponding to the target user, if the transmitted sequence d has a metric smaller than that of an erroneous sequence d , the two codeword error probability can be calculated as [2, 3] 0
2
1 0s 2 Pe = Q @ kMAk A ; 2N0
(9)
= d , d;
(10)
where
0
and the angle between the incident directions of s(t) and i(t) be and s(t) arrives perpendicular to the antenna base. We obtain Lsin( ) = ; (12) 2 where is the wavelength of the carrier signal.
Compared with the interference free performance, the projection method su ers an energy loss which can be quanti ed as
k2 : L = 10log10 kMA kAk2
Now the phase bias can be written as = 2L sin( ):
(11)
We also calculated the energy losses with respect to f using (11). The results are shown in Figure 4. We found that the frequency o set actually improves the performance since the shifted frequency spectrum of the interfering user results in less interference on the target user due to the smaller spectral overlap. This is con rmed by the simulations in the Figure 5.
It turns out that L is largely independent of , and we use = [2; ,2; 2; 0; 2; ,2], the minimum distance di erence to quantify L. From (11) we can now calculate the performance loss of the system as a function of the relative delay and phase bias of i(t) and s(t). We found that the delay does not e ect performance signi cantly ( xed phase bias). The phase bias is the parameter which dominates system performance. Signi cant correlation exists between s(t) and i(t) if 0, and performance loss can be large, see Figure 3. On the other hand, it is less than 3dB whenever > =2. In the best case of = , the interfering signals are all orthogonal to the desired signal and no degradation is experienced. The circles in Figures 3 are simulation points for bit error probability Pb . It can further be shown that the phase has no e ect on performance.
The projection receiver is very robust even in the case of very strong co-channel interference since the method is near-far resistant. Ideally the Carrier Interference Ratio (CIR) has no e ect on performance. However, since we made some approximations, (e.g., neglecting the waveform signal tails outside the branch window of width 2 symbols), the performance will start to degrade for CIR values less than -40dB.
Simulations for the Dual Antenna System
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In Figure 6 we plot the simulation results for various phase di erences. The performance loss measured from these results agree with the curve shown in the Figure 3.
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The performances for f = 0:2=T; 0:5=T and 0:8=T are also given in Figure 5, with = 0:5 and = 0:2T . For bit error probability Pb, these are the circles in Figure 9.
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Figure 4: Energy loss vs. , = 0:2T .
When three receive antennas are used at the receiver, we can analyze and simulate the system in a similar way. Assume that the three antennas are colinear and the distances between two adjacent antennas are identical. It is easy to see that if the phase di erence between antenna 1 and 2 is , the phase di erence between antenna 1 and 3 is 2.
We also want to investigate how the phase bias relates to the angles of the two signals and the separation of the two receive antennas. The receiver model shown in Figure 1 is considered. Let the distance of the two receive antennas be L 3
∆θ=0.5π, τ=0.2T
CIR=−10dB, τ=0.2T,Sampling Rate=1/0.5T,∆θ=0.4π,0.5π,0.6π and 0.8π
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Figure 4: Energy loss vs. f .
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Figure 6: Performance with various phase bias, CIR=-10dB. Triple Antenna TDMA System
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Figure 7: Energy loss vs. 1, = 0:2T .
Figure 5: Performance with various f .
Through the QR decomposition AI = QR where QT Q = I and R is an upper triangular matrix, we have AI (ATI AI ),1 ATI = QRT(RT,Q1 T QR ),1 RT QT T T = QR(R R) R Q = QQT : (15)
We calculated the energy loss with respect to in Figure 7. Compared to Figure 3, the performance of a triple antenna system is not a ected as much by phase di erences as a dual antenna system. It is easier to control the angle of the desired signal and interfering signals to keep the performance loss small.
We can write equation (14) as
Figure 8 shows simulation result for the case of = 0:4. The performance loss with respect to the single user case is about 1.45dB, agreeing with the theory.
(d) = ky0 ,QQT y0 k2 =
K X
=1
i
ky0 [i],Q[i]Q[i]T y0[i]k2;
(16) where Q[i] is de ned analogously to A[i] and M[i].
V. BLIND RECEIVER
Using the PAST (projection approximation subspace tracking) algorithm proposed in [9], the matrix Q can be calculated recursively. Under the assumption that the system parameters of the interfering user change slowly, the interfering subspace can be tracked and the interference removed by the projection receiver.
A blind version of the projection operation is also developed for this system. Using a projection approximation subspace tracking approach [9, 10], we can estimate the signal subspace recursively. De ne y0 = y , Ad, equation (5) can be rewritten as (d) = ky0 , AI (ATI AI ),1 ATI y0 k2: (14)
With the blind projection operation, we do not re4
fects of the delay, phase and frequency values of the interfering user. The theory is substantiated by simulation results. A blind receiver is also developed for the situation that system parameters are unknown.
TDMA Simulation with Triple Antenna
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REFERENCES
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(1) C. Schlegel, S. Roy, P. Alexander, and Z. Xiang, \Multiuser Projection Receivers," IEEE J. Selected Areas Commun., October 1996. (2) C. Schlegel, P. Alexander, and S. Roy, \Coded Asynchronous CDMA and its Ecient Detection," IEEE Transactions on Information Theory, in press. (3) T. Wu, C. Schlegel, \Adaptive PR Error Performance Analysis", submitted to IEEE Trans. on Information Theory, 1998. (4) H. Yoshino, K. Fukawa, and H. Suzuki, \Interference Canceling Equalizer (ICE) for Mobile Radio Communication," IEEE Transactions on Vehicular Technology, Nov. 1997. (5) S. Haykin, Adaptive Filter Theory, Prentice Hall, Englewood Cli s, New Jersey, 1991. (6) C. Schlegel, Trellis Coding,, IEEE Press, Piscataway, NJ, 1997. (7) P. Alexander, L. Rasmussen, C. Schlegel, \A Class of Linear Multi-User CDMA Receivers," IEEE Trans. Commun., 1996. (8) J. G. Proakis, Digital Communications, Third Edition, McGraw-Hill, Inc., 1995. (9) B. Yang, \Projection Approximation Subspace Tracking", IEEE Trans. on Signal Processing, January 1995. (10) S. Mo, C. Schlegel, V. J. Mathews, \A Blind Adaptive Projection Receiver for CDMA Systems", submitted to IEEE Trans. on Information Theory, October 1998.
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Figure 8: An example for 1 = 0:4. quire knowledge of the waveform or system parameters, such as delay, frequency and phase of the interfering user. This is a big advantage in practice. A simulation result of this adaptive receiver for CIR = ,3dB is shown in Figure 9. There is only a small degradation compared to the performance of receiver with complete parameter knowledge. A decision feedback approach is applied to improve the performance by using the more reliable decoded data as the initial estimates of desired data in the algorithm. Blind PR
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Figure 9: Blind Projection Receiver, CIR=-3dB, = 0:5, f = 0, and = 0:2T .
VI. CONCLUSIONS A projection receiver approach is developed for a narrowband mobile communication systems. Dual receive antennas are used to provide the signal dimensionality to cancel interference e ectively. Performance analysis is given with emphasis on the ef5
