In this paper, we proposed a novel iterative **carrier** **frequency** **offset** estimation algorithm based on the EKF algorithm and multi-antenna channel ML estimation for MIMO-OFDM systems. In the proposed scheme, we implement the EKF updating steps on the number of receive antennas and, after each cycle, the last estimated CFO of EKF is fed back to the estimator iteratively. The PSO algorithm was also used for CFO ML estimation. The proposed algorithms not only outperform the EM algorithm, but also have much lower computational complexity. The performance of our estimators was investigated by computer simulations and benchmarked with CRB. Simulation results show that the accuracy of the proposed algorithms is close to the CRB.

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The precise operating SNR for wireless LAN devices comes in the range 20 to 40 dB over which the CFO estimator presented here performs similar to the estimator used for SISO channels (IEEE 802.11a). The algorithm presented here reduces the effect of Inter-**carrier**-interference that results due to multiple **carrier** **frequency** **offset** each station experiences with respect to the access point. The CFO estimation error variance is also found to be minimal over a wide combination of **frequency** offsets.

Abstract— The demand for high-speed mobile wireless communications is rapidly growing. Orthogonal **Frequency** Division Multiplexing (OFDM) has become a key element for achieving the high data capacity and spectral efficiency requirements for wireless communication systems because of it multicarrier modulation techniques. But its main drawback is the effect of **carrier** **frequency** **offset** (CFO) produced by the receiver local oscillator or by Doppler shift. This **frequency** **offset** breaks the orthogonality among the subcarriers and hence causes intercarrier interference (ICI) in the OFDM symbol, which greatly degrades the overall system performance. In this paper we will study the effects of CFO upon signal to noise ratio (SNR) for an OFDM system, and also estimate the amount of **carrier** **frequency** **offset**. We compare three methods to combat **carrier** **frequency** **offset**: Time domain CP based method, **frequency** domain based Moose and Classen method. The improved performance of the present scheme is confirmed through extensive MATLAB simulation results.

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Sensitivity to **carrier** **frequency** **offset** (CFO) is one of the biggest drawbacks of orthogonal **frequency** division multiplexing (OFDM) system. A lot of CFO estimation algorithms had been studied for compensation of CFO in OFDM system. However, with the adoption of direct-conversion architecture (DCA), which introduces additional impairments such as dc **offset** (DCO) and in-phase/quadrature (I/Q) imbalance in OFDM system, the established CFO estimation algorithms suffer from performance degradation. In our previous study, we developed a blind CFO, I/Q imbalance and DCO estimation algorithm for OFDM systems with DCA. In this article, we propose an

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Abstract— Orthogonal **Frequency** Division Multiplexing (OFDM) has been employed in numerous wireless standards. However, the performance of OFDM systems is degraded by both the **Carrier** **Frequency** **Offset** (CFO) and the Phase Estimation Error (PER). Hence new exact closed-form expressions are derived for calculating the average BER of OFDM systems in the presence of both CFO and PER in the context of **frequency**- selective Nakagami-m fading channels. Our simulation results verify the accuracy of our exact BER analysis. By contrast, the Gaussian approximation slightly over-estimates the average BER, especially when the normalized CFO is small, the number of OFDM subcarriers is low and when the fading is less severe.

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Fading is a fundamental problem in wireless communication. However Space time block code scheme is suggested to overcome this problem. In the paper various combination of transmit and receive antenna was considered, a mathematical model was driven and applied using simulation. The relation between signal to noise ratio and bit error rate was plotted. From results it is noted that the receiver diversity better than transmitter diversity, but if both diversity is used that gives better results as shown in Multiple input Multiple Output (MIMO), also signal to noise ratio (SNR) and bit error rate (BER) with **carrier** **frequency** **offset** (CFO) and without **carrier** **frequency** **offset** was compared.

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In time-domain synchronous (TDS)-orthogonal **frequency** division multiplexing (OFDM) systems, a pseudo noise (PN) sequence is inserted instead of the cyclic prefix. The PN sequence is used not only as a guard interval but also as a training sequence for channel estimation and synchronization in the time domain. Recently, research studies on 2 × 1 multi input-single output (MISO) TDS-OFDM systems have been conducted, and different PN sequences (which are orthogonal to one another or cyclically shifted) are transmitted at each transmit antenna for channel estimation, which are modulated by binary phase shift keying in the same phase angle. However, when the absolute phase difference among the transmitted PN sequences is π , a PN sequence cancellation problem occurs, making the estimation of an accurate **carrier** **frequency** **offset** (CFO) difficult. In this paper, a CFO estimation method with the aid of PN sequences for 2 × 1 MISO TDS-OFDM systems is proposed. In the proposed method, the phase of the PN sequences at each antenna is rotated differently and transmitted to prevent a PN sequence-canceling problem. In addition, a CFO estimation scheme using channel state information is proposed to estimate an accurate CFO in time-varying channels. We show by computer simulations that the mean square error performance of the proposed method over an additive white Gaussian noise environment and time-varying Rayleigh channel is higher than that of the conventional method.

