Single Antenna Cochannel Interference ... - Semantic Scholar

Single Antenna Cochannel Interference Cancellation in Single Carrier Transmission Systems by Improved Prefiltering and Turbo Equalization Patrick Nickel, Wolfgang Gerstacker, and Wolfgang Koch Institute for Mobile Communications, University of Erlangen–Nuremberg, Cauerstr. 7, 91058 Erlangen, Germany

Abstract In this paper, a joint (multiuser) turbo equalizer performing single antenna interference cancellation (SAIC) for complex–valued modulation schemes is proposed. In order to improve the performance of a reduced–complexity equalizer for intersymbol interference (ISI) channels in different interference situations (overloaded system), an appropriate prefiltering approach is considered first. Oversampling is utilized for prefiltering in order to exploit excess bandwidth of the transmit signals. Additionally, the (inner) equalizer performance is optimized at low complexity by using an M–algorithm for generation of a survivor map on which a reduced–complexity BCJR algorithm for soft output detection is based. Performance is shown for different receiver variants, where the GSM/ EDGE system serves as an application example. It turns out that the proposed algorithm outperforms previously proposed SAIC algorithms for 8PSK, while being fully compatible to the packet data radio transmission schemes of the GSM/ EDGE standard for synchronous networks.

1

Introduction

Single antenna interference cancellation (SAIC) can be employed to improve the capacity of existing single carrier mobile radio networks like GSM/ EDGE (Enhanced Data Rates for GSM Evolution) [1], [2]. SAIC has been discussed in standardization for the downlink of the GSM/ EDGE system, and practical solutions are already available for Gaussian minimum–shift keying (GMSK) modulation, e.g. [3]–[5]. However, also complex–valued 8–ary phase–shift keying (8PSK) modulation has been introduced for GSM/ EDGE, for which algorithms based on the structure of the real– valued signal constellation adopted in GSM are not applicable. Currently, even higher–order modulations like 16–ary quadrature amplitude modulation (16QAM) are considered in standardization [6]. For these modulation schemes, the system gets overloaded in the case of cochannel interference for a single antenna mobile receiver and signals are not separable by linear operations anymore. In order to enable SAIC in a cochannel interference scenario with complex modulation, the application of joint multiuser detection is required. For this, the channel is modeled as multiple–input single–output (MISO) intersymbol interference (ISI) channel. For a mobile radio network employing frequency reuse, the average receive power levels of signals from different origins vary strongly due to large–scale fading (shadowing and path loss) and the major disturbance to the receive signal is caused by a few dominant interferers in most cases. Therefore we assume, that it is sufficient to focus on the strongest interferer within joint equalization. However, as the performance of successive (separate) joint detection and decoding is typically not sufficiently good for the overloaded case, a novel turbo equalization scheme was introduced in [7] in order to enable SAIC for complex–valued modulation with satisfying performance. In this paper, we concentrate on prefilter design and the optimization of the (inner) equalizer1, where especially the 8PSK modulation of GSM/ EDGE is taken into account. A joint detection equalizer based on joint reduced–state sequence estimation (JRSSE)

with Ungerboeck set partitioning is employed, which delivers soft output according to [10], [11]. We assume synchronized networks [2], which implies that receive bursts from different terminals or base stations are time aligned and joint channel estimation [12] is feasible, as long as different users have not the same training sequences. Turbo equalization [9] is considered for two users, where the equalizer (as inner decoder for a serially concatenated scheme) receives a priori information input from the outer channel decoder(s) of a single or both users and provides extrinsic a posteriori information output to the decoder. Each decoder processes the input from the equalizer and produces extrinsic a posteriori information on the coded bits for the respective user, so that equalization performance improves from iteration to iteration. As frequency hopping is employed in most systems, the interferer usually changes with each received burst, so that two different schemes are considered. For scheme 1, synchronous hopping is assumed, where for both considered users information can be fed back from the decoder to the equalizer. In contrast, for scheme 2, which is suitable for asynchronous hopping, only information with respect to the considered desired user is fed back. Therefore, the latter scheme is appropriate for state–of–the–art transmission systems like GSM/ EDGE. In order to improve the equalizer performance, we propose a prefilter processing the oversampled receive signal, which exploits the excess bandwidth of the transmit signals, as an extension of [13]–[15]. Furthermore, the M–algorithm [16] is used in order to improve the survivor map of the reduced–complexity joint detection (inner) equalizer. Performance is enhanced at constant overall complexity, as the M–algorithm may detect the maximum–likelihood (ML) transmit sequence with higher probability than a pure JRSSE–based equalizer and the JRSSE–based equalizer is forced to keep the 1 As the overall equalization process is comparable to the decoding of serially concatenated convolutional codes (SCCCs) [8] (regarding the ISI channel as inner code), we refer to the equalizer as the inner component of the turbo receiver [9].

