AbstractâIn this paper, a receiver based on an iterative algorithm for joint channel estimation and cochannel interference cancellation suitable for time-division ...
Single Antenna Cochannel Interference Cancellation in Asynchronous TDMA Systems Hendrik Schoeneich and Peter A. Hoeher Information and Coding Theory Lab University of Kiel Kaiserstr. 2, D-24143 Kiel, Germany Phone: +49 431 880 6134 (or 6127), Fax: +49 431 880 6128 Email: {hs,ph}@tf.uni-kiel.de
Abstract— In this paper, a receiver based on an iterative algorithm for joint channel estimation and cochannel interference cancellation suitable for time-division multiple-access cellular radio systems is proposed. The receiver is blind with respect to the data of the interfering users and training-based w.r.t the data of the desired user and it is therefore referred to as semi-blind. As opposed to concurrent receiver structures, where the number of receiving antennas must exceed the number of cochannel interferers, the proposed receiver is suitable for just one receiving antenna, i.e., the proposed receiver is also suitable for the downlink. Simulations results are presented, which indicate that with just one receiving antenna and no oversampling the proposed receiver is able to operate at a signalto-interference ratio of 0 dB in asynchronous GSM networks given a single dominating interferer.
I. I NTRODUCTION Single antenna (cochannel) interference cancellation (SAIC) is currently a hot research topic, since mobile stations are commonly (due to cost, volume, power consumption, and design aspects) equipped with just one antenna and since especially with the introduction of multimedia services the downlink became the bottleneck in 2nd generation TDMA networks. Typically, the network capacity of 2nd generation TDMA cellular radio networks is limited by cochannel interference rather than noise, unless cochannel interference cancellation is done. There are two main concepts to combat CCI and ISI – interference rejection and multiuser detection [1]. The first concept (i.e., interference rejection) is based on adaptively combining filtered received sequences before conventional equalization [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. For all of these techniques, multiple receiving antennas are a prerequisite, either conceptionally or to achieve satisfactory performance. The second concept (i.e., multiuser detection) is based on the simultaneous detection of the desired user and the interfering users [12], [13], [14]. The receiver proposed in this paper is based on this second concept. The proposed approach is based on an iterative algorithm for joint channel estimation and cochannel interference cancellation suitable
for time-division multiple-access cellular radio systems. The receiver is blind with respect to the data of the interfering users and training-based w.r.t the data of the desired user and it is therefore referred to as semi-blind. As opposed to concurrent receiver structures where the number of receiving antennas must exceed the number of cochannel interferers, the proposed receiver is suitable for just one receive antenna. No knowledge on the burst structure of the interferer is used. Hence, the proposed receiver is suitable for (but not restricted to) the downlink in asynchronous networks. An analytical lower bound on the bit error probability for joint maximum-likelihood sequence estimation in the presence of cochannel interference and ISI is presented. This lower bound is supported by simulations, which indicate that with just one receiving antenna and no oversampling the proposed receiver is able to operate at a signal-to-interference ratio of 0 dB in asynchronous GSM networks given a single dominating interferer. The proposed semi-blind receiver without knowledge about the training sequence of the interferer is compared to JLSCE/JVD with perfect knowledge of all training sequences. It is shown that the error performances of both receivers are comparable for a signal-to-interference ratio down to 5 dB assuming the TU channel model. It is also shown that the proposed receiver is superior to LSCE/VD (where the same channel information is available but the CCI is neglected) with a gain of more than 15 dB. II. C HANNEL M ODEL Throughout this paper, the complex baseband notation is used. The baud rate sampled outputs of linear transmission schemes without CCI can be described by the equivalent, discrete-time ISI channel model [15] y(k) =
L X
hl (k) · a(k − l) + η(k) ,
(1)
l=0
where k is the time index. The channel coefficients {hl (k)} , 0 ≤ l ≤ L, comprise the pulse shaping filter, the physical time-varying multipath fading channel, the receiving filter, and the sampling. The finite channel memory length L is assumed to be known at the receiver. The complex
