This paper presents a systematic approach for analyzing the bit-error probability (BEP) **of** **equalized** **OFDM** signals **in** **Rayleigh** **fading**. Closed-form expressions for BEP **performance** **of** various signal constellations [phase-shift keying (PSK), differ- ential phase-shift keying (DPSSK), quaternary phase-shift keying (QPSK)] are provided for receivers that use a linear pilot-assisted channel estimate. We also derive the optimal linear channel esti- mates that yield the minimum BEP and show that some previous known results are special cases **of** our general formulae. The results obtained here can be applied to evaluate the **performance** **of** **equalized** single-carrier narrowband **systems** as well.

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Published online: 3 February 2010
© Springer Science+Business Media, LLC. 2010
Abstract This paper presents the root-mean-squared tracking error **performance** **analysis** **of** a class **of** coherent digital delay-locked loops for multicode direct sequence spread spec- trum signals **in** bandlimited correlated **Rayleigh** **fading** channels. **In** the transmit side, multiple independent PSK-modulated data streams **in** the **in**-phase and qudrature phase branches are spread by short mutually orthogonal codes before being further complex spread by a long complex PN code. We assume that the system employs a pilot code channel to assist the receiver’s synchronization and channel estimation. The proposed code tracking loop incorpo- rates the pilot-aided channel estimator and derives the timing error from all short-code-spread subchannels. Our **analysis** takes into account the effects **of** imperfect channel estimate, corre- lated frequency selective **Rayleigh** **fading** and band-limiting. Numerical results are presented to quantify the impact **of** the resulting multipath interference within the same code channel and amongst different code channels.

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Fig. 3 shows the analytical error floors corresponding to a set **of** spreading factors L = {31, 63, 127, 255, 511, 1023} for the case **of** K = 5. The SISO RBSC system and the 2ISO RBSC system using the SML detector are treated as the baseline **systems**, and only their theoretical BERs are illustrated. One should note that for the TU120 channel model, the number **of** previous symbols resulting **in** ISI is N = 1 if L ∈ L. However, for the HT120 channel model, we have 1) N = 3 if L = 31; 2) N = 2 if L = 63; and 3) N = 1 if L ∈ {127, 255, 511, 1023}. As discussed **in** Section IV, it is the MPI, MUI, and crosstalk that cause the error floors. For the DBSC **systems**, the JML detector, being robust to the crosstalk, obtains the best **performance**, while the SML detector, ignoring the crosstalk, obtains the worst **performance**. Moreover, increasing L has three impacts on the system **performance**. First, the power **of** the total interference

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complexity and/or a more complicated **performance** **analysis**.
Two approaches, namely direct and flow-graph approaches, have been applied extensively for analyzing the **performance** **of** an acquisition system, probability mass function (PMF), and/or moments **of** the acquisition time [3], [8]–[10]. Theoretically, these two methods are only applicable to the AWGN channels because the homogeneous Markov chain modeling **of** the ac- quisition process, a fundamental assumption **of** these methods, is no longer valid for time-variant multipath **fading** channels due to the channel memory incurred by **fading**; an **analysis** without considering the correlations due to **fading** may only be considered as an approximation. Unfortunately, as to be shown, the **analysis** error due to no consideration on the channel correlations can be very large, especially for the acquisition system based on passive correlators. A more accurate **analysis** for **fading** channels is yet to be found.

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II. System model
We consider a point-to-point MIMO system with M transmit antennas and M receive antennas. **In** the mean- while, we adopt **OFDM** modulation with total N T sub- carriers and let a group **of** adjacent N T /N subcarriers form a subchannel. The total bandwidth **of** each subchan- nel is assumed to be smaller than the channel coherent bandwidth. Figure 1 shows the considered structure **of** the **OFDM**-based spatial multiplexing **systems**, where M N independent data streams are multiplexed **in** M trans- mit antennas and N subchannels. The transmit power is uniformly split to M transmit antennas. It is assumed that the length **of** the cyclic preﬁx (CP) **in** the **OFDM** system is greater than the length **of** the discrete-time baseband channel impulse response so that the frequency- selective **fading** channel indeed decouples into a set **of** parallel frequency-ﬂat **fading** channels [19]. With x n and y n denoting the M ×1 transmit and receive signal vectors, respectively, we can write

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ABSTRACT
The **OFDM** (orthogonal frequency division multiplexing) signaling is one kind **of** "Multi-Carrier" technology, which can slow down delayed transmission especially for operating at frequency non-selective **fading** channels. Therefore, it gains quite large profit making a study **of** executing efficiency at different frequency non-selective **fading** channels. The **OFDM** system has become the most popular choice **of** transmission modulation **in** the new wireless communication field. Hence, **in** this article utilize a method **of** **OFDM** modulation to explore the statistical characteristic **of** distributions **of** **Rayleigh**、Ricean、Weibull while working **in** **fading** channel.