a0 [k] a1 [k]

nr [k] Channel H[k] 1×2

r[k]

Joint Prefilter u[k] Turbo f [k] Equalization

a ˆ0 [k] a ˆ1 [k]

B[k]

Fig. 1. System model for SAIC with user signal a0 [k], interferer signal a1 [k], and disturbed received signal r[k].

inf. bits (user ξ)

ENC encoder (block)

Fig. 2.

IL

MUX

SM

interleaver

burst multiplexer

symbol mapper

transmit signal (aξ [k])

Structure of proposed transmitter.

signal2

detected path as survivor of the according hyperstate in its trellis when calculating soft output. Various turbo equalization schemes have been considered in the literature. For example in [17], a minimum mean–squared error (MMSE) turbo equalizer for multiple–input multiple–output (MIMO) systems is introduced, and in [18], an iterative cochannel interference cancellation scheme for a system with multiple receive antennas is proposed. These algorithms are not suited for the deployment in overloaded systems and to the authors’ knowledge, no comparably performing SAIC algorithms for higher order modulations are known so far. The paper is structured as follows. The system model is introduced in Section 2, and the receiver algorithm, including channel estimation and prefilter design, is presented in Section 3. In Section 4, performance is analyzed and simulation results are given. Notation: [·]m and [·]mn denote the mth element of a column vector and the (m, n)th element of a matrix, with the first elements indexed by 0 and (0,0), respectively. (·)T , (·)H and (·)∗ represent transpose, Hermitian transpose and conjugation, respectively. IN stands for the N × N identity matrix, ⊗ for the Kronecker product, ∗ for convolution, δ[k] for the discrete–time Dirac impulse, and E{·} for the expectation operator.

˜ ] ∗ a ˜ [k ] + n r˜[k ] = H[k ˜ r [k ]. (1) Generally, the symbol–spaced polyphase components ˜[k ] are given by of an No –fold oversampled signal x (ν)  x˜ [k] = x ˜[k ], with sample time instant k  = No k + ν. The polyphase components of the convolution of two oversampled sequences (also for vector– and matrix–   ˜[k ] ∗ y˜[k ], are valued signals) x ˜[k ] and y˜[k ],Noz˜−[k1] =(νx (ν) represented by z˜ [k] = μ=0 x ˜ − μ) [k] ∗ y˜(μ) [k], and we refer to the 0th polyphase component by x[k] = x˜(0) [k]. ˜ ] is the fractionally–spaced overall chanIn (1), H[k    ˜ ˜ 0 [k ] h ˜ 1 [k ] = G ˜ r [k ] ∗ H ˜ ch [k ] ∗ G ˜ t [k ], nel, H[k ] = h    ˜ ˜ ˜ where Gt [k ], Hch [k ], and Gr [k ] are the matrix–valued transmit filter (c0 –impulse of GSM/ EDGE), channel, and receiver input filter3 (square–root raised cosine filter, roll–off factor α = 0.3 [19]) impulse responses, ˜ t: 2 × 2 respectively, with the following dimensions: G ˜ ch : 1 × 2, and G ˜ r : 1 × 1. The (diagonal matrix), H ˜ [k ] = vector–valued  symbol sequence is given by a  ˜1 [k ] T , using the oversampled transmit sea ˜0 [k ] a quences a ˜ξ [k ], defined by the polyphase components  aξ [k] for ν = 0 a ˜(ν) , ξ ∈ U = {0, 1}. (2) [k] = ξ 0 otherwise The noise sequence after the receiver input filter is given by n ˜ r [k ].