¡ £ ¢ 2¤ sequence {a (k)} with E [a (k)]= 0, E |a (k)| ¡ = 1 represents£ the data¤ and the ¢ complex values η (k) with E [η (k)]= 2 0, E |η (k)| = ση2 are additive white Gaussian-distributed noise samples of a random process with one-sided power spectral density N0 . An extension to oversampled systems is straightforward by means of polyphase channels. Taking CCI into account, the received signal can be written as y(k) =
L X
hl (k) · a(k − l)
l=0
|
{z
}
yd(k)
+
Lj J X X j=1 l=0
|
gl,j (k) · bj (k − l) +η(k) {z
(2)
}
yi(k)
The first term yd (k) is the desired signal, yi (k) describes the interference signal caused by J interfering users. Every interfering user j is associated with a CIR {gl,j (k)} , 0 ≤ l ≤ Lj , 1 ≤ j ≤ J. The data sequences of the interfering ¡ £ users2 are ¤ given by {b (k)} , 1 ≤ j ≤ J with E [b (k)]=0, E |bj (k)| = j j ¢ 1 . In accordance with the GSM testing conditions and for illustrative purposes, in the following emphasis is put on one dominating interferer (J = 1) and the channel memory lengths of the desired and the interfering user are assumed to be equal. Generalizations are, however, straightforward. Whenever only one interfering user is considered, we will omit the user index j. The signal-to-interference ratio (SIR) is defined as: h i 2 E |yd (k)| i SIR = h 2 E |yi (k)| i hP L 2 E l=0 |hl (k)| i. = hP PL J 2 E |g (k)| l,j j=1 l=0
(3)
(4)
In this paper, the noise power is normalized £ PL with respect 2¤ to the desired user’s signal power, i.e., E |hl (k)| = l=0 £ PL 2¤ 1. Accordingly, E l=0 |gl (k)| =1/SIR. The mean power of the interfering user’s signal does therefore not affect the signal-to-noise ratio (SNR) Es /N0 = 1/ση2 , where Es is the energy per data symbol. III. C HANNEL E STIMATION As the channel coefficients are not known at the receiver, CE has to be applied. During the training sequence, the receiver has perfect knowledge of the data sequence of the desired user. With regard to the training sequences of the interfering users, four scenarios can be distinguished: The training sequences of the interfering users are (i) known and synchronous (best case), (ii) known and asynchronous
with known shift, (iii) known and asynchronous with unknown shift, or (iv) unknown (worst case). In the case of known and synchronous training sequences, JLSCE [13] can be applied: iT ¡ h ¢−1 bT , g b1T , · · · , g bJT h = CH · C · CH · y. {z } |
(5)
C†
The joint data matrix C = [A, B1 , · · · , BJ ] combines the training data of the desired and all interfering users. The matrix CH is the Hermitian transposition of C and the matrix C† denotes the corresponding pseudo-inverse. The elements ¤ of the £ PJ vector y = A·h+ j=1 B·gj = C· hT , g1T , · · · , gJT are the samples of the received signal corresponding to the training data of C. The number of rows in C is the length of the so-called observation interval Nobs . It can be shown that for orthogonal training sequences the mean squared error is proportional to ³ ´ PJ −1 L + j=1 Lj + J + 1 · Nobs , where the first factor is the number of channel coefficients to be estimated. Therefore it is desirable to keep Nobs large when using JLSCE. For synchronized training sequences and JLSCE, the length Nobs of the observation interval is ½ ¾ Nobs = Nt − max L, max {Lj } , (6) j
where Nt is the length of the training sequence. If the lengths of all channels are assumed to be equal, i.e., L = Lj , 1 ≤ j ≤ J, the length Nobs is the same as in the case without CCI. In the more realistic case of asynchronous training sequences (items (ii) and (iii) in the list above) and JLSCE, only the overlapping part of the training sequences of all users can be used for JLSCE, and Nobs reduces to ½ ¾ Nobs = Nt − max L, max {Lj } − max {∆j } , j
j
(7)
where ∆j is the shift in symbols of the j-th interfering user’s training sequence. Since the shift(s) may be large in asynchronous systems, the length of the observation interval may be small, which leads to a large mean squared error when using JLSCE. Additionally, the receiver has to know or estimate the shifts of the interfering users. In consideration of this, JLSCE appears to be inappropriate in asynchronous networks – even if the shift(s) of the interfering user(s) is/are known by the receiver. This motivates to interpret the interfering sequences as unknown data, so that the receiver is blind with respect both to the data and to the training sequences of the interfering users. Such a receiver is referred to as semi-blind. This case is equivalent to the last item in the list above (worst case). Note that for a semi-blind approach, a shift estimation is not required.
