Trellis-Coded-Modulation-OFDMA for Spectrum Sharing in Cognitive Environment

Transcription

1 Trellis-Coded-Modulation-OFDMA for Spectrum Sharing in Cognitive Environment Nader Mokari Department of ECE Tarbiat Modares University Tehran, Iran Keivan Navaie School of Electronic & Electrical Eng. University of Leeds Leeds, UK Hamid Saeedi Department of ECE Tarbiat Modares University Tehran, Iran Abstract In this paper, we consider an underlay spectrum sharing system and propose utilizing discrete rate Trellis Coded Modulation Orthogonal Frequency Division Multiple Access (TCM-OFDMA) technique in the secondary system. Downlink radio resource allocation schemes are then proposed for such system. Simulation results indicate that using the proposed scheme, we can significantly increase the sum rate compared to conventional uncoded OFDMA schemes with only a moderate increase in system complexity. It is also shown that in cases where the secondary network is unable to achieve higher rates by increasing the total power and/or interference threshold, utilizing TCM-OFDMA acts as a smart alternative. I. INTRODUCTION The spectrum sharing is a promising technology to use the available spectrum efficiently []. Generally, in spectrum sharing the unlicensed users (secondary users) are allowed to use the licensed spectrum bands subject to not having unexpected degrading effect on the performance of licensed users (primary users) [] and []. Utilizing efficient radio resource allocation strategies in multiuser wireless networks makes it possible to exploit inherent multiuser multichannel diversity gain []. The radio resource allocation problem for multicarrier systems is a well developed topic in wired xdsl and traditional multiuser wireless networks (see, e.g., [], and [] and references therein). It is shown that, in downlink wireless networks based on Frequency Division Multiplexing (OFDM) technology including multiple noncooperative users, OFDMA is an optimal solution for allocation of subcarriers across users to exploit inherent multiuser diversity []. The state-of-the-art trends in wireless radio resource allocation in traditional wireless networks can be found in [8] and [9]. In spectrum sharing, OFDMA provides the required flexibility to the secondary service to access separate under-utilized portions of the spectrum band and at the same time exploits the frequency selectiveness of the wireless channel []. Recently, different works have been conducted to extend and actually reform the previously obtained results in the traditional radio resource allocation into the spectrum sharing systems. In [] and [], resource allocation problems in underlay spectrum sharing environment considering Code Division Multiple Access (CDMA) as the primary service air interface has been studied. Assuming ergodic capacity as the performance measure of the secondary service, extension of the result into discrete rate allocation in underlay cognitive radio system can be found in []. A comprehensive survey on the radio resource allocation in cognitive radio networks can be found in []. One of the major differences between the traditional resource allocation problems and those of cognitive networks that use underlay strategy, is the limitation on the allocated power for each subcarrier to adhere to the imposed interference for primary receivers. Therefore, there exist some situations in which even though the secondary transmitter has more power budget, it can not allocate all power budget due to this limitation. In such cases, as opposed to the traditional case, the sum rate of the users does not increase and saturates with the increase of total allowable power. In order to increase the data rate of users, channel coding can be used as a solution. Since in most practical systems, non-binary modulations are used, the use of joint channel coding and modulation, Trellis Coded Modulation (TCM) [], can achieve high spectral efficiency and improves performance. In this paper, we propose to use adaptive trellis coded modulation [] to improve the system performance in which we allow adaptive coding rate in the optimization problem. We show that using the proposed scheme, we can significantly increase the sum rate compared to the uncoded case with only a moderate increase in system complexity. Throughout the paper, the channel between secondary users and secondary base station is called the secondary channel and the estimated secondary channel state information is abbreviated by S-CSI. We assume that this estimate is available to the secondary base station. Also, the channel between the secondary base station and primary service users is called the interference channel. For the interference channel, we consider two cases. In the first case, we assume that the interference channel state information, abbreviated by I-CSI, is available to the secondary base station. In this case, interference threshold constraint is used in the optimization problem. In the second case, we assume that the estimated I-CSI is not available to the secondary base station and instead, the interference channel distribution information abbreviated by I-CDI, is considered known. In this case, the collision probability constraint is used in the optimization problem. Consequently, we compare the performance of the two cases and show that the performance degradation due to the absence of I-CSI is tolerable given the //$. IEEE 9

