1

Iterative Single Antenna Interference Cancellation: Algorithms and Results Wei Jiang, Student Member, IEEE, and Daoben Li

Abstract— The capacity of the cellular mobile communication systems can be significantly improved by single antenna interference cancellation (SAIC) techniques. The paper analyzes several soft-input soft-output detectors in iterative SAIC receivers based on the turbo principle, and compares their performances and complexities. Among them, the concurrent MAP (maximum a posteriori probability) receiver, which detects single-user signal and exchanges the soft information between co-channel users, is found to provide a good balance between the performance and the complexity. It can perform nearly the same as the joint MAP algorithm and achieve the single-user matched-filter bound (MFB), while its complexity only grows linearly with the number of co-channel signals. Other reduced-complexity algorithms, such as the Rake Gaussian (RG) approach and soft interference cancellation with MAP equalization (SIC-MAP), also have satisfactory performance for BPSK modulation when the CCI signal can be decoded. Index Terms— Co-channel interference (CCI), inter-symbol interference (ISI), single antenna interference cancellation (SAIC), iterative receiver, turbo equalization.

I. I NTRODUCTION In the cellular mobile communication system, the capacity is in most cases limited by the co-channel interference (CCI). Especially for the downlink, where the receiver is usually equipped with only one antenna, due to the cost and size limitation, to cancel the CCI is quite difficult. Moreover, the multipath dispersion in the mobile channel causes inter-symbol interference (ISI), which adds to the complexity of the receiver. For time division multiple access (TDMA) system, such as the GSM system, complex equalizer has to be utilized to combat severe ISI. In this situation, various single antenna interference cancellation (SAIC) [1] algorithms have been proposed to combat both the CCI and ISI. It’s reported in [2] that SAIC techniques can provided significant gain in carrierto-interference ratio (CIR) and improve the system capacity by 39-57% for the GSM networks. Among various SAIC techniques, joint maximum-likelihood sequence estimation (JMLSE) [3]–[5] is the optimal algorithm, which detects the desired signal and the CCI signal jointly under the maximum-likelihood criterion. The complexity of JMLSE is prohibitive because it grows exponentially with the sum of the multipath number of the desired signal and CCI Copyright (c) 2008 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. The research was supported by National Natural Science Foundation of China (NSFC) under grant no. 90604035. W. Jiang and D. Li are both with the School of Information Engineering, Beijing University of Posts and Telecommunications, Beijing, China (e-mail: [email protected]; [email protected]).

signal. To reduce the complexity of the joint detector, many suboptimal algorithms have been suggested in the literature, such as joint reduced-state sequence estimation (JRSSE) [6], [7] and joint delayed-decision feedback sequence estimation (JDDFSE) [8], [9]. Other existing SAIC techniques try to cancel the CCI and ISI in two stages. The CCI is suppressed in the first stage, which can be implemented by a linear filter [10]–[14], or an interference canceller based on the feedback of the tentative decision of the CCI signal [15], [16], and the ISI is cancelled with an equalizer or a trellis based detector in the second stage. Most of linear-filter SAIC method is only capable of cancelling a single one-dimensional modulated interference, such as BPSK, GMSK, hence cannot be used in the highdata-rate system employing complex modulations, e.g. EDGE system. The partitioned Viterbi algorithm (PVA) proposed in [16] employs cross-coupled parallel VA detectors, each for one signal, and cancels the co-channel signal by tentative decision. Its complexity grows linearly with respect to the number of co-channel signals. Hard decision is used in the interference cancellation and there is a significant performance loss compared to the JMLSE algorithm. Recently, turbo equalization [17], [18] has been proved to be an attractive solution for the near-optimal receiver for coded transmission in ISI channel. Its iterative structure can be generalized to the detection and decoding of cochannel signals directly. The optimal joint soft-input softoutput (SISO) detector can be implemented by the joint maximum a posteriori probability (JMAP) algorithm [19]– [21], which also has prohibitive complexity, just like the JMLSE algorithm. Some low-complexity algorithms have been utilized to cancel the CCI and ISI jointly in an iterative manner, such as JRSSE/JDDFSE with soft output [22] and bidirectional list-sequential (LISS) interference cancellation [23]. However, they have notable performance loss compared to the JMAP algorithm. The paper hereby proposes an iterative receiver whose complexity only grows linearly with the number of co-channel users. It’s in a concurrent structure and is based on a modified MAP detector for single user, which accepts the soft information of the interferers. The soft information can be provided by the SISO decoders or the SISO detectors for the interfering users. Near-optimal performance can be achieved by the simplified receiver with several iterations. We also apply some other SISO detection algorithms into the reducedcomplexity iterative SAIC receiver, including soft interference cancellation (SIC) [24], [25] and Rake Gaussian [26] method. Their performances are found relatively poor in medium CIR

2

C n!

xC n ! FEC Encoder

Interleaver

Symbol Mapper

Interleaver

ISI channel

y n!

hC

La ,C

Le ,C

" FEC Encoder

Interleaver

Symbol Mapper

ISI channel

hI v n!

I n!

xI n !

Co-channel Interference

Fig. 1.

y

Le, I

II. S YSTEM M ODEL The paper concerns the wireless communications system with co-channel interference. There is only one antenna at the receiver, as is typically the case for the downlink of cellular systems. For the simplicity of presentation, we consider a simple system model depicted in Fig. 1, and assume there is only one dominant CCI signal. Two co-channel users have the same transmit structure. For each one, data bits are first encoded by a convolutional code, and then permuted by an interleaver. The bits are then mapped into BPSK symbol blocks. The SAIC algorithms presented below can be generalized to the case of multiple interferers or complex modulations, such as QPSK and 8PSK. Complex baseband notation is used throughout the paper. Denote a symbol block as x = {x(n)} (1 ≤ n ≤ N ), with x(n) ∈ {+1, −1}, and N being the length of the block. We use xC to indicate the symbols of the desired user, and xI the interfering user. Suppose the signals of the desired user and the interfering user are transmitted over the multipath Rayleigh fading channel of the same ISI length L, which are denoted as hC = [hC (0), hC (1), · · · , hC (L − 1)] and hI = [hI (0), hI (1), · · · , hI (L−1)], respectively. The received signal can be expressed as y(n) =

hC (l)xC (n − l) +

l=0

|

{z

}

|

SISO Decoder

Fig. 2.