IV. I TERATIVE S EMI -B LIND D ECISION -D IRECTED
2) Calculate the path metrics for all transitions at time index k + 1:
C HANNEL AND S EQUENCE E STIMATION
Γν,µ (k + 1) = Γν (k) + γν,µ (k + 1)
In the following, an iterative semi-blind algorithm based on a combination of the VA and the LMS algorithm [15, Chapter 11.1] is presented. We introduce the proposed receiver for J = 1 interfering user and one receiving antenna. The receiver structure can easily be extended to take more interfering users into account or to make use of antenna diversity. It can be used in any TDMA mobile radio system. However, the specific implementation below is based on the popular GSM system [16].
3) Determine the best path for every state µ at time index k+1: Γµ (k + 1) = min {Γν,µ (k + 1)} ,
i.e., let only the best branch per state survive. 4) The most likely survivor is traced back δ symbols to b − δ), b(k − δ) and b(k obtain the tentative decisions a respectively. The decision delay δ is a design parameter of the algorithm. The choice of δ is based on a trade-off between the quality of the tentative decisions and the tracking capability. 5) The channel estimates are updated using the LMS algorithm:
The first step of the algorithm is an initial estimation of the channel coefficients h and g. For the desired user’s channel the initial estimation is done, e.g., by calculating the least squares channel estimation (LSCE) with the known symbols of the training sequence without consideration of the interfering user. Consequently, this initial estimate is corrupted by CCI. Throughout this paper, the initial estimate for the interfering b = [0, 0.2, 0, · · · , 0]T . Experience indicates user is chosen as g that the second channel coefficient of the interfering channel tends to be estimated with maximum power this way. This aids to mitigate shift ambiguity (cf. Section IV-D.2).
b + 1) = h(k) b b∗ (k − δ) (11) h(k + ∆(k) · e(k) · a b ∗ (k − δ) , (12) b(k + 1) = g b(k) + ∆(k) · e(k) · b g where ¡ T b (k) · a b(k − δ) e(k) = y(k − δ)− h ¢ T b − δ) +b g (k) · b(k
(13)
is a common error signal and ∆(k) is the step size of the algorithm, which may be time-varying. 6) Increment the time index and go to step 1 until the end of the burst is reached.
B. Joint Data and Channel Estimation
(8)
(10)
ν
A. Initial Channel Estimation
In order to perform joint data and channel estimation, we propose to integrate an adaptive channel estimator into a JVD. Adaptive channel estimation is done (i) to improve the noisy estimates of the channel coefficients of the desired user, (ii) to acquire the channel coefficients of the interfering user(s), and (iii) to track the CIR of slowly time-varying channels. In the following, we use the LMS algorithm for adaptive channel estimation due to its simplicity compared to more sophisticated adaptive channel estimators. The update is done in a decision-directed fashion. Good results have been obtained by using the most likely survivor as a tentative decision of the data sequences {a (k)} and {b (k)} in conjunction with a small delay δ. Alternatively, one may use per survivor processing (PSP) [17] or LVA [14] to provide tentative decisions of the data sequences. £ eν,µ (k + 1) = e Let a aν,µ (k + 1) , · · · , e aν,µ (k − L + ¤T £ ¤T e e e 1) and bν,µ (k + 1) = bν,µ (k + 1) , · · · , bν,µ (k − L + 1) be the hypotheses of the transmitted data symbol sequences for time index k + 1 corresponding to the respective state b b(k) be the transition from state ν to state µ. Let h(k) and g channel estimates for time index k. Then joint data and channel estimation is done as follows: 1) Calculate the branch metrics of the transition from state ν at time index k to state µ at time index k + 1: ¯ b T (k) · a eν,µ (k + 1) γν,µ (k + 1) = ¯y(k + 1) − h ¯ T e ν,µ (k + 1) ¯2 . b (k) · b −g
(9)
C. Iterative Update Process As mentioned before, the proposed algorithm can be used in conjunction with an arbitrary burst structure. We use the GSM normal burst structure in Fig. 1 as an example. An application to other structures can be implemented in a similar way. According to the GSM test specifications, the whole burst is assumed to be corrupted by one dominating interferer, whose data sequence is a pseudo-noise sequence without burst structure.