2 Fig.. Schematic of the TCM Encoder. Fig.. The network model. k =,...,K. It is further assumed that c is much smaller than that of the coherent bandwidth of the wireless channel. Therefore the subcarriers undergo a flat fading. In this paper, based on the available knowledge from the interference channel at the secondary base station, two criteria are considered to represent the QoS of the primary users. In cases where only the I-CDI is available at the secondary base station, the QoS of the jth primary user which transmits on subcarrier k is denoted by a pair of parameters, (Q jk,η jk ), where Q jk is the interference threshold, and η jk is the maximum tolerable collision probability. For primary user j on subcarrier k, collision is experienced if the imposed interference by the secondary service transmission at the primary service receiver, I jk, is higher than Q jk. The collision probability constraint η jk is then defined as Pr{I jk >Q jk } η jk. () Fig.. The system model. practical difficulty in obtaining such information from primary users. Moreover, such degradation can almost be compensated using TCM. The organization of the rest of paper is as follows: In Section II, the considered system model and main assumptions are presented. The radio resource allocation problem is developed in Section III. Simulation results are presented in Section IV and a summary and conclusions are provided in Section V. II. SYSTEM MODEL We consider a secondary network including a secondary base station which serves M secondary users indexed by m =,...,M. We also consider a primary network including a primary base station which serves J primary users indexed by j =,...,J. In this paper, Our focus is mainly on the downlink radio resource allocation in the secondary network as shown in Fig.. The system under study is in fact a TCM-OFDMA system as shown in Fig.. The resource allocation is assumed to be implemented at the secondary base station which has to evaluate subcarrier assignment to each user as well as the rate and power allocation corresponding to each subcarrier. The system bandwidth is Hz which is licensed to the primary service. Hereafter, this licensed spectrum is referred to as the spectrum, unless otherwise stated. The spectrum is divided into K non-overlapping subcarriers each with c = /K Hz bandwidth. Subcarriers are indexed by k, where Traditional coding schemes such as cyclic block codes and convolutional code were initially developed using a simplifying assumption of employing the inary Phase Shift Keying (PSK) modulation over the channel. It such cases, if a higher order modulation is to be used, the decoding and modulation have to be performed separately leading to a reduction in the spectral efficiency. In 9, Ungerboeck ([], []) proposed a new coding scheme called TCM in which coding and modulation are designed and performed jointly based on the idea of set partitioning. This leads to a significant performance improvement in systems that use higher order modulations together with coding. Considering that in our system we use adaptive high order modulation, TCM will be a natural choice for channel coding method. Such utilization in cognitive networks has also been considered in [8] but not in the context of resource allocation. For each subcarrier we consider a TCM encoder which encodes and transmits the information to the secondary users (see Fig. ). ased on the discussions in [9], the achievable capacity of the secondary user m on subcarrier k is: c mk = log ( + p mk G c h mk ), () where p mk is the assigned power to user m on subcarrier k at the secondary base station, G c is the coding gain achieved by TCM, and h mk denotes the scaled channel to interferenceplus- noise ratio (CINR) at the secondary user m on subcarrier k, α mk h mk = Γ mk (σmk + I mk), () where, α mk is the power gain of the flat fading channel between the secondary base station and the secondary user m //$. IEEE 9

