Abstract
Many works have tackled on the problem of throughput and fairness optimization in cellular cooperative relaying systems. Considering firstly a two-user relay broadcast channel, we design a scheme based on superposition coding (SC) which maximizes the achievable sum-rate under a proportional fairness constraint. Unlike most relaying schemes where users are allocated orthogonally, our scheme serves the two users simultaneously on the same time-frequency resource unit by superposing their messages into three SC layers. The optimal power allocation parameters of each SC layer are derived by analysis. Next, we consider the general multi-user case in a cellular relay system, for which we design resource allocation algorithms based on proportional fair scheduling exploiting the proposed SC-based scheme. Numerical results show that the proposed algorithms allowing simultaneous user allocation outperform conventional schedulers based on orthogonal user allocation, both in terms of throughput and proportional fairness. These results indicate promising new directions for the design of future radio resource allocation and scheduling algorithms.
References
Laneman JN, Tse DNC, Wornell GW (2004) Cooperative diversity in wireless networks: efficient protocols and outage behavior. IEEE Trans Info Theory 50(12):3062–3080
Pabst R et al (2004) Relay-based deployment concepts for wireless and mobile broadband radio. IEEE Wirel Commun Mag 42(9):80–89
Zhao Y, Adve R, Lim TJ (2006) Improving amplify-and-forward relay networks: optimal power allocation versus selection. In: Proc of the IEEE international symposium on information theory, Seattle, WA
Kaneko M, Hayashi K, Popovski P, Ikeda K, Sakai H, Prasad R (2008) Amplify-and-forward cooperative diversity schemes for multi-carrier systems. IEEE Trans Wirel Commun 7(5):1845–1850
Popovski P, de Carvalho E (2008) Improving the rates in wireless relay systems through superposition coding. IEEE Trans Wirel Commun 7(12):4831–4836
Cover TM, Thomas JA (2006) Elements of information theory. Wiley, New York
Ng TC-Y, Yu W (2007) Joint optimization of relay strategies and resource allocations in cooperative cellular networks. IEEE J Sel Areas Commun 5(2):328–339
Nam W, Chang W, Chung S-Y, Lee YH (2007) Transmit optimization for relay-based cellular OFDMA systems. In: IEEE ICC, Glasgow, Great Britain
Viswanathan H, Mukherjee S (2005) Performance of cellular networks with relays and centralized scheduling. IEEE Trans Wirel Commun 4(5):2318–2328
Cho J, Haas ZJ (2004) On the throughput enhancement of the downstream channel in cellular radio networks through multihop relaying. IEEE J Sel Areas Commun 22(7):1206–1219
Li G, Liu H (2006) Resource allocation for OFDMA relay networks with fairness constraints. IEEE J Sel Areas Commun 24(11):2061–2069
Kaneko M, Popovski P, Hayashi K (2009) Throughput-guaranteed resource-allocation algorithms for relay-aided cellular OFDMA system. IEEE Trans Veh Technol 58(4):1951–1964
Salem M, Adinoyi A, Rahman M, Yanikomeroglu H, Falconer D, Kim Y-D (2010) Fairness-aware radio resource management in downlink OFDMA cellular relay networks. IEEE Trans Wirel Commun 9(5):1628–1639
Salem M et al (2010) An overview of radio resource management in relay-enhanced OFDMA-based networks. IEEE Commun Surv Tutor 12(3):422–438
Hossain MJ, Alouini M-S, Bhargava VK (2007) Rate adaptive hierarchical modulation-assisted two-user opportunistic scheduling. IEEE Trans Wirel Commun 6(6):2076–2085
Kaneko M, Hayashi K, Popovski P, Sakai H (2011) Fairness-constrained rate enhancing superposition coding scheme for a cellular relay system. In: IEEE WPMC, Brest, France
Kaneko M, Hayashi K, Popovski P, Sakai H (2011) Fairness-aware superposition coded scheduling for a multi-user cooperative cellular system. IEICE Trans Commun E94-B(12):3272–3279
Qualcomm (2001) 1× EV: 1× evolution IS-856 TIA/EIA standard airlink overview. Revision 7.2
Newton M, Thompson J (2006) Classification and generation of non–uniform user distributions for cellular multi–hop networks. In: IEEE ICC, Istanbul, Turkey, pp 4549–4553
Rappaport TS (2001) Communications, wireless, principles and practice, 2nd edn. Prentice Hall
Kushner HJ, Whiting PA (2004) Convergence of proportional-fair sharing algorithms under general conditions. IEEE Trans Wirel Commun 3(4):1250–1259
Kaneko M, Popovski P, Dahl J (2006) Proportional fairness in multi–carrier system: upper bound and approximation algorithms. IEEE Commun Lett 10(6):462–464
Kaneko M, Popovski P, Dahl J (2008) Proportional fairness in multi–carrier system with multi-slot frames: upper bound and user multiplexing algorithms. IEEE Trans Wirel Commun 7(1):22–26
Xie L-L, Kumar PR (2004) A network information theory for wireless communication: scaling laws and optimal operation. IEEE Trans Info Theory 50(5):748–767
Popovski P, de Carvalho E et al (2008) Method and apparatus for transmitting and receiving data using multi-user superposition coding in a wireless relay system. US Patent No. US2008/0227388A1
Tse D, Viswanath P (2005) Fundamentals of wireless communication. Cambridge University Press, Cambridge, UK
Acknowledgments
This work was supported by the Grants-in-Aid for Scientific Research nos. 10595739 and 24560457 from the Ministry of Education, Science, Sports, and Culture of Japan.