0
3
tail
data
3
58
k
61
87
midamble
data
26
training
2
60
86
58
145
148
tail
guard
3
144
147
1 2 n
Fig. 1.
GSM burst and sketch of the update process.
8
155
The initial channel estimate is determined according to Section IV-A. Then, channel and data estimation for both the desired and the interfering user are performed based on the algorithm described in Section IV-B. The update process of the first iteration begins at the left end of the midamble and continues to the right end of the burst in a forward recursion. This is illustrated in Fig. 1. After the end of the burst is reached, the last channel estimate is stored and is used as initial channel estimate for the following update process proceeding from the right end of the midamble to the left end of the burst in a backward recursion. The last channel estimate is again stored and can be used as an initial estimate for further iterations. One iteration consists of one forward recursion and one backward recursion. The total number of iterations is denoted by n. The final decision on the user’s data sequence corresponds to the most likely survivor after the last iteration. D. Phase and Shift Ambiguity As the receiver is completely blind w.r.t. the interfering user’s signal and the corresponding channel, the receiver uses joint hypotheses of data and channel. Some combinations of e j and g ej · g ej lead to the same product B ej . The hypotheses B e ej can be classified ambiguity of the combination of Bj and g as follows: ej · g ej = For BPSK, the condition B ¡ 1) Phase ¢ ¡ Ambiguity: ¢ e j · −e −B gj is known as phase ambiguity. The estimated interferer sequence adapts to the phase shift of the channel estimate, or vice versa. For our purposes, this ambiguity is not crucial as we are neither directly interested in the correct phase of the interfering user’s data sequence nor the corresponding channel estimates. 2) Shift Ambiguity: If both hypotheses of interfering data and corresponding channel are shifted by the same number of symbols in time, the joint estimate is the same for the shifted and the unshifted case. This is referred to as shift ambiguity. The mutual adaptation of the estimates is similar to the case of phase ambiguity. As opposed to phase ambiguity, shift ambiguity should be prevented due to the finite channel memory length used for CE. A shifted version of the CIR might cause residual ISI which leads to a performance loss. One approach to treat shift ambiguity has been described in [18] and is referred to as extended-window algorithm. The main idea is to consider a channel memory larger than L. This prevents a loss of channel coefficients. The channel update is done considering the larger memory and a dominant subset of L + 1 consecutive coefficients is chosen as the new channel estimate. Another approach has been presented in [19]. Here the receiver sets up hypotheses of the shift and estimates the most likely shift. We will introduce an alternative approach that is referred to as centering. After each iteration, the tap with the largest power is determined for the interfering user. If the first tap appears to be the dominant tap, the estimated CIR is shifted to the right by one position. If the last tap appears to be the dominant tap, the estimated CIR is shifted to the left by one
position. The iteration is repeated after centering. Centering is done not more than once per iteration. Note that centering does not increase the memory length L. This prevents an additional estimation error. Furthermore, the start indices for forward and backward recursion do not have to be changed. This prevents a shorter iteration process during the midamble. It should be noted that centering does not necessarily combat the shift ambiguity completely. It merely makes sure that the dominant tap is included in the estimated CIR. V. L OWER B OUND The bit error probability of the JMLSE receiver Pb,JMLSE can be lower-bounded by the bit error probability of the