3 on subcarrier k which we refer to as the secondary service channel power gain. In (), σmk is the background noise power, I mk is the received interference at the front-end of the secondary user s receiver m on subcarrier k, and Γ mk is the SNR gap which is obtained for a given target bit error rate, ER mk, and modulation type, as ([9] page 8) ( ) c Γ mk = c ln, () ER mk where c and c are constants which are, in practice, related to the type of modulation and noise margins Similar to []. We denote the allocated power vector to subcarrier k, corresponding to secondary users m =,...,M by p k = [p k,...,p Mk ] T, which is an M vector. Similarly, an MK secondary base station power vector is denoted across all secondary users and subcarriers by p =[p T,...,p T K ]T. The secondary service base station allocates the radio resources based on an imperfect estimation of the channel gains denoted by ĥmk, where [] h mk = ĥmk +Δ mk. () Here, Δ mk denotes the estimation error, where it is usually modeled by a zero mean complex Gaussian random variable with variance δmk. Random variables Δ mks are independent across different subcarriers and for different users. The corresponding achievable rate to the secondary user m if assigned to subcarrier k is ( ) r mk = log +p mk G c ĥ mk. () III. OPTIMAL RADIO RESOURCE ALLOCATION In this section, we consider the optimal radio resource allocation strategy in which we assume that the secondary system is able to provide discrete bit rates. Our objective is to maximize the weighted sum rate at the secondary service base station which is defined as Δ M K R S = (r mk ), () ω m k= where we consider ω m s as higher layer system coefficients to imply fairness in resource allocation and changing users priorities such that m ω m =. In (), subtraction of one from the allocated rate on the each subcarrier is considered to r r+ TCM represent the redundant bit which is used in a rate encoder (see Fig. ). The radio resource optimization problem is then defined as follows: Problem O : max r R s.t. ω m (r mk ), (8) p mk P T, (9) { M } Pr p mk g jk Q jk η jk, k, j, () Pr {r mk log ( + p mk G c (r mk )h mk )} ζ mk k, m. () Since in practice, the systems use Square M-array Quadrature Amplitude Modulation (MQAM) constellations, we consider a practical case in which the base station only supports a set of discrete rates for transmission. The allocated rate to any user m on subcarrier k is r mk χ, where χ = {(j ) j =,...,Q}. () The feasible rate set, R, is defined as R = R... R K. ased on the OFDMA assumption in which each subcarrier is corresponded to only one user, we define R k, k =,...,K as and R k = {r k r k,r mk r ˆmk =, m ˆm}, () r k Δ =[rk,...,r Mk ] T. () In O, (9) represents the maximum transmission power constraint at the secondary base station, i.e., the total allocated power across all secondary users and different subcarriers must be smaller than the maximum allowable transmission power P T. Moreover, () denotes the collision probability constraint on each subcarrier across all primary service receivers in which g jk is a random variable that indicates the I-CSI of power gain for primary service receiver j on subcarrier k. Furthermore, () represents the outage probability constraint in the secondary system with the maximum allowable outage probability ζ mk. This is a direct consequence of the imperfect S-CSI at the secondary base station for all the secondary users and across all subcarriers. In order to investigate the performance of the case with perfect S-CSI in O, we define a new optimization problem of Ô in which the outage probability constraint () is removed. To solve O and Ô, we use an approach similar to []. We also study the problem of radio resource allocation based on the availability of the I-CSI instead of I-CDI. In this case, the primary service QoS is modelled through the following constraint p mk ĝ jk Q jk, k, j, () where ĝ jk indicates the estimated of I-CSI of power gain for primary service receiver j on subcarrier k. The optimization problem for allocating the resources at the secondary base station can be easily obtained by exchanging () with collision probability constraint () in O as follows: Problem Õ: The problem for uncoded case is similar to O except that (9) is modified to max r R ω m (r mk ) and the coding gain G c is set to //$. IEEE 9

4 max r R s.t. ω m (r mk ), () p mk P T, () p mk ĝ jk Q jk, k, j, (8) Pr {r mk log ( + p mk G c (r mk )h mk )} ζ mk k, m. (9) We solve Õ using an approach similar to []. IV. SIMULATION RESULTS In this section we investigate different system aspects through simulations. We consider a single cell TCM-OFDMA system as the secondary service. The total bandwidth of the system is KHz which is divided into 8 subcarriers. There are primary users which all have equal interference thresholds. We also consider secondary users. The performance measure is the sum rate of the secondary service, which has been normalized to the total channel bandwidth. The data rate on the each subcarrier belongs to the set χ = {,,, } and the coding gain vector is G c =[.9..9] []. We also consider c =. and c =. [9]. In Fig., we plot the sum rate of secondary users versus the maximum secondary base station transmission power, P T, for different values of interference thresholds. In this simulation we assume that the I-CSI is not available. As it is observed, increasing P T results in increasing the achievable sum rates. Moreover, by increasing the interference threshold, the achievable sum rate is increased although the maximum transmission power P T is kept constant. It is mainly due the fact that increasing the level of acceptable interference at the primary service receiver enables the base station to transmit with a higher transmit