Iterative SAIC receiver with joint SISO detector

(CIR) as h i hP i 2 L−1 2 E |C(n)| E l=0 |hC (l)| C i = hP i. = h 2 L−1 2 I E |I(n)| E l=0 |hI (l)|

hI (l)xI (n − l) +v(n), {z

I(n)

}

(1) where {v(n)} is the complex valued i.i.d Gaussian noise with mean zero and variance N0 /Eb , and Eb is the average received energy of the desired signal per bit. The first term C(n) in Eq. (1) is the signal of the desired user, and the second term I(n) is the interference. We define the carrier-to-interference ratio

(2)

The second equality in Eq. (2) holds because the symbol sequences can be regarded as i.i.d random variables with unit variance. III. I TERATIVE SAIC WITH J OINT MAP D ETECTOR Based on the turbo principle, the iterative receiver for SAIC can be implemented by employing SISO decoder and joint SISO detector, as illustrated by Fig. 2. The joint detector accepts the received symbol sequence and the extrinsic information about the coded bits of the desired user and the CCI user, which is usually in the form of logarithm likelihood ratio (LLR) and is provided by the SISO decoders. The output of the joint detector includes the extrinsic information about the coded bits of all users, which is then deinterleaved and passed into the SISO decoders. The extrinsic LLR output of the decoders is fed back to the SISO detector as the a priori information. The iteration goes on until a specific stopping criterion is satisfied. Since we concentrate on the performance and complexity of the SISO detector only, the decoder is always implemented with the optimal MAP algorithm throughout this paper. The optimal joint SISO detector [23] calculates the a posteriori LLR of each symbol after receiving the noiseimpaired sequence y = [y(1), y(2), · · · , y(N + L − 1)]. It can be expressed as L [x(n)] = ln

P [x(n) = +1|y] P [x(n) = −1|y] P

= ln P

(xC ,xI ):x(n)=+1

P [(xC , xI )|y]

(xC ,xI ):x(n)=−1 P

l=0

C(n)

Deinterleaver

Interleaver

range. The remainder of this paper is organized as follows. The following section presents the model of communications system with CCI and ISI. The iterative receiver with joint MAP detector is described in section III. The reduced-complexity receivers, implemented with the RG approach and the SIC-MAP algorithm, are presented in section IV and V, respectively. And in section VI, the modified MAP detector accepting the soft information of the interferers is introduced. The concurrent iterative receiver using the proposed detection algorithm is presented in this section as well. The numerical results are given in section VII. At last, the conclusion is outlined in section VIII.

L−1 X

SISO Decoder

Joint SISO Detector La , I

Communications system model with CCI and ISI

L−1 X

Deinterleaver

[(xC , xI )|y]

(3) ,

where x(n) can either be a symbol of the desired user or the interfering user. The calculation of the LLR in Eq. (3) can be implemented by the trellis-based MAP algorithm [19]– [21]. Since the ISI length is assumed to be the same for the two co-channel users, and binary symbol is used in the transmission, the number of states in the trellis equals 22(L−1) . The complexity of the joint MAP algorithm is prohibitive even for moderate L. The increase of the interferer number also makes the algorithm infeasible.

3

IV. I TERATIVE SAIC WITH R AKE G AUSSIAN A PPROACH The Rake Gaussian approach has been utilized to detect the interleave-division multiple-access (IDMA) [26] signal in frequency selective fading channels. This method approximates the mixture of the multiple-access interference (MAI) and the ISI as random Gaussian noise, which makes the complexity of the receiver only grows linearly with the co-channel user number and the ISI length. Combined with the low-rate errorcorrecting code, the RG detector can achieve satisfactory performance for IDMA system. Due to the similarity of the signal model between the IDMA system and the CCI model targeted in this paper, the RG approach can be used in the SAIC receiver naturally. Of course, since the co-channel users share the same interleaver, they can only be distinguished by the wireless channels, which should be independent because of the spacial separation of different transmitters. To illustrate the principle of the RG approach, we rewrite Eq. (1) as y(n, l) =hC (l)xC (n − l) L−1 X

+

hC (l′ )xC (n − l′ ) + I(n) + v(n),

(4)

l′ =0,l′ 6=l

{z

|

w(n,l)

}

where w(n, l) is the combination of the CCI, ISI and additive noise impairing the l-th delayed sample of symbol xC (n − l). As in [26], we approximate w(n, l) as Gaussian distributed random variable. Its mean and the variance can be calculated based on the a priori LLR of the symbols. Suppose the a priori LLR of interferer symbol xI (n) is La,I (n) = ln [P (xI (n) = +1) /P (xI (n) = −1)], then the a priori mean and variance of xI (n) are [25]   La,I (n) I , (5a) µa,x (n) = tanh 2 2 2,I σa,x (n) = 1 − µIa,x (n) . (5b)

Similarly, according to the a priori LLR of the target-user symbol La,C (n), we can get the mean and variance of xC (n), 2,C denoted as µC a,x (n) and σa,x (n), respectively. Because of the independence of the symbols, the mean and the variance of w(n, l) can be calculated as L−1 X

µw (n, l) =

′ hC (l′ )µC a,x (n − l )

l′ =0,l′ 6=l

+

L−1 X

hI (l′ )µIa,x (n − l′ ),

(6a)

l′ =0

2 σw (n, l) =

1 2

L−1 X

2

2,C |hC (l′ )| σa,x (n − l′ )

l′ =0,l′ 6=l

L−1 1X 2 2,I + |hI (l′ )| σa,x (n − l′ ) + σ 2 , 2 ′

(6b)

l =0

2

where σ = N0 /(2Eb ), and the variances of w(n, l) on the in-phase and quadrature components are assumed to be equal.