2

3

System Model

Fig. 1 depicts the system model in equivalent discrete– time complex baseband representation for our scenario with one dominant cochannel interferer. a0 [k] and a1 [k] represent the linear modulation symbols of the desired user and of the (dominant) interferer, respectively, which are the inputs of the 2 × 1 multiple–input single– output (MISO) ISI channel with discrete–time impulse response H[k] of order qh , which includes transmit pulse shaping and receive filtering. The received signal r[k] is disturbed by additive Gaussian noise (after receive filtering) nr [k]. A suitable SAIC prefilter with impulse response f [k] concentrates the energy of the overall channel and prefilter impulse response of the two considered users (discrete–time matrix–valued impulse response B[k] of order qb ) without significant noise coloration and optimizes the performance of reduced–state equalization. Subsequently, joint turbo equalization delivers estimates a ˆ0 [k], a ˆ1 [k] (as well as estimates of the transmitted information bits). The desired user signal a0 [k] and the interferer signal a1 [k] are both modeled as i.i.d. with variances σa2 . The (mutually independent) transmit signals are generated separately by coding and interleaving of the information bit sequences for both users, cf. Fig. 2. After burst multiplexing and mapping to symbols, 4 bursts of 120 symbols each are transmitted over the channel for each code word. In order to exploit the excess bandwidth of the transmit signals, we consider the oversampled received

Receiver Structure

For each burst, channel estimation is performed and the prefilter is calculated. The (inner) equalizer then uses a priori information on the considered encoded transmit bits (in the 0th iteration no a priori information is available) and delivers extrinsic and a posteriori information on these as output based on the observed received signal after prefiltering using the overall channel and prefilter impulse response of the considered users. As soon as the information for a whole block has been collected, the block is decoded and the corresponding extrinsic information on the encoded data bits is used as a priori information for the next iteration in a turbo equalization [9] fashion.

3.1 Turbo Equalization 3.1.1 Coding and Mapping Different turbo equalization schemes have been discussed in [7] for multiuser turbo equalization and extrinsic information transfer (EXIT) chart analyses [20] have been given. Fading has a major impact on the receiver performance, therefore coding and interleaving are performed over 4 bursts of a block using a single block–wise code combined with Gray mapping. For 2 The derivations are given for two users and an oversampling factor No = 2, but can easily be extended to multiple users and higher oversampling factors. 3 If oversampling is employed, the receiver input filter is merely needed for channel separation and to prevent aliasing after sampling.

simulations, a convolutional code with constraint length K = 7 and an code rate of R = 1/2 [21] is considered. Different interleaver types did not reveal big performance differences for the considered relatively small block lengths. Therefore, for the overlaying two users, different S–random [9] interleaver realizations are used.

hs0 [k]

··· 0

hs1 [k]

