Diversity Interference Cancellation for GSM/ EDGE using Reduced-Complexity Joint Detection

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1 Diversity Interference Cancellation for GSM/ EDGE using Reduced-Complexity Joint Detection Patrick Nickel and Wolfgang Gerstacker University of Erlangen Nuremberg, Institute for Mobile Communications, Germany {nickel, Abstract: In cellular mobile radio systems, multiple access is causing interference that limits capacity of the networks. The GSM system with multiple users can be interpreted as MIMO system with a desired user and (cochannel and adjacent channel) interferers. Using a multiple input multiple output (MIMO) multiuser joint detection approach for desired signal and one or more (strongest) interferers, network capacity can be significantly increased. In this paper, we compare different multiuser detection methods that can be applied to GSM/ EDGE (Enhanced Data Rates for GSM Evolution) systems with Gaussian minimum shift keying (GMSK) modulation in up- and downlink and 8 ary phase shift keying (8PSK) in the uplink, respectively. Since an optimal solution is not feasible in these applications, joint MIMO reduced state sequence estimation (RSSE) with adaptive thresholds in metric computations is applied to reduce computational complexity. The M-algorithm is explored as a second method for joint detection with reduced complexity. Algorithms for multiuser detection are compared with interference rejection methods, where interferers are suppressed by filtering. A performance comparison is done by simulations for the GSM/ EDGE equalizer test (EQ) and typical urban (TU) channel profiles with known channel impulse responses at the receiver. 1. Introduction Second generation mobile radio networks are interference limited systems. Using conventional equalization approaches, time division multiple access (TDMA) schemes like GSM/ EDGE systems need to be designed in such a way, that cochannel interference from neighboring cells is small enough that a single input single output (SISO) receiver ignoring the disturbing signal can be employed. Due to spectrum limitations, recent developments aim at significantly increasing GSM capacity [1, 2]. A promising way for this are interference suppression and multiuser joint detection. Using these methods, receivers are able to cope with much higher interference power levels than conventional receivers. This property can be exploited in network layout, employing a smaller frequency reuse factor. In this paper, we introduce a multiple input multiple output joint reduced state sequence estimation (MIMO JRSSE) equalizer with an adaptive threshold in the path metric computation. By this, complexity can be further reduced compared to a traditional MIMO JRSSE receiver. For the single user case the threshold approach has been introduced in [3]. Here, the threshold calculation is extended to diversity reception of multiple (two) users and performance is analyzed by simulations. The adopted MIMO JRSSE has been proposed in [4] using uniform set partitioning (USP). For our application, we apply joint detection to the signal of desired user and one interferer. Either signal constellation is separately partitioned using Ungerböck set partitioning. The system is presented for the two user case, but can be extended to a general scenario of K users (consisting of one desired user and (K 1) interferers) in a straightforward way. A second approach to improve equalization performance is based on the M-algorithm [5] applied to MIMO equalization. For the case of Gaussian minimum shift keying (GMSK) modulation, which may be considered as filtered binary phase shift keying (BPSK) modulation, we can exploit the fact that the transmitted signals are real valued in equivalent complex baseband (ECB) representation [2]. Thus, we can apply MIMO equalization to an equivalent diversity reception signal model also in the case of only one receive antenna in order to obtain high performance. The corresponding algorithms are preferable for mobile terminals, where usually only one antenna is available. The paper is organized as follows. First the system model is introduced. Then, MIMO JRSSE with adaptive threshold and the M-algorithm are presented. Finally, numerical results from simulations are shown. 