Then, based on the received y(n + l, l) and the Gaussian approximation of w(n + l, l), we are able to calculate the extrinsic LLR of xC (n) by Lle,C (n) = ln = ln

P [y(n + l, l)|xC (n) = +1] P [y(n + l, l)|xC (n) = −1] i h 2 w (n+l,l)−hC (l)| exp − |y(n+l,l)−µ 2σ2 (n+l,l) w

2 (n + l, l) 2πσw

h i 2 w (n+l,l)+hC (l)| exp − |y(n+l,l)−µ 2 2σ (n+l,l)

(7)

w − ln 2 (n + l, l) 2πσw   y(n + l, l) − µw (n + l, l) =2ℜ h∗C (l) · . 2 (n + l, l) σw

Assuming the extrinsic information obtained from the L paths is independent, the total extrinsic LLR of xC (n) can be obtained by Rake combining: Le,C (n) =

L−1 X

Lle,C (n) .

(8)

l=0

The extrinsic LLR of interferer symbol xI (n) can be calculated similarly. Then the extrinsic information provided by the RG detector is delivered to the SISO decoders on the co-channel branches, and one iteration is completed by feeding back the extrinsic information output of the SISO decoders. The process is the same as that shown in Fig. 2. It’s obvious that the complexity of the RG detector only grows linearly with the number of co-channel users and the ISI length. V. S OFT I NTERFERENCE C ANCELLATION AND MAP E QUALIZATION The complexity of the joint MAP detector described in section III is prohibitive because it grows exponentially with the number of co-channel users. If we decouple the CCI signals first and then use the MAP equalizer [21] to calculate the symbol LLRs of individual users, the complexity can be reduced significantly. A simple approach to decouple the CCI signals is by cancellation. Previous works on SAIC use hard decision to cancel the co-channel interference [15], [16], which may introduce error propagation and limit the performance. With the aid of the SISO decoder, the CCI can be cancelled in a soft manner [24], [25], and the receiver performance can be improved by soft-information exchange between the interference canceller, the MAP equalizer and the SISO decoder. The structure of the iterative SAIC receiver with SIC-MAP detector is illustrated in Fig. 3, which is similar to that of the PVA algorithm [16]. The cancellation of the co-channel interference is performed as follows. According to the a priori LLR of the symbols xI (n), La,I (n), provided by the SISO decoder on the interference branch, the mean of xI (n), µIa,x (n), is calculated as in Eq. (5a). And the mean of the interference I(n) is µa,I (n) =

L−1 X

hI (l′ )µIa,x (n − l′ ).

(9)

l′ =0

Then the interference is cancelled by y ′ (n) = y(n) − µa,I (n).

(10)

4

La ,C

y′

y

MAP Equalizer

Le,C

MAP Equalizer

Le, I

a posteriori LLR of the symbol can be calculated according to P [xC (n) = +1|y] LC (n) = ln P [xC (n) = −1|y] P (11) ′ (s′ ,s):xC (n)=+1 P (s , s, y) = ln P . ′ (s′ ,s):xC (n)=−1 P (s , s, y)

Interleaver

Deinterleaver

SISO Decoder

Deinterleaver

SISO Decoder

Soft Interference Canceller

La , I

Interleaver

The joint probability P (s′ , s, y) can be rewritten [21] by Fig. 3. Iterative SAIC receiver with soft interference cancellation and MAP equalization xC ( n )

C (n)

y (n)

ISI channel

y

n−1 1

y ( n)

s′ n − 1 xC ( n ) , C ( n ) v ( n) + I ( n)

(a)

α n −1 ( s′ )

γ n ( s′, s )

N + L −1 n +1

y s n

βn ( s )

(b)

Fig. 4. (a) Simplified signal model for single-user detector and (b) the state transition diagram

P (s′ , s, y) = αn−1 (s′ ) · γn (s′ , s) · βn (s),

where αn−1 (s′ ) is the joint probability P s′ , y1 that the trellis is in state s′ at time n − 1 and the received signal n−1 sequence before
time n is y1 , and βn (s) is the probability N +L−1 N +L−1 P yn+1 |s that the received signal after time n is yn+1 when the trellis is in state s at time n, both can be calculated recursively: X αn (s) = γn (s′ , s)αn−1 (s′ ), (13) s′

βn−1 (s′ ) = The sequence {y ′ (n)} is then passed to the MAP equalizer for the target signal, which corresponds to the upper branch in Fig. 3. The cancellation of CCI for the other co-channel user is performed likewise. Since the co-channel signals are processed separately, the complexity of this SAIC receiver only grows linearly with the number of co-channel users. Though, because the MAP equalizer is used in each branch, the complexity still grows exponentially with the ISI length. VI. C ONCURRENT MAP I TERATIVE SAIC R ECEIVER The RG approach discussed in section IV assumes the extrinsic information derived from different delayed samples is independent, which is not true due to the inter-symbol constraint. This simplification may limit the SAIC receiver performance. For the SIC-MAP receiver, this is not a problem, because the ISI is cancelled by the MAP equalizer, which is optimal in the single-user sense. However, the SIC-MAP receivers assumes the CCI is totally removed at the SIC stage, which in fact is impossible. The assumptions made for the reduced-complexity SAIC receivers may cause performance loss compared to the optimal JMAP receiver. In this section, we introduce the concurrent MAP (CMAP) iterative SAIC receiver, which combines the ideas behind the RG approach and the SIC-MAP method. In the CMAP receiver, CCI is approximated as Gaussian distributed, and its soft information is utilized in the MAP single-user detection (SUD). The a priori information of the interferers can be provided either by the detectors or by the decoders on the other branches, as leads to two different types of iterative receiver. A. SISO Single-User Detector The system model shown in Fig. 1 can be simplified to Fig. 4(a) for the detection of the target signal. Based on the trellis representation of the signal model shown in Fig. 4(b), where s′ and s are the states of a trellis path at time n − 1 and n, the

(12)


n−1

X

γn (s′ , s)βn (s).

