Spectral Efficiency Comparison of Ofdm and Mc-Cdma with Carrier Frequency Offset

RADIOENGINEERING, VOL. 26, NO. 1, APRIL 2017 221 Spectral Efficiency Comparison of OFDM and MC-CDMA with Carrier Frequency Offset Junaid AHMED Dept. of Electrical Engineering, COMSATS Institute of Information Technology, Tarlai Kalan, 45550 Islamabad, Pakistan [email protected] Submitted March 4, 2016 / Accepted December 15, 2016 Abstract. Inter-carrier interference and multiple access ficiency degradation of MC-CDMA, in the presence of CFO, interference due to carrier frequency offset (CFO) are two over a frequency selective Rayleigh fading environment is major factors that deteriorate the performance of orthogonal studied in [10], [11]; a lower bound of spectral efficiency in frequency division multiple access (OFDMA) and multicar- the presence of asynchronous interferers is derived. Previous rier code division multiple access (MC-CDMA) in wireless research work on the performance of OFDMA in the presence communication. This paper presents a new mathematical of CFO has mostly focused on symbol/bit error rate [12–16]. analysis for spectral efficiency of OFDMA communication The analyses mostly use Gaussian or improved Gaussian ap- systems over a frequency selective Rayleigh fading environ- proximation, which are not accurate due to correlation in ment in the presence of multiple users. It also compares the frequency response of the adjacent subchannels, especially spectral efficiency performance of OFDMA and MC-CDMA at low bit error rates [17]. In [18–20], average capacity/ spec- at different load, signal-to-noise ratio, CFO and delay spread tral efficiency of OFDM with CFO in Rician and Rayleigh conditions. MC-CDMA is found to be more resilient to CFO fading environment is analyzed respectively. However, their in general, however, OFDMA performs better at high load. analysis can not be extended to multiuser OFDMA that con- siders interference from other users (though in [19] accurate conditional Gaussian approximation is used). The presence Keywords of multiple users, which act as interferers, is worth consid- ering because CFO results in MAI to other users. Each OFDM, MC-CDMA, spectral efficiency, carrier fre- transmitter has different CFO as compared to the receiver, quency offset, inter-carrier interference, multiple access therefore, CFO mitigation techniques are unable to cater for interference all the different CFO’s due to transmitter heterogeneity. In this paper, we derive a new expression for the 1. Introduction lower bound of spectral efficiency of an asynchronous uplink OFDMA system that takes into account degradation due Orthogonal frequency division multiple access to CFO in the presence of multiple transmitters. We use this (OFDMA) is a well known technique used in both wire- expression to compare the spectral efficiency of OFDMA less and wired communication applications. It offers high with that of MC-CDMA. We base our analysis on accurate data rate, high spectral efficiency and multiple access ca- conditional Gaussian approximation for ICI and MAI, and pability. It is used in standardized wireless communication consider the fading experienced by subcarriers to be corre- techniques like long term evolution (LTE), WiMax, digital lated. The complexity of the numerical calculations of our video broadcasting, etc. Multicarrier code division multiple result depends on the number of subcarriers, and does not access (MC-CDMA) is a promising future communication increase with an increase in the number of transmitters. In technique [1]. It combines OFDM and code division multiple Sec. 2, we present the system model, and in Sec. 3, we an- access (CDMA) to give advantages of both, including high alyze the spectral efficiency. Numerical results are given in data rate, high spectral efficiency, robustness to frequency Sec. 4, and Sec. 5 concludes the paper. selective fading, multiple access capability and narrow band interference rejection among others [2–4]. However, due to carrier frequency offset (CFO) both OFDMA and MC- 2. System Model CDMA systems suffer from inter-carrier interference (ICI) and multiple access interference (MAI), [5–9]. The CFO Consider an asynchronous OFDMA uplink mobile appears due to frequency difference of local oscillators in communication system with K transmitters in a small ge- transmitter and receiver, and the Doppler shift in frequency ographical area. Let the transmitted signal of the kth trans- due to motion of transmitter and/or receiver. The spectral ef- mitter, be represented during an arbitrary signaling interval as DOI: 10.13164/re.2017.0221 APPLICATIONS OF WIRELESS COMMUNICATIONS 222 J. AHMED, SPECTRAL EFFICIENCY COMPARISON OF OFDM AND MC-CDMA WITH CARRIER FREQUENCY OFFSET N −1 T Xc K Nc −1 p p j2π fn;k t 1 ∗ − π f t X X π f t sk (t) = En;k bn;k e ; t 2 −Tg; T : (1) Z = G e j2 1;1 EG b ej2 n; k T ˆ 1;1 n;k n;k n=0 f g k= n = 0 * 1 k 0 . 