following genie-aided receiver. The concept of the proposed lower-bound is known in the context of multiuser detection [20] and is applied here to co-channel interference cancellation and extended to take frequency-selective channels into account. Assume there exists a genie who knows the sent data sequences of the desired user and all J interfering users of length K. Given an error matrix that affects the desired user E ∈ ΦK , the genie verifies whether the sent matrix X is compatible with E or not, i.e., if X ∈ ΨK (E). If it is, the genie tells the receiver that the correct X is in the set {X, X − 2 · E}. The receiver determines the most likely of the two hypotheses employing the ML criterion, which is equivalent to a simple threshold decision with two decision regions. If X ∈ / ΨK (E), the genie reveals X to the receiver, so that no bit error can be made. Because the number of hypotheses is reduced to two for X ∈ ΨK (E) and no errors occur for X ∈ / ΨK (E) , the BEP of this genie-aided receiver cannot be larger than Pb,JMLSE . For uniformly distributed X, the BEP of this genie-aided receiver is s d2 (E) Es · Pb,genie1 (E) = w(E)·2−w(E)−1 ·erfc 4 N0 ≤ Pb,JMLSE , (14) where w(E) is the number of symbol errors corresponding to error matrix E and d2 (E) is the squared Euclidian distance corresponding to error matrix E. The error matrices E and −E are compatible to disjoint sets of symbol matrices, i.e., ΨK (E) ∩ ΨK (−E) = ∅, but lead to the same distance and weight values and therefore to the same Pb,genie1 . To make use of this insight, the genie-aided receiver can be extended in the following way. Before revealing X to the receiver in the case X ∈ / ΨK (E), the genie verifies if X ∈ ΨK (−E) . If it is, the genie tells the receiver that the correct X is in the set {X, X + 2 · E} . The BEP of this second genie-aided receiver is s d2 (E) Es · Pb,genie2 (E) = w(E)·2−w(E) ·erfc 4 N0 ≤ Pb,JMLSE . (15) The inequality in (15) holds for any E ∈ ΦK . Nevertheless, it is desirable to tighten the inequality by picking an error
E∈ΦK
(16)
The corresponding error probability PLB
= Pb,genie2 (Emax ) ≤ Pb,JMLSE
(17)
is the tightest lower bound that can be attained by the preceding considerations. For a given data sequence length K, the lower bound of (17) requires an exhaustive search through the set ΦK . As the cardinality of ΦK grows exponentially with K, the computational complexity of such an exhaustive search is prohibitive for large K. Alternatively, the maximization can be done on a subset of ΦK . The resulting lower bound is termed simplified lower bound. A straightforward way to choose such a subset is to restrict the length of the considered error sequences. Let K / be an error sequence length such that 1 ≤ K / ≤ K. Then a simplified lower bound of the minimum error probability is obtained by n o (18) PLB,K / = max Pb,genie2 (E) . E∈ΦK / A simple example of such a subset of ΦK is Φ1 , where the simplified lower bound can be displayed in the following form: n o PLB,1 = max Pb,genie2 (E) E∈Φ1 v uL 1 uX 2 Es = max erfct |hl | , 2 N0 l=0 v u L uX 1 E 2 s (19) erfct |hl ± gl | 4 N0
v = 50 km/h (TU50) at a carrier frequency of fc = 900 MHz [16]. Perfect frequency hopping is done from burst to burst, which is the worst case with respect to channel estimation. The burst of the desired user and the interferer are asynchronous with unknown shift. Only one receiving antenna is used. No oversampling is done. The step size for the LMS algorithm is not changed more than once per iteration and is chosen to be in the range from ∆ = 0.04 to ∆ = 0.01; the first iteration starts with the highest value. The tentative decision delay is chosen to be δ = 1. Since the effective channel memory length of the TU channel is L = 3, 22L = 64 states are considered for the joint trellis used for semi-blind CE and JVD. The SNR is Es /N0 = 20 dB. For the determination of the bit error rates (BERs), only bit errors of the desired user are considered.