2. System Model Synchronized networks promise a substantial gain in network capacity [2], if they are combined with the implementation of interference cancellation, and therefore are assumed in the following. The considered scenario comprises two users, namely the desired user and the interferer, that transmit via independent channels to the receiver, as shown in Fig. 1. The desired user signal a 0 [k] and the interferer signal a 1 [k] are considered as i.i.d. and mutually independent with variances σa. 2 The output signals of the channel, cf. Figs. 1(a), (b) (for the two antenna case), are r 0 [k] and r 1 [k]. We collect the receive signals in a vector r[k] =[r 0 [k] r 1 [k]] T and the transmit signals in a vector a[k] =[a 0 [k] a 1 [k]] T, respectively (( ) T : transposition). The input output relation of the equivalent MIMO channel describing a GSM transmission with interference and two branch diversity reception is r[k] = H[κ] a[k κ]+n[k], (1) with n[k] =[n 0 [k] n 1 [k]] T, cf. Fig. 1. H[ ] denotes the causal FIR impulse response of order of the overall channel including continuous time transmit and receive filtering and n i [k] is the additive white Gaussian noise (AWGN) process of the ith receive sequence with variance σ 2 n. The noise processes are assumed to be spatially

2 a 0 [k] a 1 [k] a 0 [k] a 1 [k] Channel H(z) 2 2 Channel H(z) 2 2 n 0 [k] n 1 [k] n 0 [k] n 1 [k] r 0 [k] r 1 [k] r 0 [k] r 1 [k] Prefilter F(z) 2 2 (a) Prefilter F(z) 1 2 (b) Reduced- State Equalization Reduced- State Equalization â 0 [k] â 1 [k] â 0 [k] Figure 1: System models: (a) System model for joint detection, (b) system model for interference suppression. and temporally white, E{n[k + κ] n H [k]} = σn 2 I 2 δ[κ] (E{ }: expectation, ( ) H : Hermitian transposition, I 2 : 2 2 identity matrix, δ[κ]: unit pulse sequence). The transfer function representing the discrete time MIMO channel is denoted by H(z) = H[κ] z κ. Ideal channel knowledge at the receiver is assumed throughout this paper in order to show general performance limits of interference suppression and multiuser detection algorithms MIMO Receiver Structure For reduced state trellis based MIMO equalization, a suitable front end MIMO FIR prefilter with causal impulse response F[ ] of order q f should be used [4, 6, 7]. For our simulations, we apply the optimum MIMO MMSE DFE prefilter as described in [4, 6]. With this filter, energy is concentrated in the front matrix taps of the overall impulse response (including channel and prefilter). The postcursor ISI after prefiltering is represented by the feedback filter transfer function B(z) on which equalization is based [4, 6, 7]. A low complexity algorithm for MIMO prefilter computation with high performance is given in [8, 9] GMSK System Model For GMSK modulation, we can apply the proposed equalization methods also to single antenna receivers, because the GMSK transmit signal can be considered as filtered BPSK signal. According to this, symbols of desired user and interferer, respectively, are assumed as real valued (a i [k] R). Transmitting both signals to a receiver with only one antenna, the in-phase and quadrature components of the received signal can be considered as independent receive observations [2]. Using (1) with the 1 2 channel matrix H[κ] =[h 00 [κ] h 01 [κ]], r[k] =r 0 [k] and n[k] =n 0 [k], weget r 0 [k] = H[κ] a[k κ]+n 0 [k]. (2) With h mn [κ] = Re{h mn [κ]} + j Im{h mn [κ]}, Re{a i [k]} = a i [k] and Im{a i [k]} =0, real and imaginary part of r 0 [k] can be represented separately resulting in where r[k] = r[k] = H[κ] a[k κ]+ñ[k], (3) [ ] Re{r0 [k]}, ñ[k] = Im{r 0 [k]} [ ] Re{n0 [k]}, Im{n 0 [k]} and [ ] Re{h00 [κ]} Re{h H[κ] = 01 [κ]}, Im{h 00 [κ]} Im{h 01 [κ]} which is equivalent to the 2 2 channel shown in Figs. 1(a) and (b). Therefore, we can apply MIMO equalization to the BPSK single antenna system Interference Suppression To demonstrate performance improvements of joint detection, linear suppression of the interfering signal is regarded as reference receive algorithm. For this, a system model as shown in Fig. 1(b) with two receive antennas is regarded. The linear prefilter F(z) can be designed in a way, that the interfering signal is suppressed [10]. The remaining ISI in the desired user signal is treated in the following stage consisting of a reduced state SISO equalizer. Thus, the complexity of the equalizer is identical to that of a single user receiver, since there is no need to consider also the interferer in equalization. Using this prefiltering technique, noise power is increased to some extent. This can be avoided by multiuser joint detection presented in the next section. 3. Joint Reduced State Sequence Estimation Joint reduced state sequence estimation (JRSSE) [4] is the space time extension of RSSE proposed in [11] for SISO equalization. JRSSE is applied to improve system performance for a GSM/ EDGE transmission by interpreting the overall transmission model as a MIMO system. Doing so, accuracy of estimation of the desired user signal is improved. For joint RSSE, a similar equalizer structure as for joint delayed decision feedback sequence estimation (JDDFSE) is valid. As shown in [4], the signal after MIMO prefiltering can be described by x[k] = = q f q b F[κ] r[k κ] B[κ] a[k q d κ]+e[k], (4) where B[κ] are the 2 2 matrix filter taps of the FIR feedback filter B(z) of order q b, q d is the decision delay of detection which has to be chosen suitably, and e[k] the error vector. e[k] is spatially whitened using the whitening filter W = U 1,whereUresults from the error autocorrelation matrix Φ ee = E{e[k]e H [k]} via Φ ee = UU H. The signal x[k] =Wx[k] is the input signal of the JRSSE block: x[k] = q b B[κ] a[k q d κ]+ē[k], (5)