(14)

s

γn (s′ , s) in Eq. (12) is the branch transition probability: γn (s′ , s) = P (y(n)|s′ , s) P (xC (n)) .

(15)

The SISO detector has three inputs, which are the received signal y(n), the a priori information of xC (n), and the a priori information of the CCI signal I(n). It has been shown that the CCI signal can be approximated as colored Gaussian noise when detecting the desired signal [27]. With this assumption, we can use its mean and variance to measure the distribution of the interference. Let µa,I (n) be the a priori mean of I(n), 2 and σa,I (n) be the variance on the in-phase and quadrature components of I(n). We ignore the correlation of I(n), which 2 is reasonable when σa,I (n) is relatively lower than σ 2 . Then the conditional probability density function of y(n) in Eq. (15) is 1 P (y(n)|s′ , s) = 2 (n)) 2π(σ 2 + σa,I   2 ′ |y(n) − µ (n) − C(n, s , s)| . a,I  · exp − 2 (n) 2 σ 2 + σa,I (16) where C(n, s′ , s) represents the target ISI signal on the branch from state s′ to state s. Given the a priori LLR of xC (n), La,C (n), we can get the probability distribution of xC (n) as P (xC (n)) =

exC (n)La,C (n)/2 . + e−La,C (n)/2

eLa,C (n)/2

(17)

According to Eq. (16) and (17), γn (s′ , s) can be calculated as   2 ′ |y(n) − µa,I (n) − C(n, s , s)|    γn (s′ , s) =K · exp − 2 (n) 2 σ 2 + σa,I   1 · exp xC (n)La,C (n) , 2 (18)

5

La ,C

Interleaver La ,C

µa , I , σ a2, I

Le,C

Deinterleaver

SISO SUD y

µ e ,C , σ

µa , I , σ a2, I La , I

Le, I

SISO SUD

SISO SUD

SISO Decoder

a priori mean and variance calculator

2 e ,C

µe , I , σ e2, I

µa ,C , σ a2,C

Deinterleaver

µ a ,C , σ

Deinterleaver

SISO Decoder

Le, I

Deinterleaver

SISO Decoder

2 a ,C

La , I

Interleaver

Interleaver

Fig. 6. Fig. 5.

Interleaver

y

SISO SUD

SISO Decoder

Le,C

Iterative concurrent MAP SAIC receiver of type II

Iterative concurrent MAP SAIC receiver of type I

where K is a coefficient irrelevant to the calculation of LLR in Eq. (11). The output of the SISO detector includes the extrinsic information of the symbols xC (n) and the a posteriori mean and variance of the target signal C(n). The extrinsic information of xC (n) is obtained by excluding the a priori information from the a posteriori LLR [20], i.e., Le,C (n) = LC (n) − La,C (n),

(19)

which is passed to the SISO decoder in the iterative receiver. The mean and variance of C(n) can be used as the a priori information for other CCI branches in the concurrent receiver, as will be described in the next subsection. They are calculated based on the a posteriori probability of the branches at stage n, which is P (s′ , s, y) Pn (s′ , s|y) = P . P (s′ , s, y)

(20)

(s′ ,s)

The a posteriori mean of C(n) is X µe,C (n) = Pn (s′ , s|y)C(n, s′ , s),

(21)

(s′ ,s)

and the a posteriori variance of C(n) on the in-phase and quadrature components is 1 X 2 2 σe,C (n) = Pn (s′ , s|y) |C(n, s′ , s) − µe,C (n)| . (22) 2 ′ (s ,s)

The SISO detection algorithm presented above is based on the MAP detection algorithm in the ISI channel [21], except that the a priori information of the interferers is required, and it outputs the a posteriori mean and variance of the ISI signal. Its complexity is similar to the traditional MAP algorithm, with the extra complexity in calculating the mean and variance. The total complexity is proportional to the number of states in the trellis, which equals to 2L−1 . The MAP SISO-SUD algorithm can be simplified by the log-domain implementation. Other simplification method, like the Max-Log-MAP algorithm, the SOVA algorithm, etc, can also be used in the SISO single-user detection. The readers can refer to [28], [29] for details. B. Iterative Concurrent MAP SAIC Structure The SISO single-user detector presented in the last subsection is used for the detection of the desired user signal.