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We have shown that the primary effect of **carrier** **frequency** **offset** on a cooperative Alamouti STC OFDM system is OFDM ICI, a well-studied phenomenon with performance degradation given by (7) and (16). With perfect channel and **frequency** **offset** knowledge, we can completely eliminate the contribution due to CPE using (13). Unlike the non- cooperative SISO case, the receiver cannot eliminate the ICI even with perfect knowledge. However, the effect of ICI is no worse than that experienced by a regular SISO system with similar (albeit non-differential) **frequency** **offset**.

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This paper presents an implementation of a GFSK receiver based on matched Þ ltering of a sequence of successive bits. This en- ables improved detection and superior BER performance but re- quires matched Þ lters of considerable complexity. Exploiting redundancy by performing phase propagation of successive single- bit stages, we propose an ef Þ cient receiver implementation. Re- sults presented highlight the bene Þ ts of the proposed method in terms of computational cost and performance compared to stan- dard methods. We also address **carrier** **frequency** **offset**, and sug- gest a blind algorithm for its elimination. Performance results are exemplarily shown for a Bluetooth system.

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In conventional method to estimate the **carrier** **frequency** **offset**, two repetitive training symbols are used and then compare of the phases between the successive identical symbols is a simple, useful technique, which was first proposed in 1994 by P.H.Moose.[3]. This method gives the simple correlation of two identical signals to find the Signal to Noise ratio (SNR) and Bit error ratio (BER).

As will be seen from computer simulation in Section 5, the performance of the proposed CFO estimator for large CFOs is better than for small CFOs. This is because when the **frequency** error is large, both the numerator and denom- inator in the arccos function (20) are dominated by their first parts since the noise term is very small after sum operation. Therefore, the proposed estimator provides a more consis- tent CFO estimation. When the **frequency** error is small, both the numerator and the denominator are more dependent on the noise terms and therefore, the estimation result is less accurate. When ε is very close to zero (say ε <0.005), both numerator and denominator in (20) will approach to zero. The summations M(P n = 1 − 2) z 2 (n) and 2

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The numerical investigation of the outage probability for a reverse link MC-CDMA wireless cellular system with either ideal beamforming or imperfect beamforming in the pres- ence of CFO is given in this section. The spreading gain L (or total number of subcarriers) for each user is set to L = 32. There are total K = 16 active users in the system. The Nakagami-m channel fading is assumed over each sub- **carrier** for all users. The required SINR threshold γ 0 is set to 6 dB. The signal-to-noise ratio (SNR) is defined as

The research is targeted to improve the QoS of WC systems aﬀected by diﬀerent parameters introduced in section 1.3. Ideal detection algorithms are designed with an assumption that the CSI is perfectly known to the receiver and it maintains **frequency** synchronization with the transmitter. However, practical systems require estimating the channel fading parameters and the CFO. The objective of the work presented in the thesis is to design detection algorithms for a receive diversity system with one transmit and multiple receive antenna in the presence of these estimation errors. The aim is to achieve optimal detection of the transmitted message signal with the erroneous estimates of CSI and CFO available to the receiver. The algorithms are designed for three prevalent detection techniques and their performance is analyzed in terms of BER.

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Hexagonal multicarrier modulation (HMM) system is the technique of choice to overcome the impact of time-**frequency** dispersive transmission channel. This paper examines the eﬀects of insuﬃcient synchronization (**carrier** **frequency** oﬀset, timing oﬀset) on the amplitude and phase of the demodulated symbol by using a projection receiver in hexagonal multicarrier modulation systems. Furthermore, eﬀects of CFO, TO, and channel spread factor on the performance of signal-to-interference-plus-noise ratio (SINR) in hexagonal multicarrier modulation systems are further discussed. The exact SINR expression versus insuﬃcient synchronization and channel spread factor is derived. Theoretical analysis shows that similar degradation on symbol amplitude and phase caused by insuﬃcient synchronization is incurred as in traditional cyclic prefix orthogonal **frequency**-division multiplexing (CP-OFDM) transmission. Our theoretical analysis is confirmed by numerical simulations in a doubly dispersive (DD) channel with exponential delay power profile and U-shape Doppler power spectrum, showing that HMM systems outperform traditional CP-OFDM systems with respect to SINR against ISI/ICI caused by insuﬃcient synchronization and doubly dispersive channel.

