The use of guard bands to mitigate multiple access interference in the OFDMA uplink

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1 The use of guard bands to mitigate multiple access interference in the OFDMA uplink Mathias Bohge, Farshad Naghibi, Adam Wolisz TKN Group, TU Berlin, Einsteinufer 25, 1587 Berlin, Germany {bohge Abstract The usual approach to mitigate multiple access interference (MAI) in the uplink of cellular OFDMA based systems is to use relatively large cyclic prefixes as time domain guard periods. In this paper, we suggest to use a combination of short time domain guard periods and frequency domain guard bands to protect against MAI instead. Guard bands can be added and removed as necessary and, thus, increase the MAI protection flexibility. We show that, if optimally applied, the use of guard bands can significantly increase the system s uplink capacity or minimum capacity per user. 1 I. INTRODUCTION A major challenge in realizing uplink transmissions in OFDMA (Orthogonal Frequency Division Multiple Access) systems lies in synchronizing the participating entities in the time, as well as the frequency domain. This is mainly due to the fact that in the OFDMA uplink each transmitted OFDM symbol is constructed out of components that are contributed by different terminals. Even though there are numerous methods to combat timing and frequency offsets in according systems (see [1] for a comprehensive overview), there is always a chance for residual offsets among the terminals and the base station in a cellular OFDMA-based system [2], especially in the time domain. These residual offsets susp the orthogonality among the OFDM sub-carriers and, thus, lead to multiple access interference (MAI). In order to suppress MAI, a common approach is to use large time-domain guard periods that assure orthogonality among sub-carriers. As an alternative approach, in this paper we explore the usage of frequency-domain guard bands to efficiently suppress MAI due to timing offsets. Moreover, it is well known that applying dynamic resource allocation to downlink transmissions of OFDMA systems provides a significant performance increase, by taking advantage of diversity effects [3]. It is tempting to consider exploiting these diversity 1 This work has been supported by the German Ministry of Education and Science (BMBF) and Ericsson Research, Germany, in the context of the project ScaleNet. effects also in the uplink of the respective systems. Most approaches to optimize resource allocation in OFDMA uplink systems assume perfectly orthogonal sub-carriers (e.g. [4] or [5]), and, thus, do not incorporate the MAI mitigation into the optimization problem. However, since the MAI strongly deps on the distribution of sub-carriers among the terminals, it needs to be considered when dynamically assigning sub-carriers to terminals. In this paper, we incorporate the mitigation of MAI into the subcarrier allocation process by using guard bands between frequencies assigned to individual terminals. The usage of guard bands to mitigate MAI due to timing offsets in OFDMA systems has first been studied in [6]. However, to the best of our knowledge, it has never been incorporated into the dynamic resource allocation processes known from the OFDMA downlink. The remainder of this paper is organized as follows. In the following section, we introduce our system model. Then, in Section III, we introduce the approach of using guard bands in combination with short guard periods. We present the guard band incorporated resource assignment optimization problem in Section IV. In Section V, we present our simulation methodology and parameterization and present our results. We conclude our work and mention some future issues in Section VI. II. SYSTEM MODEL We consider a single cell c of a cellular system consisting of a base station and user terminals. The cell has a radius of r cell. J terminals are distributed among the cell following a uniform distribution. Each terminal is moving at a speed of v. The time offset l j between a terminal j and the base station is bounded by the maximum delay T max. A. Physical Layer The system under consideration uses OFDM as transmission scheme for uplink data transmission. It has a total uplink bandwidth of B UL [Hz] at center frequency f c. The given bandwidth is split into S

2 sub-carriers (with a spacing of B UL /S and a symbol length of T s each). Prior to the transmission of the OFDM symbol, a cyclic prefix of length T g is added as guard period in time domain. The maximum transmission power P max per cell is statically distributed over the sub-carriers (P T = P max /S). B. User Data Multiplexing Time is slotted into transmission time intervals (TTI) of duration T TTI. During a single TTI, uplink data multiplexing is done by frequency division multiple access (FDMA), where the smallest addressable bandwidth-unit is a sub-channel. In the frequency domain, a sub-channel consists of a well defined number of adjacent sub-carriers. In the time domain, a sub-channel spans all OFDM symbols available for user data transmission of the respective TTI. Two cases of terminal/sub-channel assignments are considered: static block-wise, and a dynamic assignment. In the dynamic case, the