10
-1
JLSCE/JVD Noiseless CE/JVD Lower bound for JMLSE 10
-2
Bit Error Rate
matrix Emax that maximizes the value of Pb,genie2 : ½ n o¾ Emax = arg max Pb,genie2 (E) .
10
10
-3
-4
-10
0
10 20 Signal-to-Interference Ratio (dB)
30
BER versus SIR, TU50 channel model, Es /N0 = 20 dB, lower
Fig. 2.
bound and JVE performance with unperfect JLSCE (with and without residual ISI)
l=0
10
0
LSCE/VD JLSCE/JVD Proposed semi-blind receiver 10 Bit Error Rate
It can be clearly seen that the optimum lower bound given a subset of error matrices is not necessarily related to the minimum distance of the subset. This is due to the different factors 2−w(E) which take into account that different error matrices have different numbers of compatible data combination matrices X. The lower bound described so far is valid for a particular set of fixed channel coefficients. For a given channel type with varying realizations, the lower bound is determined by averaging over the lower bound values of a sufficiently large number of realizations. Such an averaged lower-bound is applied in chapter VI of this paper.
10
10
-1
-2
> 15dB
-3
VI. S IMULATION R ESULTS The capability of the proposed receiver to combat CCI and ISI in the presence of one dominating interferer (J = 1) without knowledge of the interferer’s training sequence is investigated by means of computer simulations. The GSM system was chosen to exemplify the performance of the proposed receiver. In the numerical examples, emphasis is on the GSM 05.05 typical urban channel model with a velocity of
10
-4
-10
0
10 20 Signal-to-Interference Ratio (dB)
30
Fig. 3. BER versus SIR, TU50 channel model, proposed semi-blind receiver compared to conventional receiver, Es /N0 = 20 dB.
In Fig. 2, the proposed averaged lower-bound is compared
to JVD with noisy JLSCE and noiseless JLSCE, respectively. The difference between the two results shows the performance degradation due to a channel estimation error, which can be traced to channel noise. The averaged lower-bound is virtually identical to the bit error probability of the JMLSE receiver, which is therefore not depicted. The performance difference to the case of noiseless CE for low SIR values is due to residual ISI, that results from a neglect of averagely strong interferer channel taps in the low SIR region. In Fig. 3, simulation results for the BER versus SIR are depicted for the proposed receiver with six iterations. The authors observed that a higher number of iterations does not lead to further improvements. The BER simulation results show that the proposed receiver is capable to significantly reduce the BER compared to a conventional GSM receiver. For an SIR down to 5 dB the BER performance is comparable to JLSCE/JVD, which requires the perfect knowledge and synchronization of the training sequences of the desired and the interfering users. This result indicates that synchronous GSM networks are not necessary. For an SIR down to 0 dB (where the average signal power of the interfering user is equal to the signal power of the desired user) the BER is below 10−2 .
VII. C ONCLUSIONS A receiver based on a sub-optimum iterative algorithm to combat CCI by means of joint CE and CCI cancellation was presented. It is semi-blind in the sense that the data and the training sequence of the interfering users are assumed to be unknown. The receiver can be implemented in any – even existing – TDMA mobile radio system. It is downward compatible to conventional TDMA receivers. The branch metric (8) and thus the receiver can easily be extended to take antenna diversity into account. However, unlike concurrent receivers, antenna diversity is not mandatory. This makes an implementation possible for both uplink and downlink. Simulation results were presented for the popular GSM system. It was shown that in spite of its sub-optimality and its simplicity, the proposed receiver is capable to achieve a good BER performance even for frequency-selective fading channels like TU with moderate velocity. For an SIR down to 0 dB, the BER is below 10−2 at an SNR of Es /N0 = 20 dB. The proposed receiver is also suitable for the case that training symbols of the interfering users are available. In this case, the performance will improve further. Unlike JLSCE, the proposed receiver does not need overlapping training sequences and can therefore be used with arbitrary large shifts of the training sequences in asynchronous networks. A modification to accept a priori information and to deliver soft outputs is straightforward.
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