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
We derive the achievable rate and optimal power allocation for the 2L-PF-SC scheme.
-
Step 1
For the decoding at the RS,
$$ R_{\mathrm{b1}} \leq C \left(\dfrac{(1-\alpha) \gamma_{\mathrm{R}}}{1+\alpha\gamma_{\mathrm{R}}} \right) = R_{\mathrm{b1}}^{\mathrm{A}}, $$(64)$$ R_{\mathrm{2}} \leq C (\alpha\gamma_{\mathrm{R}} ), $$(65)which ensure that the RS can decode \({\bf x}_{\mathrm {b1}}\), \({\bf x}_{\mathrm {2}}\), respectively.
-
Step 2
For the decoding at MS\(_1\), we get
$$ R_{\mathrm{R2}} \leq C (\gamma_{\mathrm{R1}} ), $$(66)$$ R_{\mathrm{b1}} \leq C ((1-\alpha) \gamma_{\mathrm{D1}} ) = R_{\mathrm{b1}}^{\mathrm{B}} , $$(67)which ensure that MS\(_1\) can decode \({\bf x}_{\mathrm {R2}}\) (\({\bf x}_{\mathrm {2}}\)), \({\bf x}_{\mathrm {b1}}\). For the decoding at MS\(_2\), we obtain
$$\begin{array}{@{}rcl@{}} R_{\mathrm{R2}} \leq & C (\gamma_{\mathrm{R2}}) , \end{array} $$(68)which ensures that MS\(_2\) can decode \({\bf x}_{\mathrm {R2}}\). Equation 66 is satisfied a fortiori given that \(\gamma _{\mathrm {R2}}<\gamma _{\mathrm {R1}}\), so only (68) will be considered for \(R_{\mathrm {R2}}\). \(R_{\mathrm {b1}}^{\mathrm {A}}\), \(R_{\mathrm {b1}}^{\mathrm {B}}\) denote the two constraints on \(R_{\mathrm {b1}}\) to be satisfied.
In Step 1, the BS transmits \(M(\min (R_{\mathrm {b1}}^{\mathrm {A}},R_{\mathrm {b1}}^{\mathrm {B}})+R_{\mathrm {2}})\) bits, where \(M\) is the number of symbol times. In Step 2, the RS forwards \(MR_{\mathrm {2}}\) bits. The sum rate can thus be written
and the PF constraint between MS\(_1\) and MS\(_2\) is given by
Next, we consider the different cases arising from the conditions on \(R_{\mathrm {b1}}\).
Case 1
\(R_{\mathrm {b1}}^{\mathrm {A}} \leq R_{\mathrm {b1}}^{\mathrm {B}} \Leftrightarrow \alpha \geq \alpha ^*=\frac {1}{\gamma _{\mathrm {D1}}}-\frac {1}{\gamma _{\mathrm {R}}}\). In this case, \(R_{\mathrm {b1}}=R_{\mathrm {b1}}^{\mathrm {A}}\). Condition (70) becomes
which gives by straightforward calculations,
From (72) and (69), we obtain the achievable rate in this case,
Inserting (72) into condition \(\alpha \geq \alpha ^*\), the rate expression is valid for
Case 2
\(R_{\mathrm {b1}}^{\mathrm {A}} > R_{\mathrm {b1}}^{\mathrm {B}} \Leftrightarrow \alpha < \alpha ^*\). In this case, \(R_{\mathrm {b1}}=R_{\mathrm {b1}}^{\mathrm {B}}\). Condition (70) becomes
We denote \(f(\alpha )=1+(1-\alpha )\gamma _{\mathrm {D1}}\) and \(g(\alpha )=(1+\alpha \gamma _{\mathrm {R}})^{\frac {\bar {R}_1}{\bar {R}_2}}\). \(f(\alpha )\) is a monotonically decreasing function of \(\alpha \) over \([0,1]\) with \(f(0)=1+\gamma _{\mathrm {D1}} \geq 1\) and \(f(1)=1\). \(g(\alpha )\) is a monotonically increasing function of \(\alpha \) over \([0,1]\) with \(g(0)=1\) and \(g(1)=(1+\gamma _{\mathrm {R}})^{\frac {\bar {R}_1}{\bar {R}_2}}\geq 1\). Thus, there exists a unique value \(\tilde {\alpha }\) in \([0,1]\) such that \(f(\tilde {\alpha })=g(\tilde {\alpha })\), which can be easily determined numerically. Thus, the achievable rate (69) is expressed as
in the case \(\gamma _{\mathrm {D1}} < \frac {\gamma _{\mathrm {R}}}{(1+\gamma _{\mathrm {R}})^{\frac {\bar {R}_2}{\bar {R}_1+\bar {R}_2}}}\).
Rights and permissions
About this article
Cite this article
Kaneko, M., Hayashi, K., Popovski, P. et al. Proportional fair scheduling with superposition coding in a cellular cooperative relay system. Ann. Telecommun. 68, 525–537 (2013). https://doi.org/10.1007/s12243-012-0337-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12243-012-0337-4