In fact, it can also be used for the co-channel interferer, as long as its channel state information (CSI) has been acquired by the receiver. When detecting the CCI signal, the desired signal {C(n)} is regarded as the interference, and its mean and variance are used as the a priori information. Based on this understanding, we design the iterative SAIC receiver using the SISO detectors for single users, as illustrated by Fig. 5. Since the receiver is in concurrent structure, and the SISO single-user detector employs the modified MAP algorithm, we call it Concurrent MAP (CMAP) receiver. In the receiver shown in the figure, the a priori information of CCI is provided by the SISO detectors, which we denote as type-I structure. The CMAP receiver has two concurrent iterative detection branches, each for one user. In Fig. 5, the upper branch is for the desired user, where the SISO-SUD module accepts the channel output y, the a priori LLR delivered by the SISO decoder, and the a priori mean and variance of the interferer provided by the SISO-SUD module for the CCI signal in the other branch. The extrinsic LLR output of SISO-SUD is deinterleaved and passed to the SISO decoder. The extrinsic information output of the decoder is fed back to the SISO-SUD to perform turbo iteration. The case is the same for the lower branch for the CCI signal, in which the a priori information of the interference is provided by the SISO-SUD module in the upper branch. To start the iteration, the a priori LLR of xC (n) and the a priori mean of the interferer can be initialized as La,C (n) = 0, ∀n µa,I (n) = 0, ∀n

(23)

2 and the a priori variance σa,I (n) can be initialized based on the estimation of the interference power. The a priori information on the CCI branch can be initialized likewise (parallel iteration), or it can wait for the output of the upperbranch SISO-SUD (serial iteration). The CMAP SAIC receiver can also be implemented in type II, where the a priori mean and variance of CCI is calculated based on the soft information output of the SISO decoders. Taking the detection of the target signal as the example, given the a priori LLR of xI (n), La,I (n), the mean and the variance of xI (n) can be calculated by Eq. (5). Then, the mean of the CCI signal, I(n), is calculated by Eq. (9), and the variance of

6

I(n) is

0

2 σa,I (n)

1 = 2

′

2

|hI (l )|

2,I σa,x (n

′

− l ).

(24)

l′ =0

The mean and the variance of C(n) can be obtained from La,C (n) likewise. The a priori LLR La,I (n) and La,C (n) are set zero in the first iteration. Fig. 6 depicts the principle of the type-II CMAP receiver. Note that for this type receiver, the SISO SUD algorithm described in the last subsection can be simplified, because the calculation of the a posteriori mean and variance by Eq. (21) and (22) is not needed. The overall complexity of the type-II CMAP receiver is a little lower than type I, because the calculation of the a priori mean and variance for the former only has linear complexity with respect to L, rather than exponential for the latter. The CMAP SAIC receivers discussed above are only for the joint detection of two co-channel users. The generalization to more-user case is straightforward. If the number of co-channel users is J, then we use J concurrent iterative detectors at the receiver, each for one user. When detecting one user, the other J − 1 users act as the interference, so the a priori means and variances, obtained from the detectors or the decoders, are summed up and fed to the input of the SISOSUD module for the desired user. Since we only need to add one concurrent branch for one additional CCI user, the complexity of the receiver grows linearly with the number of co-channel users for joint detection. So the complexity is proportional to J · 2L−1 , if the ISI channels of all users have L taps. Note that for the joint MAP receiver, the complexity grows exponentially with J, that is 2J(L−1) . So the proposed concurrent MAP receiver has relatively lower complexity, yet near-optimal performance can be achieved, as will be shown in the next section. VII. N UMERICAL R ESULTS A. Simulation Conditions The performance of the iterative SAIC receivers presented in this paper is evaluated and compared with each other by numerical simulations. In the simulations, a rate-1/2 convolutional code with 16 states is used. One coded data frame is divided into ten symbol blocks, each with two hundred symbols. Random interleaver of length 2000 is utilized, which is the same for the two co-channel users. At the receiver, the SISO decoders employ the MAP algorithm, and the maximum iteration number is set to be ten in most cases. The channel is assumed to be Rayleigh distributed in amplitude and uniformly distributed in phase. The channel is in quasi-static block fading, i.e., the fading coefficients keep constant during one symbol block transmission, and is independent for different blocks. The ISI channels for two cochannel users are both assumed to have four independent taps, i.e., L = 4, and the average power on each tap is the same. The channel state information of both users, as well as the noise power, is perfectly known at the SAIC receiver. The presented SAIC receivers are extended to complex modulation, e.g. QPSK, in the simulations. Though, BPSK is mainly considered for the convenience of comparison with

Mean Square Error and a posteriori Variance

10

L−1 X

mean square error a posteriori variance CMAP I

−1

10

−2

10

E / N = 4 dB b

−3

0

CMAP II

10

Eb/ N0 = 6 dB −4

10

−5

10

1

2

3

4

5 6 7 Number of Iterations

8

9

10

Fig. 7. Mean square error of the soft decision and the a posteriori variance (normalized by the signal power) for the target user signal in the iterative CMAP receiver of two types, Case I, C/I = 0dB, BPSK modulation.

other conventional algorithms. For the number of interference, we consider two cases: • Case I: Only one CCI user. The ratio of the target signal power to the CCI power is denoted as CIR. • Case II: One dominate interferer and four equal-power residual interferers. Different dominant-to-residual interference ratio (DIR) is considered. CIR is defined as the ratio of the target user power to the total interference power in this case. Only the dominate interference is considered in various SAIC receivers. To make the comparison more comprehensive, we also evaluate the following receivers: • Conventional single-user receiver, where MAP algorithm is used for iterative detection and decoding, and CCI is ignored. It’s denoted as SMAP receiver below. • Mono interference cancellation (MIC) [13] algorithm followed by MAP turbo equalization. A four-tap linear filter adapted to the channel state is used to cancel CCI perfectly. Note that MIC algorithm is only capable of dealing with one-dimensional modulated interference. • JDDFSE algorithm combined with turbo iteration [9], [22]. Fixed state allocation is used, and the number of states is set to 16 and 256 for BPSK modulation and QPSK modulation respectively, so that its complexity is not lower than CMAP receiver. Basically, the desired signal and the dominate interference are assumed frame-synchronous, so that both can be decoded. The more practical case when the two users’ frames are nonsynchronized is also considered, and corresponding results will be shown blow. B. Convergence of Iterative SAIC Receivers We first examine the effectiveness of the CMAP receiver by comparing the a posteriori variance of the target signal, which is obtained from either the SISO detector (type I) or the SISO decoder (type II), to the mean square error (MSE) of the a