ka0

3.1.2 Equalization For equalization, reduced–complexity variants of the BCJR algorithm [10], [11], [22] are employed, which are based on joint reduced–state sequence estimation (JRSSE) with Ungerboeck set partitioning [23]. In order to obtain a low–complexity equalizer, only a low number of states compared to joint maximum– likelihood sequence estimation (JMLSE) may be allowed. Due to the early merging of paths from different states during the forward recursion of the reduced– complexity BCJR algorithm, the quality of stored path information of the forward and backward recursion degrades and the generated soft output information of the (inner) equalizer gets imprecise. Furthermore, the ML path may be lost due to early path merging, so that the generation of the intermediate conditional/ joint probabilities in the algorithm is based on wrong decisions. For the reduced–complexity BCJR algorithm, a survivor map is created prior to or within the forward recursion, so that the selected states within all considered hyperstates of each detection step are identical for the forward and backward recursion, and all determined probabilities of the BCJR algorithm are based on the same values [7], [10]. It has been observed, that in a reduced–complexity equalization scheme a huge performance degradation results if the ML path is lost. Different equalization algorithms for multiuser joint detection have been considered in [15], [24], and it turns out, that the (joint) M–algorithm [16] is a better candidate for tracking of the ML path than a JRSSE at comparable complexity. Therefore, we use the M–algorithm as a preliminary stage of the JRSSE–based BCJR algorithm in order to obtain a better estimate of the ML path (JRSSE-M). The M–algorithm belongs to the class of sequential decoding schemes and is a purely breadth–first algorithm, extending all paths of a certain depth at once and then selecting the M paths with the best metrics4 before proceeding forward. The tree to be searched by the algorithm is given by all possible combinations of transmit sequences of desired user and interferer, and an ambiguity check [16] is needed in order to take the finite impulse response (FIR) channel properties into account. In the subsequent JRSSE–based BCJR stage, the symbol sequence detected by the M–algorithm is used as side information and the algorithm is forced to keep the corresponding transition branch and path register of the respective hyperstate as survivor in each detection step, even if a different incoming path may have a better (local) metric value. For all other hyperstates different from the current best (hyper)state of the M–algorithm, the JRSSE is carried out without any modification. The resulting algorithm requires a balanced complexity spent for the M–algorithm in the first step and the JRSSE–based BCJR algorithm in the second step. If M is chosen too small, the algorithm detects the wrong path and forces the JRSSE–based BCJR algorithm to work on a false hypothesis. Compared to 4 The M–algorithm is based on the same metric as the JRSSE– based BCJR algorithm and utilizes the available a priori information from each preceding turbo equalization iteration, if available.

···

ka0 +qw

··· 0

ka1

ka1 +qw

··· kb

···

qh +qf

k

··· kb

qh +qf

k

Fig. 3. Overall channel and prefilter impulse response of desired user, hs0 [k], and interferer, hs1 [k], respectively.

other soft output M–algorithms, the proposed combined scheme has the essential advantage, that the derived soft information is approximately uniformly degraded for all bits by the state reduction of JRSSE, so that the reliability of different bits is comparable. For other M–algorithm–based schemes it might occur, that information on some bits is lost, if the stored survivor paths represent only a single corresponding bit state [25].

3.2 Prefilter Design After filtering the received signal with a (scalar) FIR prefilter with impulse response f˜[k ] of order qf , u ˜[k ] = f˜[k ] ∗ r˜[k ] (3) is obtained. For prefilter optimization, the (symbol– spaced) overall channel prefilter impulse response  and  ˜ (0) [k] h ˜ (0) [k] , with h ˜ sξ [k ]= Hs [k]= hs0 [k] hs1 [k] = h s0 s1   ˜ ˜ f [k ] ∗ hξ [k ], is considered (cf. Fig. 3). The decision delay introduced by the prefilter is given by k0 = min{ka0 , ka1 }, and the order of the feedback filter B[k] by qb = kb − k0 (ka0 , ka1 , qw , qf , and qb are design parameters to be optimized). B[k] represents the causal part of the combined forward impulse response and equalization is based on u[k + k0 ] = u ˜(0) [k + k0 ] = B[k] ∗ a[k] + nu [k], (4) where nu [k] denotes the sum of the noise after prefiltering np [k] and residual ISI components. The degree of freedom in joint detection, that the detection delay of desired user (ka0 ) and interferer (ka1 ) may differ by an arbitrary value qΔ = ka0 − ka1 with |qΔ | ≤ qb is exploited. The following vector and matrix definitions2 are needed for prefilter design:  T hsξ = hsξ [0] hsξ [1] . . . hsξ [qh + qf ] = Hξ f , (5)  (0)   (0) T (−1) T T (1) with Hξ = Hξ | Hξ , and f = f |f ,  (ν)  (ν)  ˜ [m − n] for 0 ≤ m − n ≤ qh h ξ , Hξ mn = 0 elsewhere m ∈ {0, . . . , qh + qf }, n ∈ {0, . . . , qf }, and (6)  T f (ν) = f˜(ν) [0] f˜(ν) [1] . . . f˜(ν) [qf ] . (7) According to [15], we consider the overall channel and prefilter impulse responses and determine the prefilter impulse response in a way, that the ratio Pu (8) J= Pi + Pn of the signal power Pu , constrained on the impulse response taps within the range Kuξ = {kaξ , . . . , kaξ + qw }, to residual ISI power (not considered within equalization) Pi , represented by the energy of the impulse response taps in the range