3 l =2 l =3 l =1 l =0 e 3 e 4 e 5 e 2 e 1 e 0 e 6 e 7 e 0 e 4 e 2 e 6 e 1 e 5 e 3 e 7 Figure 2: Ungerböck set partitioning tree for 8PSK constellation. with B[κ] =WB[κ] and ē[κ] =We[κ]. As for DDFSE, trellis states are combined into hyper states for RSSE and state dependent feedback registers are used in metric calculations. However, hyper states can be formed more flexible than for DDFSE, where only states can be fused that contain the same past symbols starting at a special point in memory. This means, that the first taps of the channel are taken into account by the trellis states and the last ones only by decision feedback. In RSSE, an Ungerböck set partitioning tree as shown in Fig. 2 is used, forming hyper states by fusing symbols of a chosen modulation sub alphabet for each tap. Ungerböck set partitioning of 8 ary phase shift keying (8PSK) yields 4 different layers (l {0, 1, 2, 3}), where the number of subsets in each layer is L =2 l and the number of symbols within each subset is 2 (3 l).for JRSSE we use uniform set partitioning (USP) for desired user and interferer signal [4]. The branch metric for the trellis diagram of JRSSE is λ(ǎ[k q d ], Šr[k q d ]) = x[k] B[0] ǎ[k q d ] q b B[κ] â[k q d κ, Šr[k q d ]] 2 (6) κ=1 ( ˇ : trial symbols and states, 2 : L 2 norm), where the hyper states are defined by Šr[k q d ]=[ˇm T 1 [k q d 1] ˇm T 2 [k q d 2]... ˇm T q b [k q d q b ]] T, with the hyper symbol vectors ˇm κ [ ] representing the subset numbers for desired user and interferer symbols for tap κ. â[, Šr[k q d ]] is the path register with symbols corresponding to the survivor path of state Šr[k q d ]. The number of trellis states of JRSSE is given by qb κ=1 LU κ q b κ=1 LI κ. Here, L U κ and L I κ are the number of subsets for the κth channel tap of the desired user (U) and the interferer (I), respectively (L U κ,l I κ {1, 2, 4, 8}). The subset numbers need to fulfill the condition L 1 L 2... L qb for both desired user and interferer [11]. To distinguish between different partitionings, we characterize them by the number of used subsets: (L U 1 L U 2...,L I 1 L I 2...). For instance, (2 2 2, 2 2) means L U 1 = 2, L U 2 = 2, L U 3 = 2 and L U κ =1 κ 4 for the desired user symbols, and L I 1 =2, LI 2 =2and LI κ =1 κ 3 for the interferer symbols. The overall number of hyper states is given by 2 5 =32for this example. For DDFSE which may be seen as a special case of RSSE we have L κ {1, 8} for 8PSK. The adopted representation is also used for BPSK, where L κ {1, 2}. 4. Adaptive Threshold The path metrics of JRSSE usually are distributed over a wide range of values. Since states with low path metric are much more probable to survive finally than those with high metric, the adaptive threshold algorithm described in [3] computes a threshold T (dependent on a given path error probability p c ) that determines the range of metric values to be considered in the next trellis step. In each step, the metric values of all states are compared to the smallest value Γ min and only those are kept, that are within the interval [Γ min, Γ min + T ]. We extend this algorithm to the two user MIMO case and investigate its performance by simulations. Considering the branch metric of joint maximum likelihood sequence estimation (JMLSE) for time k and transition from state i to state j similar to [3], we have λ ij [k] = r[k] H[κ] ǎ[k κ] 2 (7) (ǎ[ ]: trial symbols of transition). We assume now, that i is the correct state at time k, where the correct path with branch metric λ c [k] and an incorrect path with branch metric λ i [k] bifurcate. The threshold T is computed in a way, that the probability of removing the correct path at the ηth branch of the minimum distance error event (given that the correct path is maintained up to the (η 1)th branch) fulfills { } Pr λ c [k + κ] > λ i [k + κ]+t p c,η Q, (8) where Q +1is the number of branches of the minimum distance error event and p c the maximum path error probability. Defining the symbol error vector [k] = [ a 0 [k] a 0 [k 1]... a 0 [k ] a 1 [k] a 1 [k 1]... a 1 [k ]] T, a ν [k] =a c ν[k] a i ν[k], ν {0, 1} (a c ν[k]: correct symbols, a i ν[k]: incorrect symbols), and channel vectors as h ι = [h ι0 [0] h ι0 [1]... h ι0 [ ] h ι1 [0] h ι1 [1]... h ι1 [ ]] T for ι {0, 1}, we obtain λ c [k + κ] = ( n 0 [k + κ] 2 + n 1 [k + κ] 2 ), (9) ( λ i [k + κ] = ht 0 [k + κ]+n 0 [k + κ] 2 + λ i [k + κ] λ c [k + κ] = + ht 1 [k + κ] +n 1 [k + κ] 2), (10) ( ht 0 [k + κ] 2 + ht 1 [k + κ] Re{ h T 0 [k + κ]} Re{n 0 [k + κ]} +