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posteriori mean, which can be regarded as the estimation of the target signal. The MSE is calculated based on the statistics of 100, 000 symbols, and the a posteriori variance is also averaged over these samples. The results for CCI Case I with C/I = 0dB are shown in Fig. 7, where the MSE and the a posteriori variance are both normalized by the power of the target signal. It can be found that the a posteriori variance matches the MSE well for both two types of CMAP receiver. The MSE floor of the two types is almost the same, but that of the typeII CMAP receiver is reached by fewer iterations, which is because the soft information provided by the SISO decoder is more accurate than the detector output in the same iteration. Based on this, similar performance can be predicted for the two types, as well as faster convergence of type-II receiver. To show the difference in efficiency of various iterative SAIC algorithms, we compare the average number of iterations required to decode the target-user data bits correctly for different SNRs and CIRs in case I. In the simulation, if a data block cannot be correctly decoded after ten iterations, the required number of iterations is recorded as ten for this block. The results are given in Fig. 8. We find that for C/I = 0dB, the SMAP receiver always costs the most iterations, because it can hardly decode the data bits correctly. On the other hand, the JMAP algorithm needs the least iterations, and one iteration is enough in most cases when Eb /N0 > 8dB. The type-II CMAP receiver needs about one more iteration than the JMAP receiver on average, and the type-I CMAP receiver needs additional half iteration. The RG approach requires about two more iterations than JMAP, which is a little more than that of the SIC-MAP receiver. The iteration number for MIC and JDDFSE is high for low SNR, but it goes down close to JMAP when SNR is high enough. When CIR varies, the results shown in Fig. 8(b) indicate that for iterative SAIC receivers, the mean iteration number is small in the low CIR and the high CIR region, but is relatively large in the medium CIR region.

C. Performance in Case I Fig. 9 shows the bit error rate (BER) performances of the target user with respect to SNR in case I for various iterative SAIC receivers. BPSK modulation is used, and CIR is set to 0dB to get these results, which means the received CCI signal has the same power as the desired signal. Also shown in the figures is the matched filter bound (MFB) [30] for single user with the same convolutional coding in the same channel, where the multipath is assumed to be ideally separated, and maximum-ratio combining is employed to achieve multipath diversity gain. Since this is the ideal case of perfect ISI elimination and no CCI presence, the MFB is a lower bound for the iterative SAIC receivers. It’s shown in Fig. 9(a) that the MFB can be achieved by the joint MAP receiver within six iterations. But the BER of the SMAP receiver keeps in a high level in the presence of the strong interference, and it can hardly be lowered down by turbo iterations. As to the other simplified receivers, the RG receiver and the SIC-MAP receiver, have about 2dB loss compared to MFB after six iterations, and this gap cannot be narrowed by further iterations. The performance of MIC and JDDFSE is even worse. For instance, MIC has about 5dB loss compared to MFB, though it can significantly lower the error floor of SMAP receiver. Considering that the RG algorithm has the lowest complexity and can achieve relatively good performance, it is a practical choice for the low-cost mobile devices. The performance of the CMAP receiver is shown in Fig. 9(b). Both the type I and type II receiver can achieve the single-user MFB after several iterations. Fig. 10 shows the performance of different receivers with varying CIR for case I, when Eb /N0 of the desired user is 4dB. We see that the algorithms perform differently in different CIR regions. In the low CIR region (lower than −4dB in the simulated case), RG, SIC-MAP and CMAP receivers almost perform as well as the JMAP receiver after six iterations. This is because the interfering co-channel signal is strong, hence can be correctly detected and removed in the

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iterations. In the medium CIR region (near 4dB), however, the CMAP receivers perform much better than RG receiver and SIC-MAP receiver, and there is only a small margin between JMAP and CMAP receivers when Eb /N0 = 4dB. When the CIR grows to more than 12dB in the simulation, most of the receivers, including the SMAP receiver, almost perform the same after six iterations. The simple RG receiver or the SMAP receiver is more preferable then. The JDDFSE algorithm is worse than SMAP for high CIR. This is because fixed state allocation is used, by which the last tap of the target signal is always discarded in the reduced-state trellis. Adaptive state allocation proposed in [9] can improve its performance. It’s interesting to note that while the BER of the SMAP receiver decreases with the increase of CIR, that of the iterative SAIC receivers have the peak at medium CIR, more exactly, when CIR is close to SNR. Moreover, their performances at higher CIR are a litter worse than low CIR. Similar results

have also been observed for the JMLSE receiver [1], [31] and other joint detection SAIC algorithms [9], [23]. It’s explained by the fact that when the power of the CCI signal is close to that of the noise, it’s more difficult for the receiver to distinguish them, and that when the CCI power is high enough, the path distance in the joint trellis may larger than low CCI power. The extension of the iterative SAIC algorithm to QPSK modulation produces the results in Fig. 11, where the CIR is set 0dB in Case I. Note that MIC receiver is unworkable in this case, and JMAP receiver is too complex to be implemented. RG receiver performs quite poor in this situation and its performance is not shown. The CMAP receivers require 12 iterations to get the performance close to MFB at high SNR, and they gain about 6dB compared to SIC-MAP and JDDFSE receivers.

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0dB, the gap between the simplified JMAP and single-user MFB is about 1dB, and the simplified CMAP receiver of two types have about further 1dB loss at high SNR compared to JMAP. Though, there is significant advantage (about 3dB gain) for CMAP comparing to MIC SAIC algorithm. In the low-CIR and high-CIR range, the CMAP receivers can still perform nearly the same as JMAP after six iterations.