Kiξ = {0, . . . , kaξ −1 } ∪ {kb + 1, . . . , qh + qf }, plus power of (possibly colored) noise Pn is maximized. With the (qh + qf + 1) × (qh + qf + 1) diagonal matrices5 Dξu and Dξi , Pu and Pi can be expressed,  ξ  ξ  1 m = n ∈ Ku/i , (9) Du/i mn = 0 otherwise 1  ξ hH (10) Pu/i = σa2 sξ Du/i hsξ . ξ=0

Because np [k] = n ˜ p [k] and n ˜ p [k ] = f˜[k ] ∗ n ˜ r [k ], the    ˜ autocorrelation of n ˜ r [k ] = Gr [k ] ∗ w[k ˜ ] (ϕw˜ w˜ [k ] =  ∗  2    ˜ + k ] = σw δ[k ]) is required6 to calcuE w ˜ [κ ] w[κ ˜ r [k ] ∗ late the power of np [k]. We obtain ϕn˜ r n˜ r [k ] = G ∗     ˜ ϕw˜ w˜ [k ] ∗ Gr [−k ]. ϕw˜ w˜ [k ], ϕn˜ r n˜ r [k ], and ϕn˜ p n˜ p [k ] represent the autocorrelation sequences of the noise before and after the receiver input filter, and after the prefilter, respectively. The noise power after prefiltering is   Pn = E n∗p [k] np [k] = ϕn˜ p n˜ p [0] = f H Φn˜ r n˜ r f , (11) using the autocorrelation matrix

(0) Φn˜ r n˜ r Φ(1) n ˜r n ˜r , (12) Φn˜ r n˜ r = Φ(−1) Φ(0) n ˜r n ˜r n ˜r n ˜r with (qh +qf + 1) × (qh + qf + 1) matrices Φ(ν) n ˜r n ˜ r , defined by Φ(ν) = ϕ [2(m − n) + ν], m, n∈ n ˜ n ˜ r r n ˜r n ˜ r mn {0, . . . , qh + qf }. With (5), (10) and (11), (8) can be written as  1 ξ H f H σa2 ξ=0 HH  f Φu f ξ Du Hξ f . = H J =  1 ξ f Φin f f H σa2 ξ=0 HH ˜r n ˜r f ξ Di Hξ + Φn For the given parameters, maximization is performed via the derivative of J obtained by the Wirtinger calculus [26]: δJ Φu f · f H Φin f − f H Φu f · Φin f = . (13) ∗ δf (f H Φin f )2 Setting the derivative to zero, the following condition for the optimum prefilter vector results: Φu f · (f H Φin f ) = (f H Φu f ) · Φin f . (14) (0)

H

Φu f , the generalized eigenvalue problem With λ = ffH Φ in f Φu f = λ Φin f arises. Eigenvalue decomposition provides the eigenvector fmax corresponding to the maximum eigenvalue and power ratio Jmax . Different sets of parameters ka0 , ka1 and qw are used and the corresponding optimum power ratio is computed: (Jmax ) . (15) Jopt = 0max 1 ka ,ka ,qw