power. Therefore, a larger portion of P T can be utilized. We also compare the coded and uncoded cases. As it is seen in Fig., without adopting TCM, for lower values of P T, the network is in fact not feasible and the sum rate is zero. For higher values of P T, the sum rate saturates and is not increased by increasing P T. This, however, is not the case for the coded case, resulting in significantly higher rates. Moreover, for higher interference thresholds, the increase in interference threshold does not add to the sum rate for the uncoded case. y deploying TCM, however, one can take advantage of the permitted higher interference threshold. Therefore, in cases where the secondary network is unable to achieve higher rates by increasing total power and/or interference threshold, utilizing TCM-OFDMA acts as a smart alternative. In this paper, we also compare the case where the estimated I-CSI is available, with the case where only the I-CDI is available. The error in I-CSI estimation is modeled as in () where instead of δ mk, the variance of estimation error in I-CSI is denoted by δ jk = δ. In Fig. we plot the average collision Sum Rate of Secondary Users [it/sec/hz] TCM OFDMA & Q=N TCM OFDMA & Q=N TCM OFDMA & Q=.N OFDMA & Q=N OFDMA & Q=N OFDMA & Q=.N P T Fig.. Sum rate of the secondary users for O vs. maximum transmission power at the secondary base station, P T, for different values of the interference threshold Q jk = Q, j, k. The system parameters are: η jk =., j, k, δmk =., ER mk = m, k, and ζ mk =., m, k. probability versus the variance of I-CSI estimation error. As it is seen, for δ =, i.e., perfect I-CSI estimation, the collision probability is zero as expected. However, by increasing the estimation error, the probability of collision quickly increases and exceeds the collision probability constraint. This suggests that in case of uncertainty about the correct estimation of CSI, it might be better to use I-CDI and allow a controlled level of collision probability in the optimization. It is also seen that in case of imperfect I-CSI estimation adopting TCM is able to compensate for the impact of estimation error. For example for δ =., TCM-OFDMA reduces the collision probabiltiy to almost half of that of OFDMA. Average of Collision Probability OFDMA and Collision probabilty based on estimated I CSI TCM OFDMA and Collision probabilty based on estimated I CSI. TCM OFDMA and Collision probabilty based on I CDI OFDMA and Collision probabilty based on I CDI δ Fig.. Collision probability in O and Õ vs. the variance of interference channel estimation error, δ jk = δ, j, k. The system parameters are: ζ mk =., m, k, Q jk = N, j, k, P T = Watts, δmk =., m, k, and ER mk = m, k. In Fig., we study the impact of the collision probability constraint, η, on the sum rate of the secondary service for different ER s. As it is seen, for a given maximum transmission power of the secondary base station, P T, by increasing η, the sum rate of the secondary service is also increased. Another important observation is that for ER of and η<., only by adopting TCM the system is able to provide a nonzero sum rate. It is also seen that for ER of, adopting //$. IEEE 9

5 TCM results in a higher achieved sum rate for the secondary system. Sum Rate of Secondary Users [it/sec/hz] TCM OFDMA & ER= OFDMA & ER= TCM OFDMA & ER= OFDMA & ER= Fig.. Sum rate of the secondary users for O vs. the collision probability constraint η jk = η, j, k for different values of ER mk = ER, m, k. The system parameters are: ζ mk =., m, k, Q jk = N, j, k, P T = Watts, and δmk =., m, k. In Fig. for the case of availability of I-CDI, we compare two cases where perfect and imperfect S-CSI is available. We consider both coded and uncoded cases. As expected, the sum rate performance degrades in case of imperfect estimation. It is, however, very interesting to observe that the performance degradation due to this imperfectness is considerably lower for the coded case. This suggests another great advantage of using TCM-OFDMA. Sum Rate of Secondary Users [it/sec/hz] 8 Perfect S CSI & TCM OFDMA Perfect S CSI & OFDMA Imperfect S CSI ζ=. & TCM OFDMA Imperfect S CSI ζ=. & OFDMA η P T Fig.. Sum rate of the secondary users based on I-CDI in O and Ô vs. the maximum transmission power at secondary base station, P T, for different values of ζ mk = ζ, m, k. The system parameters are: η jk =., j, k, Q jk = N, j, k, δmk =., m, k, and ER mk = m, k. V. CONCLUSIONS In this paper, we considered an underlay spectrum sharing system and proposed utilizing discrete rate TCM-OFDMA technique in the secondary system. Downlink radio resource allocation schemes were then proposed for such system. Simulation results indicated that using the proposed scheme, we can significantly increase the sum rate compared to the uncoded case with only a moderate increase in system complexity. Moreover, we observed that TCM-OFDMA can almost compensate for the performance degradation caused by using I-CDI instead of I-CSI. 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