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D. Performance in Case II We consider the more practical case when there are multiple interferers. The situation is defined as Case II above, where various SAIC receivers only try to cancel the dominate interference. The bit error rate performance of the SAIC receivers in case II is shown in Fig. 12, where Eb /N0 is 12dB and different CIR and DIR values are considered. For moderate DIR value being 3dB, Fig. 12(a) shows the CMAP receiver of two types can perform the same as JMAP receiver, while JDDFSE receiver has about 4dB lose in CIR. The RG receiver and the SICMAP receiver have similar performance, both are worse than CMAP by about 2dB. Fig. 12(b) shows the variance of SAIC receiver performance with DIR when CIR is 0dB. Again, RG and SIC-MAP algorithms perform poorer than CMAP by about 2dB. The BER of SMAP grows slightly with the increase of DIR. This is because the white Gaussian noise approximation of the interference is more accurate for low DIR. E. Frame Non-synchronized Case We have assumed above that the desired user and the dominate interferer are frame-synchronous, so that both can be decoded in the turbo iteration, which is quite an ideal assumption in practice. If the interferer is not frame-synchronized with the desired user, the decoding of the co-channel signal is not feasible. In this case, supposing the two co-channel users are bursesynchronous, we simplify the proposed CMAP receivers by removing the decoder for the interferer and still use SISO SUD to detect co-channel signals. Then, the detector in the CCI branch receive no a priori information La,I . For the type-II CMAP receiver, the a priori mean and variance of the interference are calculated based on the LLR output of SISO SUD. JMAP receiver can be simplified likewise. Fig. 13 compares the performance of the simplified CMAP receivers with JMAP and MIC in CCI case I. When C/I =

Concurrent MAP iterative SAIC receiver is introduced in this paper. The SISO detector for each co-channel signal branch used in the CMAP receiver is based on the MAP algorithm, which accepts the a priori information, i.e., the mean and variance, of the CCI signal, and outputs the a posteriori mean and variance of the target ISI signal. The a priori information of the CCI signal in the CMAP receiver can be provided by the SISO detectors or the SISO decoders in the other branches. The latter scheme makes the iteration converge faster. Since the CMAP receiver is based on singleuser detection, its complexity only grows linearly with the number of co-channel users. The performance of the CMAP receiver is compared to other iterative SAIC receivers by numerical simulations, including JMAP, RG, SIC-MAP, MIC, and JDDFSE. It’s found that the CMAP receivers are superior to other reduced-complexity algorithms on the condition that perfect channel state information for co-channel users can be obtained. They perform nearly the same as the optimal JMAP receiver, and can achieve the single-user matched filter bound when CIR is as low as 0dB. However, the RG receiver and the SIC-MAP receiver also have satisfactory performance for BPSK modulation when the CCI signal can be decoded. The RG approach is suggested in this case because of its low complexity. To achieve near-optimal performance in the medium CIR situation, CMAP receiver should be utilized. For the case when CIR is sufficiently high, the MAP equalizer ignoring CCI is also applicable. Ideal channel estimation for both co-channel users is assumed in the simulations. Practical estimation can be implemented by pilot signal aided algorithms, e.g. joint channel estimation [4], or adaptive semi-blind channel estimation techniques [31] when the training sequence of co-channel signal is unavailable. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for pointing out the references [10], [13], [16], [22] and their suggestions that improved the manuscript. Wei Jiang would also like to thank Dr. Yong Mo for helpful discussion about the work. R EFERENCES [1] P. A. Hoeher, S. Badri-Hoeher, W. Xu, and C. Krakowski, “Singleantenna co-channel interference cancellation for TDMA cellular radio systems,” IEEE Wireless Communications, vol. 12, no. 2, pp. 30–37, 2005. [2] A. Mostafa, R. Kobylinski, I. Kostanic, and M. Austin, “Single antenna interference cancellation (SAIC) for GSM networks,” in IEEE 58th Vehicular Technology Conference (VTC 2003-Fall), vol. 2, Orlando, Florida, USA, 2003, pp. 1089–1093.

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Fig. 12.

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[3] W. Van Etten, “Maximum likelihood receiver for multiple channel transmission systems,” IEEE Transactions on Communications, vol. COM-24, no. 2, pp. 276–283, 1976. [4] P. A. Ranta, A. Hottinen, and Z.-C. Honkasalo, “Co-channel interference cancelling receiver for TDMA mobile systems,” in IEEE International Conference on Communications (ICC), vol. 1, Seattle, WA, USA, 1995, pp. 17–21. [5] K. Giridhar, J. J. Shynk, A. Mathur, S. Chad, and R. P. Gooch, “Nonlinear techniques for the joint estimation of cochannel signals,” IEEE Transactions on Communications, vol. 45, no. 4, pp. 473–484, 1997. [6] M. V. Eyuboˇglu and S. U. H. Qureshi, “Reduced-state sequence estimation with set partitioning and decision feedback,” IEEE Transactions on Communications, vol. 36, no. 1, pp. 13–20, 1988. [7] J. Zhang, A. M. Sayeed, and B. D. Van Veen, “Reduced-state MIMO sequence detection with application to EDGE systems,” IEEE Transactions on Wireless Communications, vol. 4, no. 3, pp. 1040–1049, 2005. [8] A. Duel-Hallen and C. Heegard, “Delayed decision-feedback sequence estimation,” IEEE Transactions on Communications, vol. 37, no. 5, pp. 428–436, 1989. [9] P. A. Hoeher, S. Badri-Hoeher, S. Deng, C. Krakowski, and W. Xu, “Single antenna interference cancellation (SAIC) for cellular TDMA

[10]

[11]

[12]

[13]