assignment selection is based on available channel state information (CSI) and the predicted interference situation per TTI. In both cases, the scheduler determines the appropriate modulation type per sub-channel, again based on the CSI. We assume the sub-channel per terminal and modulation per sub-channel assignments to be delivered on a separate reliable control channel. For a discussion on system performance constraint to control channel reliabilty see [7]. C. Wireless Channel Model Terminal j s instant signal-to-interference-plusnoise ratio (SINR) value γ (t) j,s per sub-carrier s varies over time due to its varying channel gain (reflecting path-loss, shadowing, and fading) and MAI caused by surrounding terminals: γ (t) j = P j,s,s, (1) J 1 M j (s l j ) (t) + σ 2 j=,j j where P j,s = P T (h (t) j,s )2 denotes the average received power on sub-carrier s of terminal j (and h (t) j,s denotes terminal j s average channel gain on sub-carrier s versus the base-station), M j (s l j ) (t) is the average power of the MAI generated on the s-th sub-carrier by the j-th user conditioned on its time offset l j relative to user j (as described in the next section), and σ 2 denotes the noise power per subcarrier. We assume a maximum number of N p fading paths. The individual path gains are indepent with zero mean each. D. Multiple Access Interference According to [2], [6], the average power of the MAI generated on the s-th sub-carrier by the j- th user conditioned on its relative time offset l j is computed as M j (s l j ) = A s,k,lj k Γ j P j,k S 2 sin 2 ( π (2) S (s k)) if the transmitted symbols are assumed i.i.d. with zero mean, thus, the MAI has zero mean, too. Note that Γ j is the set of sub-carriers assigned to user j. The A s,k,lj deps on the user s delay l j and the distance (s k) in frequency between the assigned sub-carrier s and the interfering sub-carrier k. An according formula is provided e.g. in [6]. III. THE USAGE OF FREQUENCY DOMAIN GUARD BANDS In order to mitigate MAI a common approach is to use large cyclic prefixes per OFDM symbol as time domain guard periods. However, the selection of an appropriate guard period has a significant impact on the system performance: choosing too large periods limits the system capacity more than necessary, whereas choosing too short ones increases the probability of MAI, and, thus, the error probability [6]. As an alternative to using long cyclic prefixes per OFDM symbol, frequency-domain guard bands can be used to separate frequency regions of users that experience different timing offsets versus the base station l j [6]. Using guard bands allows for short time domain guard periods, as guard bands can be added or omitted as needed, deping on the current sub-carrier assignment situation. As an example, we envision a modification of a Worldwide Interoperability for Microwave Access (WiMAX, IEEE82.16e) [8]. The modified system features short cyclic prefixes in combination with frequency domain guard bands. Originally, a guard period length of T g = 11.4µs is suggested for the standard WiMAX uplink [9]. This number is quite large compared to the expected maximum delay spread (e.g. τ ds < 2µs in an urban environment [1]). In our modified system approach, we, assume a guard period length of T g = 3µs. It is, thus, large enough to cope for the maximum delay spread, but does not protect against user timing offsets. Hence, the overall OFDM symbol duration T in the modified system is shorter by the difference = 11.4µs 3µs = 8.4µs). Accordingly, more OFDM symbols can be sent per TTI. To integrate the guard bands into the existing WiMAX standard, we apply a simple policy: each user can use its allocated sub-channels

3 Avg. SINR [db] Impact of MAI No MAI MAI Long CP MAI Short CP Avg. SINR [db] Effect of guardband Short CP GB GB1 GB2 9 Subchannel index (a) The impact of MAI on the average SINR per subchannel in the static block-wise assignment scenario for long and short cyclic prefixes (CPs). 9 Subchannel index (b) The usage of frequency-domain guard bands (GB) effectively mitigates MAI. Fig. 1. The impact of multiple access interference (MAI) on the SINR, and the usage of guard bands (GBs) to suppress MAI. either as data sub-channel or as guard band subchannel at the border of its frequency region. Thus, a trade of exists: the higher the number of guard bands in use, the better the protection against MAI, but the lower the number of sub-channels available for data transmission. TABLE I CAPACITY COMPARISON [KBITS/FRAME]. Long Guard Period - Block Assignments Avg. cell capacity (no MAI) Avg. cell capacity (w. MAI) Short Guard Period - Block Assignments Avg. cell capacity (no MAI) Avg. cell capacity (w. MAI) 65.2 Figure 1(a) shows the impact of MAI on the SINR of a user in a WiMAX system with static block-assignments for a sample configuration (1 users, 1 adjacent sub-channels per user, described in Section V in detail). It can be seen that in the case of long cyclic prefixes (CPs), the MAI protection is better than in the case of short CPs. However, in Table I it is shown that, even if MAI is considered, the capacity is larger, if short cyclic prefixes are used. Apparently, the gain in capacity due to the transmission of additional OFDM symbols per