For the considered JRSSE–based equalizer with state reduction to 16–64 states, qw = 1 was found to give the best performance for our application. Furthermore, a fully anticausal prefilter (k0 = qf ) with qb = qh is chosen. The optimization of the pairs (ka0 , ka1 ) (cf. (15)) remains to be done, which we limit to a search within the set {(k0 , k0 ), (k0 , k0 + 1), (k0 , k0 + 2), (k0 + 1, k0 ), (k0 + 2, k0 )}, as this represents the most relevant cases for synchronous transmission. An accurate estimate of the noise autocorrelation is crucial for the proposed scheme. If no information on residual (additional) cochannel interferers (resulting in 5 Different (user dependent) weight allocations (Dξ , Dξ ) can be u i used in a generalized version of the algorithm [14]. 6 The noise before the receiver input filter is modeled as an equivalent discrete–time white Gaussian process w[k ˜ ].

colored disturbance on the channel) is available, at least the power of the residual interferers should be taken into account in Φn˜ r n˜ r for prefilter design.

3.3 Channel Estimation Training sequence based channel estimation of the oversampled overall channel is considered in the following. Joint ML estimation of the two2 considered users’ impulse responses (regarded within joint detection) is performed [27]. As synchronous transmission within GSM/ EDGE is assumed [1], the GSM/ EDGE training sequences consisting of Nt = 26 symbols are used. For a more general performance assessment, Gold [28] training sequences of length Nt = 31 are additionally considered, as these sequences have better crosscorrelation properties than the GSM/ EDGE sequences. The probability density function (pdf) ˇ frt (rt |At, h) ˇ H Φ−1 ˇ (16) ∝ exp − (rt − At h) (rt − At h) n ˜ rt n ˜ rt

of the oversampled received signal (corresponding to the training sequence), cf. (1) and (2), 1  ˜ tξ [k ] ∗ a r˜t [k ] = ˜tξ [k ] + n ˜ rt [k ] (17) h ξ=0

is regarded for ML estimation, where r˜t [k ] is written as signal vector  T (1) T T rt = r(0) | rt , (18) t  (ν) T (ν) (ν) (ν) rt = r˜t [qh ] r˜t [qh + 1] . . . r˜t [Nt − 1] (part without ISI from previous segment). The pdf is maximized with respect to  (0) T (1) T (0) T (1) T T ˇ ˇ ˇ ˇ= h ˇ |h |h |h , (19) h 0 0 1  (ν) T 1 (ν) (ν) (ν) (ν) ˇ ˇ ˇ ˇ ˇ hξ = hξ [0] hξ [1] . . . hξ [qh ] , where hξ [k] are the hypothetical taps of the polyphase components of the oversampled (overall) channel impulse response of the ξth user. With the   (Nt − qh ) × (qh + 1) convolutional matrices Atξ mn = atξ [m − n], m ∈ {qh , . . . , Nt − 1}, n ∈ {0, . . . , qh }, the training sequence matrix of the two considered users is defined as   (20) At = I2 ⊗ At0 | I2 ⊗ At1 , and assumed to be known in the following. The autocorrelation matrix of the noise n ˜ rt [k ] is given as

(0)  Φn˜ r n˜ r Φn(1) ˜ n ˜ rt rt t t Φn˜ rt n˜ rt = , (21) Φ(−1) Φn(0) n ˜r n ˜r ˜r n ˜r t

t

t

t

with (Nt − qh ) × (Nt − qh ) matrices Φ(ν) n ˜ rt n ˜ rt , de (ν)  fined by Φn˜ r n˜ r mn = ϕn˜ r n˜ r [2(m − n) + ν], m, n ∈ t t {0, . . . , Nt − qh − 1}. Finally, the ML channel estimate is obtained by ˇ maximizing (16) with respect to h:  H −1 −1 H −1 ˇ ML = A Φ h At Φn˜ r n˜ r rt . (22) t n ˜ rt n ˜ rt At t t Due to the non–zero secondary block diagonals in (21), the estimation of the channel impulse response polyphase components is coupled. Otherwise, the standard T–spaced least–squares (LS) solution would be obtained for both sets of user polyphase components (resulting in worse performance of turbo equalization with the considered prefilter in difference to [27]). The estimation of the channel impulse responses may be extended to the iterations within turbo equalization [29], which is not in the scope of this paper.