[14]

networks by means of joint delayed-decision feedback sequence estimation,” IEEE Transactions on Wireless Communications, vol. 5, no. 6, pp. 1234–1237, 2006. P. Chevalier and F. Pipon, “New insights into optimal widely linear array receivers for the demodulation of BPSK, MSK, and GMSK signals corrupted by noncircular interferences-application to SAIC,” IEEE Transactions on Signal Processing, vol. 54, no. 3, pp. 870–883, 2006. J. C. Olivier and W. Kleynhans, “Single antenna interference cancellation for synchronised GSM networks using a widely linear receiver,” IET Communications, vol. 1, no. 1, pp. 131–136, 2007. S. Badri-Hoeher, P. A. Hoeher, and W. Xu, “Single antenna interference cancellation (SAIC) for cellular TDMA networks by means of decoupled linear filtering/nonlinear detection,” in IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), 2006. R. Meyer, W. H. Gerstacker, R. Schober, and J. B. Huber, “A single antenna interference cancellation algorithm for increased GSM capacity,” IEEE Transactions on Wireless Communications, vol. 5, no. 7, pp. 1616–1621, 2006. A. A. Mostafa, “Single antenna interference cancellation (SAIC) method in GSM network,” in IEEE 60th Vehicular Technology Conference

11

(VTC2004-Fall), vol. 5, 2004, pp. 3748–3752. [15] H. Arslan and K. Molnar, “Cochannel interference suppression with successive cancellation in narrow-band systems,” IEEE Communications Letters, vol. 5, no. 2, pp. 37–39, 2001. [16] C. L. Miller, D. P. Taylor, and P. T. Gough, “Estimation of co-channel signals with linear complexity,” IEEE Transactions on Communications, vol. 49, no. 11, pp. 1997–2005, 2001. [17] C. Douillard, M. Jezequel, C. Berrou, A. Picart, P. Didier, and A. Glavieux, “Iterative correction of intersymbol interference: turboequalization,” European Transaction on Telecommunications, vol. 6, no. 5, pp. 507–511, 1995. [18] M. T¨uchler, R. Koetter, and A. C. Singer, “Turbo equalization: principles and new results,” IEEE Transactions on Communications, vol. 50, no. 5, pp. 754–767, 2002. [19] L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Transactions on Information Theory, vol. 20, no. 2, pp. 284–287, 1974. [20] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo-codes,” in IEEE International Conference on Communication (ICC), vol. 2, Geneva, Switzerland, 1993, pp. 1064–1070. [21] G. Bauch, H. Khorram, and J. Hagenauer, “Iterative equalization and decoding in mobile communications systems,” in European Personal Mobile Communications Conference (EPMCC), Bonn, Germany, 1997, pp. 307–312. [22] P. Nickel, W. Gerstacker, and W. Koch, “Turbo equalization for single antenna cochannel interference cancellation in single carrier transmission systems,” in IEEE Global Telecommunications Conference (GLOBECOM), Washington, D.C., US, 2007. [23] C. Kuhn and J. Hagenauer, “Single antenna interference cancellation using a list-sequential (LISS) algorithm,” in IEEE Global Telecommunications Conference (GLOBECOM), vol. 3, 2005, pp. 1604–1608. [24] J. Hagenauer, “Forward error correcting for CDMA systems,” in IEEE 4th International Symposium on Spread Spectrum Techniques and Applications Proceedings, vol. 2, 1996, pp. 566–569. [25] X. Wang and H. V. Poor, “Iterative (turbo) soft interference cancellation and decoding for coded CDMA,” IEEE Transactions on Communications, vol. 47, no. 7, pp. 1046–1061, 1999. [26] P. Li, L. Liu, and W. K. Leung, “A simple approach to near-optimal multiuser detection: interleave-division multiple-access,” in IEEE Wireless Communications and Networking Conference (WCNC), vol. 1, New Orleans, LA, United States, 2003, pp. 391–396. [27] S. N. Diggavi and A. Paulraj, “Performance of multisensor adaptive MLSE in fading channels,” in IEEE 47th Vehicular Technology Conference (VTC), vol. 3, 1997, pp. 2148–2152. [28] P. Robertson, P. Hoeher, and E. Villebrun, “Optimal and sub-optimal maximum a posteriori algorithms suitable for turbo decoding,” European Transactions on Telecommunications, vol. 8, no. 2, pp. 119–125, 1997.

[29] G. Bauch and V. Franz, “A comparison of soft-in/soft-out algorithms for turbo-detection,” in International Conference on Telecommunications (ICT), 1998. [30] F. Ling, “Matched filter-bound for time-discrete multipath Rayleigh fading channels,” IEEE Transactions on Communications, vol. 43, no. 2-4, pp. 710–713, 1995. [31] H. Schoeneich and P. A. Hoeher, “Single antenna interference cancellation: Iterative semi-blind algorithm and performance bound for joint maximum-likelihood interference cancellation,” in IEEE Global Telecommunications Conference (GLOBECOM), vol. 3, San Francisco, CA, United States, 2003, pp. 1716–1720.

Wei Jiang received the B.S. degree in telecommunications engineering in 2003 from Beijing University of Posts and Telecommunications (BUPT), Beijing, China. He is currently working towards the Ph.D. degree in signal and information processing in BUPT. His research interests include communications signal processing, wireless transmission technologies and error correcting codes.

Daoben Li is a tenured professor of Beijing University of Posts and Telecommunications, and an honorary professor of Southwest Jiaotong University. He is a member of Technical Committee of Signal and Information Processing of Chinese Society of Aeronautics & Astronautics and a member of Information & Communication Theory Committee of China Institute of Communication. As a visiting scholar he studied wireless communications at UCLA and Univ. of Hawaii from 1981 to 1984. From 1989 to 1991 he was a visiting professor of Northeast University Boston. From 1994 to 2000, he had been a senior technical consultant of Cylink Inc. and InterDigital Inc. USA. From 1999 to 2005, he had been the Chief scientist of Linkair Comm. Ltd. He mainly focuses on the research of signal and information processing, modulation and coding, and CDMA technology.