4 +2Im{ h T 0 [k + κ]} Im{n 0 [k + κ]} + +2Re{ h T 1 [k + κ]} Re{n 1 [k + κ]} + ) +2Im{ h T 1 [k + κ]} Im{n 1 [k + κ]}. (11) The noise process of (11) for the two user MIMO case is similar to the expression given in [3] and has variance 2(σ n x(η)) 2 and mean x 2 (η), wherex(η) = ( ( h T 0 [k + κ] 2 + h T 1 [k + κ] 2 ) ) 0.5. Thus, with [3], we obtain the result T =max { max 1 η Q, [ ] { } 2Cσ n x(η) x 2 (η), 0 } (12) with C =erfc 1 (2p c ) (erfc 1 ( ): inverse complementary error function). The minimum distance error sequence has to be found over all possible difference sequences [ ]. Since this is too complex for a practical application, we use the maximum value T max =(Cσ n ) 2 of (12) with respect to x for simulations, which is not strictly optimum but also results in a high gain in performance if applied to JRSSE, where metric values are compared to the computed threshold similar to JMLSE. Another way to avoid high complexity is to consider error events, where an error occurs only for a single instant k, causing a 0 [k] 0and/ or a 1 [k] 0. Investigations for 8PSK signals have shown that for moderate noise power, the calculated values of T for single errors are close to T max in most cases, justifying T max as threshold value adjusted to the noise variance. The solution for a general N K MIMO scenario (N: number of receive antennas, K: number of simultaneous users) can be obtained by extending the symbol error vector [k] and channel vectors h ι appropriately. The additional receive branches can be taken into account in (9) and (10). The result is again given by (12) with modified x(η) = ( N 1 ι=0 h T ι [k +κ] 2) 0.5, but with the same maximum value T max = (Cσ n ) 2 as for the 2 2 case, if maximization is performed over x. 5. M-algorithm The M-algorithm [5] belongs to the class of sequential decoding schemes and is a purely breadth-first algorithm, processing all branches of a certain depth at once and selecting the M paths with the best metrics before proceeding forward. Here, we consider the M- algorithm for multiuser joint detection. The tree to be searched by the algorithm is given by all possible transmit sequences of user and interferer. Since all paths to be compared have the same number of symbols at each processing step, the same metric as for JRSSE can be applied. In terms of complexity, the M-algorithm is similar to JRSSE with M states for moderate M. 6. Numerical Results For simulations we use the GSM/ EDGE equalizer test (EQ) and typical urban (TU) channel profiles. The channel is assumed to be constant within each burst but varies independently from burst to burst. Furthermore, perfect channel knowledge at the receiver side is assumed. The EQ channel TU channel Figure 3: BER vs. 10 log 10 (NE S /N 0 ) for GMSK, N = 1, 10 log 10 (CIR) = 0 db. strength of interference is described by the carrier to interference ratio (CIR), which is the ratio of the average received symbol energy of desired user and interferer. Fig. 3 shows the bit error rate (BER) of the desired user versus NE S /N 0 (E S : average received symbol energy of desired user, N 0 : noise power density at each receive antenna, N: number of receive antennas) for GMSK transmission. JRSSE (which is equivalent to JDDFSE for GMSK/ BPSK) is considered with and without adaptive threshold, respectively, and N =1is valid. When the adaptive threshold method is applied, we label the curves additionally with AT and the value of log 10 (p c ). For BER, the algorithm with adaptive threshold and p c =10 6 performs very close to JRSSE without adaptive threshold at a lower complexity. Figs. 4, 5, 6 and 7 show simulation results for 8PSK and N = 2. To measure complexity of JRSSE with adaptive threshold, we count the number of states that have at least one incoming path. For these states, all transition metrics have to be computed in the next trellis step. The number of path metric computations of the JRSSE-AT algorithm, normalized to that of the equivalent JRSSE algorithm without threshold, is shown in Figs. 6 and 7. The results promise high gains for deployment of joint detection methods compared to interference suppression methods. Comparing SISO DDFSE (8 8) with MIMO JRSSE (2 2 2, 2 2 2), Figs. 4 and 6 indicate a gain of about db at a BER of for the EQ and the TU channel, respectively, for 10 log 10 (CIR) = 0 db. For higher CIR (15 db), the gain is still about 2.5 db. According to Fig. 7, the worst conditions in general are given for moderate CIRs, while a very good performance results for low and high CIRs, respectively, because in these cases one of both signals can be reconstructed almost error free. The results for 8PSK reveal gains of the algorithm with adaptive threshold in terms of power efficiency compared to conventional JRSSE with the same complexity. As observed for the investigated channels, it is sufficient for JRSSE to assign only two subsets to each