TTI is higher than the loss due to an increased MAI. Figure 1(b) shows that the impact of the usage of guard bands in the short CP case: if two subchannels per user are used as guard bands MAI can be completely mitigated. However, since there is a trade off between the guard band size and the system bandwidth available for data transmission, simple guard band assignment strategies may lead to system capacity decreases. Consequently, there is a need for an intelligent way to place the guards. IV. OPTIMIZATION MODEL It is well known that applying dynamic resource allocation to downlink transmissions of OFDMA systems provides a significant performance increase in terms of system capacity by taking advantage of diversity effects [3]. In the downlink of such systems each sub-carrier, or small group of sub-carriers (subchannel), is individually assigned to the user that can use it best in order to achieve the system optimization target (e.g. max. system throughput, or max. peruser throughput). For the uplink direction, we would like to modify the existing downlink optimization models to include the decision on guard bands to mitigate MAI. An according approach based on maxmin capacity optimization (see [11]) is the following: s.t. a) b) n j max ε (3) [ ] F sinr2bit (γ (t), P err) ε j 1 n, where is a binary optimization variable that maps sub-channel n to user j at time t, γ (t) is the instant SINR of user j on sub-channel n at time t: γ (t) = σ 2 + j j;k Γ j P M j (n k, l j ) j,k, (4) and F sinr2bit (γ (t), P err) is a function that maps a perceived SINR to a certain modulation (i.e. number of bits per symbol) subject to an admitted maximum error rate P err. Constraint b) assures that each subchannel is assigned to at most one user at a time. Since the sum is allowed to take values smaller than

4 1, i.e. (since is a binary optimization variable), a sub-channel might not be assigned to any user and, thus, act as a guard band. A sub-channel is selected to be a guard band, if the capacity gain due to the the suppression of MAI and the resulting improvement in SINR is larger than the loss in capacity that is due to not using the sub-channel for data transmission. Constraint a) compares the capacity assigned to each user with a lower threshold ε. Since optimization goal (3) maximizes this threshold, the capacity of the weakest user is maximized. However, since in contraint a) γ (t) is multiplied by x(t), this optimization problem is non-linear. It, thus, cannot be solved with the linear program solvers, and is hard to handle. Consequently, in Equation (5) we come up with a linear program that, in combination with Algorithm 1, yields a sub-optimal guard band placement strategy that significantly improves the system performance. s.t. a) b) n j,m max ε (5) [ ] F sinr2bit (ˆγ (t), P err),1 ε j,m = 1 n c) if (,1 = 1 & x(t) 1,1 = ) 1, = 1 j, n Here, the optimization variable,m has three dimensions: the user j, the sub-channel n, as well as the mode of operation m. The latter takes either the value 1 for data transmission or for guard band operation. Since each sub-channel either is used as guard band or for data transmission, the sum over all assignment variables per sub-channel in constraint b) must be equal to 1. Constraint c) assures that between any two sub-channels assigned to different users there is at least one sub-channel used as guard band. In this case, ˆγ (t) in constraint b) is the simple signal-to-noise ratio: ˆγ (t) = P σ 2 (6) Hence, this optimization model is linear. The outcome is an optimal partitioning of the bandwidth among the users, where the regions of any two users are separated by a guard band. However, since we do not consider MAI in the optimization problem, some of the selected guard bands might not be necessary, if there is no or a very small relative time offset between neighboring users. To avoid this wastage of capacity, Algorithm 1 is applied on the outcome: Data: X (t) gb : Vector of GB sub-channel indexes. 1 for (n X (t) gb ) do 2 find j and j so that 1,1 = 1 & x(t) +1,1 = if T j T j < δ th then if γ (t) > γ(t) j,n then 5,1 = 1 else 6 j,n,1 = 1 Algorithm 1: Guard band deselection Here, T j is user j s time offset relative to the base station, γ (t) is the SINR according to Equation (1), and δ th is the delay threshold that decides on the necessity of guard band usage. Parameters TABLE II SYSTEM PARAMETERS. Value Carrier Frequency 2.5 GHz Channel Bandwidth 1 MHz Number of mobile stations (MS) 1 MS Maximum TX Power 23 dbm MS Maximum Time Offset 2 µs MS Maximum Speed 3 km/h Maximum admitted bit error rate 1 3 Sub-carrier Spacing 1.94 khz Sub-carriers per Sub-channel 9 Guard Interval (GI) - long 11.4 µs Guard Interval (GI) - short 3.µs OFDM Symbol Duration (w/o GI) 91.5 µs Propagation Model COST 231 Urban Microcell Cell Radius 5 m Delay Spread 1.8 µs Penetration Loss 1 db Lognormal Shadowing SD 1 db Fading Model Rice V. PERFORMANCE EVALUATION We have simulated the system as described in Section II using the free C++ simulation library OMNeT++ [12]. Several runs of 2 uplink phases have been simulated. The instances per phase of optimization problem (5) have been passed to and solved by ILOG s CPLEX solving software. The simulation parameters are given in Table II.