4

Numerical Results

10

0

Ideal channel knowledge

7 The

BLER after channel decoding, most relevant for coded transmission over fading channels, is adopted as performance measure in this paper. For the static channel, the bit error rate (BER) is usually chosen [9]. 8 Performance close to convergence is achieved after 4 iterations.

GSM tr.seq. (Nt = 26) Gold tr.seq. (N = 31) t

Symbol−spaced prefilter

BLER →

Fractionally−spaced prefilter 10

10

−1

Iteration 0

−2

Iteration 4 0

2

4

6

8

10

12

14

16

10 log10 (CIR) [dB] →

18

20

Fig. 4. BLER vs. 10 log10 (CIR) for 10 log10 (DIR) = 20 dB, 8PSK, 10 log10 (ES /N0 ) = 35 dB, TU channel. Comparison of the symbol–spaced prefilter to the fractionally–spaced prefilter with joint turbo equalization (scheme 2, JRSSE (8, 8)) including channel estimation based on different sequences. 10

0

JRSSE (8,8) JRSSE (4,4) JRSSE−M (8,8), M=64 JRSSE−M (4,4), M=64

BLER →

Iteration 0 10

10

Iteration 4

−1

−2

0

2

4

6

8

10

12

14

16

10 log10 (CIR) [dB] →

18

20

Fig. 5. BLER vs. 10 log10 (CIR) for 10 log10 (DIR) = 20 dB, 8PSK, 10 log10 (ES /N0 ) = 35 dB, TU channel, ideal channel knowledge. Fractionally–spaced prefilter with joint turbo equalization (scheme 2) using different equalization parameters for JRSSE and JRSSE-M. 0

1

10

BLER →

0.9 0.8

IEQ out , ICC in

The GSM/ EDGE typical urban (TU) channel profile is used (qh = 5) for Monte–Carlo simulations of the proposed turbo SAIC receiver. Mutually uncorrelated block fading channels are assumed for all users and different bursts (corresponding to ideal frequency hopping). The carrier–to–interference power ratio (CIR) is defined as ratio of the average receive power of the desired user to that of the total interference. Additionally, the dominant interferer power ratio (DIR) characterizes the interference situation of one dominant and 4 remaining interferers with equal average powers [1], [5], and is defined as ratio of the average power of the dominant interferer (treated in joint equalization) to the total average power of the remaining other interferers (not taken into account in equalization). ES /N0 is fixed during simulations at 35 dB (ES : average received symbol energy of desired user; N0 : single–sided power spectral density of the underlying passband noise process), which is a typical value for GSM/ EDGE receivers. Applying JRSSE for equalization, 1 q the number of trellis states is given by ξ=0 κb= 1 Lξκ , where Lξκ represents the number of subsets for the κth channel tap of the desired user (ξ = 0) and the interferer (ξ = 1), respectively (8PSK: Lξκ ∈ {1, 2, 4, 8}). Partitionings are distinguished by the number of used subsets: (L01 × L02 × . . . , L11 × L12 × . . .). For delayed decision–feedback sequence estimation (DDFSE), as a special case of RSSE, Lξκ ∈ {1, 8} is used for 8PSK. In simulations, JRSSE with partitionings (8, 8) (64 states) and (4, 4) (16 states) is applied. The block error rate (BLER) performance7 of the JRSSE–based turbo SAIC receiver (scheme 2) with ideal channel knowledge and channel estimation based on different training sequences, respectively, is shown in Fig. 4 versus CIR for 10 log10 (DIR) = 20 dB for the 0th (separate equalization and decoding) and 4th iteration8 . Comparing the results of Fig. 4 to those for a conventional receiver without interference cancellation applying turbo equalization (results not shown, cf. [7]), the joint turbo equalization approach yields a gain of about 9 dB at BLER = 10%, even if channel estimation is taken into account. A large performance loss (especially for the fractionally–spaced prefilter) results for the GSM sequences (compared to e.g. Gold sequences) due to their poor crosscorrelation properties. The improvement due to turbo iterations is about 4.5– 5.5 dB at BLER = 1–10% for the proposed scheme. Using oversampling and the fractionally–spaced prefilter, a gain of about 1–2 dB compared to the conventional symbol–spaced prefilter [15] is observed. In Fig. 5, improvements also due to the JRSSE-M algorithm can be recognized. Without the M–algorithm, state reduction from (8, 8) to (4, 4) would result in a large performance loss, but using the (better) survivor map of the M– algorithm (M = 64), better performance is achieved at slightly increased complexity. Generally, the M– algorithm gives the largest performance improvements in the low CIR domain (cf. [15]). EXIT chart analyses have been carried out for the (inner) equalizer and the (outer) decoder in [7], where static and fading channels have been considered. For scheme 1, equal a priori information values IEQ in for each user are taken as input for the equalizer