5 MIMO M (16) MIMO M (64) MIMO M (256) 20 db Prefiltering+SISO DFE Prefiltering+SISO DDFSE (8 8) MIMO JDDFSE (8,8) MIMO JRSSE (2 2,2 2) db log 10 (CIR) [db] Figure 4: BER vs. 10 log 10 (NE S /N 0 ) for 8PSK, N = 2, 10 log 10 (CIR) = 0 db, TU channel. Figure 5: BER vs. 10 log 10 (CIR) for 8PSK, N =2, 10 log 10 (NE S /N 0 ) = 20dB and 25 db, respectively, TU channel. memory tap but to use as many channel taps as possible to obtain high performance. Using the algorithm with adaptive threshold, more channel taps can be considered while keeping complexity at an approximately constant level. Fig. 6 shows an improvement of about 0.8 db at a BER of comparing JRSSE (2 4 =16states) with JRSSE-AT6 (max. number of states: 2 6 = 64, but on average only 6% of all 64 states considered in computations as observable from the lower diagram of Fig. 6). Here, only 24% of the overall metric computations of JRSSE with 16 states are needed for JRSSE- AT6. Hence, improvement in power efficiency and complexity can be obtained with JRSSE-AT. Figs. 5 and 7 show the performance of the M-algorithm used for joint detection of desired user and interferer. Results for different numbers M of paths are presented in Fig. 5. It can be observed that even for small values, e.g. M = 16, low BERs are achieved. Since user and noise power are fixed during simulations (10 log 10 (NE S /N 0 )=20dB), changes of the CIR merely effect the power of the interferer in Figs. 5 and 7. For this reason, curves do not exhibit an even symmetry. At a CIR level of 10 log 10 (CIR) = 20 db interference power is of the same order as noise power and for higher levels even smaller. Hence, for high CIR levels, a lot of sequences (hypotheses) different with respect to the interferer exist, that yield metrics close to the minimum value. Due to the limitation to a relatively small number M of stored paths, less hypotheses different with respect to the desired user signal are left in the stored paths, therefore resulting in a performance degradation with respect to the desired user. For CIR the performance tends towards JDFE performance as observable from Figs. 5 and 7. Simulations for the EQ and the TU channel profile (results not shown) indicate, that for 10 log 10 (CIR) = 0 db performance of the M-algorithm with M 16 is slightly better than that of JRSSE (2 2 2, 2 2 2) for all considered E S /N 0. Here, the curves for M =16,...,1024 are almost identical. For M<16 performance degrades and becomes equal to JDFE for M =1. At an interference power lower than the noise power, performance of the M-algorithm is worse compared to JRSSE (Figs. 5 and 7). The performance of the M- algorithm can be improved by forcing the algorithm to store the best M U different paths according to the desired user subtree in each step and the best M I different paths according to the interferer subtree, respectively, with M = M U + M I. However, complexity is increased due to the necessity to build subtrees with respect to each user. 7. Conclusion Joint detection reveals a performance advantage compared to linear interference suppression methods at the expense of some additional complexity, if applied to GSM/ EDGE. Our numerical results demonstrate high performance for the reduced complexity JRSSE algorithm using an adaptive threshold method. The algorithm reduces computational complexity as the conditions in terms of NE S /N 0 and CIR get more favorable and outperforms the conventional JRSSE of same complexity. Furthermore, the M-algorithm has been considered for joint detection and has been shown to exhibit high performance in the range of moderate to high interference power levels at a very low complexity. For practical systems a good tradeoff for the entire range of conditions can be achieved by adjusting the equalization method to the current CIR level, i.e., selecting the M-algorithm for low CIR and JRSSE otherwise. REFERENCES [1] P. Rysavy. Voice Capacity Enhancements for GSM Evolution to UMTS. White Paper developed for 3G Americas, July [2] M. Austin. 3G Americas SAIC working group. SAIC and Synchronized Networks for Increased GSM Capacity. 3G Americas, White Paper, September 2003.

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