5 Avg. capacity [bits/frame] Block Short CP Avg. capacity [bits/frame] Max Min Opt. Short CP Avg. capacity [bits/frame] 4 x Raw rate Optimal Fig. 2. Capacity results of all ten users for the block-wise, the max min optimization, and the raw rate maximization case. A. Results The results shown in Figure 2 and Table III indicate two major facts: Using guard bands in a static way (non adaptive to the actual MAI) as described in Section III leads to improvements in the SINR, but decreases the capacity per user, as the capacity gain from the increased SINR is smaller than the loss that stems from turning data sub-channels into guard bands. However, using guard bands in the context of dynamic resource allocation improves the performance according to the respective optimization goal. Incorporating guard bands e.g. in the max min linear program following Equation (5) yields an valuable increase in worst user capacity. Integrating guard band selections into the raw rate/sum cell maximization linear program as described in [11] yields a higher overall system capacity. TABLE III CAPACITY IN DIFFERENT ASSIGNMENTS [KBITS/TTI]. Raw-rate optimal Avg. cell capacity (w.o. GB) Avg. cell capacity (w. GB) Max-min optimal Worst user s avg. capacity (w.o. GB) Worst user s avg. capacity (w. GB) VI. CONCLUSIONS We have demonstrated that the usage of frequency domain guard bands is an efficient means to mitigate multiple access interference (MAI) in the uplink of OFDMA based cellular systems. We have shown that, even with a simple realization of guard bands based on unused sub-channels, significant increases in system capacity or minimum user capacity can be achieved in a WiMAX like system, if the distribution of data and guard band sub-channels is carefully determined. As demonstrated, already the usage of the simple definition sub-channel sized guard bands leads to valuable improvements. Future research will address more fine-grained allocation of guard bands. REFERENCES [1] M. Morelli, C.-C.J.Kuo, and M.-O. Pun, Synchronization techniques for orthogonal frequency division multiple access (OFDMA): A tutorial review, Proceedings of the IEEE, vol. 95, no. 7, pp , July 27. [2] X. Wang, T.T. Tjhung, Y. Wu, and B. Caron, SER performance evaluation and optimization of OFDM system with residual frequency and timing offsets from imperfect synchronization, IEEE Transactions on Broadcasting, vol. 49, no. 2, pp , June 23. [3] C.Y. Wong, R.S. Cheng, K.B. Letaief, and R. Murch, Multiuser OFDM with adaptive subcarrier, bit and power allocation, IEEE Journal on Selected Areas of Comm., vol. 17, no. 1, pp , Oct [4] Z. Cao, U. Tureli, and P. Liu, Optimum subcarrier assignment for OFMDA uplink, in Proceedings of the 37th Asilomar Conference on Signals, Systems and Computers, Nov. 23, vol. 1, pp [5] K. Kim, Y. Han, and S.-L. Kim, Joint subcarrier and power allocation in up-link OFDMA systems, IEEE Communication Letters, vol. 9, no. 6, June 25. [6] A.M. Tonello, N. Laurenti, and S. Pupolin, Analysis of an asynchronous multi-user DMT OFDMA system impaired by time offsets, frequency offsets, and multi-path fading, in Proc. of 52nd IEEE Vehicular Technology Conference (VTC-Fall ), Boston, MA, USA, Sept. 2, pp [7] M. Bohge, A. Wolisz, A. Furuskar, and M. Lundevall, Multi-user OFDM system performance subject to control channel reliability in a multi-cell environment, in Proceeding of the IEEE International Conference on Communications ICC 8, Bejing, China, May 28. [8] IEEE, Standard for local and metropolitan area networks part 16: Air interface for fixed and mobile broadband wireless access systems amment 2: Physical and medium access control layers for combined fixed and mobile operation in licensed bands and corrigum 1, February 26, IEEE Std 82.16e-25. [9] WiMAX Forum, Mobile WiMAX - Part II: A comparative analysis, v3.3, 26. [1] Spatial Channel Model Ad-Hoc Group 3GPP, Spatial channel model text, scm-132, SCM Text V5., Apr. 23. [11] M. Bohge, J. Gross, and A. Wolisz, The potential of dynamic power and sub-carrier assignments in multi-user OFDM-FDMA cells, in Proc. of IEEE Globecom 25, St. Louis, MO, USA, Nov. 25. [12] Andras Varga, OMNeT++ User Manual 3.2.