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

−1

10

Symbol−spaced, JRSSE (8,8) Fractional−spaced, JRSSE (8,8) Fract.−s., JRSSE−M (8,8), M=64 10 log10(ES/N0) = 17 dB 10 log10(ES/N0) = 19 dB Conv. code (R = 1/2 , K = 7) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

IEQ in , ICC out

(a)

−2

10

10

15

20

10 log10 (ES /N0 ) [dB] →

1

(b)

Fig. 6. (a) EXIT chart (90% quantile of all fading channel realizations) for two user equalization (scheme 1, identical IEQ in used), 8PSK, 10 log10 (CIR) = 0 dB, 10 log10 (DIR) = ∞, 10 log10 (ES /N0 ) = 17 dB and 19 dB, TU channel. EXIT chart for convolutional code of rate R = 1/2 (constraint length K = 7). (b) BLER vs. 10 log10 (ES /N0 ) after 4 iterations.

EXIT chart characteristic, so that for the given scenario identical extrinsic output information IEQ out is preserved for each user on average (depending on the used channel realizations). In Fig. 6 (a), results are shown for the TU channel, where 1000 channel realizations have been drawn, and the corresponding input–output transfer characteristic has been stored for each. In order to get an adequate measure corresponding to the BLER performance for the EXIT chart of the fading channel, the average extrinsic information pertaining to 4 randomly picked fading channel realizations (according to the interleaving of a block over 4 transmission bursts) is calculated for each considered user, and the 90% quantile of this random quantity has been determined for each value of the a priori information IEQ in separately. Finally, the 90% contour is depicted in the diagram, which means that performance of only 10% of all transmission blocks is worse on average. For the simulated curves, the parameters 10 log10 (DIR) = ∞ and 10 log10 (CIR) = 0 dB are used. The curve for the adopted convolutional code is drawn in the same diagram, where the a priori input information ICC in is shown versus the extrinsic output information ICC out (swapped axes), so that convergence of turbo equalization can be predicted from the diagram. Fig. 6 (b) depicts the BLERs of different equalizers (scheme 1) versus ES /N0 . For example, it can be observed from Fig. 6 (a), that the bottleneck between equalizer and decoder characteristic is open at about 10 log10 (ES /N0 ) = 17 dB for the JRSSE-M equalizer scheme. Comparing this to Fig. 6 (b), it can be seen, that BLER = 10% is obtained for 10 log10 (ES /N0 ) ≈ 16.2 dB. Furthermore, improvements due to the proposed prefilter and the JRSSE-M algorithm can be identified from Figs. 6 (a) and (b).

5

Conclusion

In this paper, a prefilter design has been proposed, which is especially suited for SAIC based on turbo equalization with reduced–complexity joint detection as inner component. It is more general and delivers better performance than other known approaches, e.g. [14], [15], [27]. Furthermore, the (inner) equalizer performance was enhanced by using an additional M–algorithm to keep track of the ML path in the reduced–complexity (JRSSE– based) BCJR algorithm. Simulation results show, that already a low number of turbo iterations improve the detection performance of the SAIC algorithm enormously even for scenarios with residual interference and channel estimates of moderate quality.

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