4 j2π k t We consider k = 1 as the desired transmitter and the , ×e T + η (t) : (4) rest (k > 1) as other users or interferers. In (1), bn;k are the modulated symbols; these are assumed to be complex valued, independent and identically distributed random vari- The decision variable can be separated into four dis- tinct components Z = S + I + I + N, where S, I , I and N ables with unit variance. En;k is the energy assigned to 1 2 1 2 represent, respectively, desired signal, MAI, ICI and AWGN subcarrier n, where n = 0; 1; 2;:::; Nc − 1. We assume channel state information (CSI) is only available at the re- component. These are given respectively as follows: ceiver and not at the transmitter, hence, the total energy is T p 4 the same for each user and uniformly distributed over Nc 1 2 j2π 1 t S = Eb1;1 jG1;1j e T dt; subcarriers, E0;k = E1;k = ::: = En;k = E. We also as- T ˆ sume that all transmitters use the same number of subcar- 0 th th riers. fn;k is frequency of the n subcarrier, used by k p T K N − c 1 4 transmitter. All subcarriers are assumed to be equally spaced E ∗ − π f t X X π f t π k t I = G e j2 1;1 G b ej2 n; k ej2 T ; in frequency, giving fn;k − fm;k = (n − m) =T, where T is 1 T ˆ 1;1 n;k n;k k= n= the symbol duration and T is the length of cyclic prefix. 0 2 0 g .* /+ The transmitted signal is subjected to a frequency-selective p T (5) Nc −1 E , X 41 - multipath Rayleigh fading channel with a transfer function, ∗ −j2π f1;1t j2π fn;1t j2π T t PL−1 −j2π f τ I2 = G1;1 e Gn;1 bn;1e e ; Gn;k = gl;k e n l; k , where gl;k and τl;k are complex T ˆ l=0 n=0;n,1 amplitude and propagation delay of the lth path, respectively, 0 * + . (6)/ ≤ ≤ ≤ and τ0;k τ1;k ::: τL−1;k . We assume that all gl;k T , - 1 are zero mean uncorrelated complex Gaussian random vari- N = G∗ e−j2π f1;1t η (t) : PL−1 2 T ˆ 1;1 ables with normalized power, such that, l= E gl;k = 1. 0 0 Therefore, fG ;:::; G − g are jointly complexf Gaussiang 0;k Np 1;k random variables with non-zero cross correlation. We adopt It is worth mentioning that I2 is due to ∆1 only, and Jakes’ model [21] and the assumptions therein to calculate it goes to zero when ∆1 is zero, where ∆1 is the CFO of the cross correlation, which is given as desired transmitter with the receiver. ∆1 is a determinis- tic quantity that can be estimated. For simplicity, we re- 1 E G G∗ = (2) place ∆ with just ∆ in the rest of the paper. As far as i;k j;k + πσ( f − f ) 1 f g 1 j2 i j the statistics of MAI in (5) and ICI in (6) are concerned, these are large sums of correlated random variables and due where σ represents channel delay spread and Doppler fre- to correlation the central limit theorem is not applicable. quency has been assumed to be zero. Hence, the assumption of I1 and I2 being Gaussian random We assume that cyclic prefix duration is selected such variables can not be justified. However, if we condition G ;:::; G ;:::; G ;:::; G that, Tg > τL−1;k; hence intersymbol interference is com- on 0;1 Np −1;1 0;K Np −1;K then the cen- pletely avoided. Perfect time synchronization is also assumed tral limit theorem is applicable as bn;k and bn;1 are indepen- between the transmitter-receiver pair. Let r(t) be the received dent, identically distributed random variables. We, therefore, signal, after removing the cyclic prefix, it can be represented approximate Z as a conditional Gaussian random variable, as conditioned on G0;1;:::; GNp −1;K : The conditional variance is given in (12), shown in Appendix, conditional mean is K Nc −1 X X p 4k given as follows: j2π fn; k t j2π t r(t) = EGn;k bn;k e e T + η (t) (3) r k=1 n=0 E 2 E ZjG ;:::; G − = jG j sinc (π4 ) : (7) 0;1 Np 1;K T 1;1 1 where η (t) is additive white Gaussian noise (AWGN) with f g two sided power spectral density of N0=2. The CFO of k-th The instantaneous SINR is therefore a random variable ∆ =T ∆ given in (13), shown in Appendix, which can be simplified transmitter and the receiver is k , where k represents as: CFO normalized to the frequency separation between adja- 2 cent subcarriers.

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