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A multiple-input multiple-output (MIMO) wireless communication system with orthogonal **frequency** division multiplexing (OFDM) is expected to be a promising scheme. However, the estimation of the **carrier** **frequency** oﬀset (CFO) and the channel parameters is a great challenging task. In this paper, a maximum-likelihood- (ML-) based algorithm is proposed to jointly estimate the **frequency**-selective channels and the CFO in MIMO-OFDM by using a block-type pilot. The proposed algorithm is capable of dealing with the CFO range nearly ± 1/2 useful OFDM signal bandwidth. Furthermore, the cases with timing error and unknown channel order are discussed. The Cram´er-Rao bound (CRB) for the problem is developed to evaluate the performance of the algorithm. Computer simulations show that the proposed algorithm can exploit the gain from multiantenna to improve eﬀectively the estimation performance and achieve the CRB in high signal-to-noise ratio (SNR).

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Despite of the attractive advantages, OFDM is vulnera- ble to various disturbances in practice. **Carrier** **frequency** oﬀset (CFO) is one of most well-known disturbances for OFDM. It generates inter-**carrier** interference (ICI) and degrades OFDM performance [1]. In order to mitigate the negative inﬂuence, CFO is usually estimated and compen- sated accordingly during OFDM reception. CFO estima- tion for OFDM systems had been excessively studied and various algorithms had been proposed in literatures such as [6-8]. In [6], maximum likelihood (ML) CFO estima- tion for OFDM systems in additive white Gaussian noise (AWGN) channel was presented, while its performance degrades in multi-path dispersive channel. Liu et al. pro- posed in [7] a MUSIC-like blind CFO estimator which was proved in [9] to be equivalent to ML estimator in fading channel.

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Orthogonal **frequency**-division multiplexing (OFDM) is widely used in modern wireless communications for its good ability to reduce the multipath effect. As OFDM is used in a multiple access (MA) system, the combination of the **frequency** division multiple access (FDMA) method draws a lot of attention to next generations of wireless communications. The OFDM multiple access (OFDMA) technology separates groups of OFDM subcarriers allocated to different subscribers for simultaneous uplink transmission from subscriber stations (SS) to a base station (BS). WiMAX and LTE are typical OFDMA systems proposed for the application of wireless metropolitan area networks (MANs) [1]. However, in an OFDMA system, imperfect synchronization due to different **carrier** **frequency** offsets (CFOs) at individual transmitting terminals can introduce inter-**carrier** interference (ICI) among subcarriers and multiple access interference (MAI) among subscribers [2]-[4]. Although some methods can be exploited to initiate the synchronization at transmitters, the CFOs are hard to be completely eliminated since different local oscillators are implemented at the transmitters. Hence, a CFO

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Orthogonal **frequency** division multiplexing (OFDM) is a novel technology which stands as a promising choice for future data rate system. This technology has been adopted in European digital audio broadcasting and video broadcasting system. It has high spectral efficiency transmission scheme. Currently OFDM is widely used in wireless communication because of its high transmission rate and high bandwidth efficiency. It divides wideband signal into many orthogonal subcarriers and induces a symbol period .Orthogonal **frequency** division multiplexing (OFDM) is a method of encoding the digital data on multiple **carrier** **frequency**. The channel response might change during an OFDM symbol period in a high-mobility environment therefore, the orthogonality among the subcarriers destroys [4] currently, and multicarrier transmission is popular because of its high data transmission rate. Orthogonal **frequency**- division multiplexing (OFDM) is a special case of multicarrier transmission also considered an effective technique for **frequency**-selective channels because of its spectral efficiency and its robustness in different multipath propagation and its ability of combating inter symbol interference. One of the major drawback for OFDM system is **carrier** **frequency** **offset** (CFO). The OFDM systems are sensitive to the **frequency** synchronization errors in form of **Carrier** **Frequency** **Offset** (CFO) because it can cause the Inter **Carrier** interference which can lead to the **frequency** mismatched in transmitter and receiver .[2][3]

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Spatial multiplexing multiple-input multiple-output (MI- MO) technology significantly increases the wireless system capacity [1–4]. These systems are primarily designed for flat-fading MIMO channels. A broader band can be used to support a higher data rate, but a **frequency**-selective fading MIMO channel is met, and this channel experiences intersymbol interference (ISI). A popular solution is MIMO- orthogonal **frequency**-division multiplexing (OFDM), which achieves a high data rate at a low cost of equalization and demodulation. However, just as single-input single-output- (SISO-) OFDM systems are highly sensitive to **frequency** o ﬀ set, so are MIMO-OFDM systems. Although one can use **frequency** o ﬀ set correction algorithms [5–10], residual **frequency** o ﬀ sets can still increase the bit error rate (BER).

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