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V. C ONCLUSION
Different transmitter-based preprocessing methods are jointly inves- tigated with spreading pattern optimization and multiuser scheduling for the 2-D **OFDM**-CDMA forward-link **systems** from an information- theoretic viewpoint. The ergodic sum data rate serves as the perfor- mance index for **performance** comparisons under the assumption **of** perfect CSI. Examples are given to illustrate the important issue **of** spreading pattern optimization. ZF-MWF performs the best among the preprocessing methods that were investigated, including ZF and the MMSE. Moreover, as expected, multiuser scheduling gives a significant **performance** improvement.

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VI. C ONCLUSIONS
**In** this paper, we review the NSD and its three special cases, namely, the CR, DR, and VR. Based on the estimator-detector structures, a hierarchical interpretation **of** the NSD and its spe- cial cases are also presented. Then the NSD and its special cases are applied to the differential **OFDM** **systems** with diversity re- ception. Moreover, assuming sufficient CP, we provide a simple closed-form BER expression for differential **OFDM** **systems** employing the CR with diversity reception **in** the time-varying multipath **Rayleigh** **fading** channels. Numerical results have revealed that, with multi-antenna diversity reception, the per- formance **of** the CR is improved significantly. However, when few receive antennas are available, the implementation **of** the DR or VR is necessary for achieving better and satisfactory **performance**.

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ABSTRACT
**In** this paper the system **performance** **of** **OFDM** (orthogonal frequency division multiplexing) with the cases **of** MRC (maximal ratio combining) and dual branch SC (selective combining) diversities over correlated-Gamma distributed and correlated-Weibull **fading**, respectively, are investigated. Since the reason **of** an alternative expression **of** the Q-function is adopted for deriving the results **of** average BER (bit-error rate) **of** the **OFDM** system, the obtained formulas are not only calculated much simpler but the conducting **of** numerical **analysis** is also arrived at easily and accurate. It is valuable to claim that the system **performance** **of** the **OFDM** system is definitely dominated by the propagation environments, which is decided by the **fading** parameters both **of** the Nakagami-m and Weibull distributed, **of** the transmission **of** the radio **systems**. Furthermore, both **of** the conditions **of** equal and unequal signal intensities at the output **of** SC diversities are adopted as the scenarios for the discussion **of** **OFDM** **systems**.

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To significantly reduce the complexity and achieve high **performance** at the same time, this paper proposes three efficient non-coherent cell ID detection methods based on a new optimization metric and its simplifications. These new methods are not only suitable for IEEE 802.16 and IEEE 802.16e **systems** but also suitable for other preamble-based **OFDM** **systems**. By combining a preamble matching process and a multiplication-free smoothing scheme, the proposed techniques achieve better performances than the existing tech- niques **in** multipath **Rayleigh** **fading** channels. Based on our preliminary work [1], which introduces a basic concept **of** smoothing for cell ID detection, this paper generalizes the design concept and provide a statistical characterization for the proposed methods. Moreover, for further reducing the complexity, we introduce the decimation factor 𝑑 into the conventional and proposed methods as shown **in** the section **of** simulation results. With the decimation, all the methods can achieve lower computational complexities. For a sys- tem suffering the burst error, reducing the complexity by decimation may be better than reducing the complexity by directly shortening the correlation length **in** [22]. Therefore, by appropriately choosing the value **of** decimation factor 𝑑, the proposed methods can achieve the similar complexities as [22], but with better system performances.

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Publisher Item Identifier S 0090-6778(02)03505-5.
function. The 2-D function takes into account the correlations **of** the **fading** process **in** time and frequency domains. We can also use a one-dimensional (1-D) function to model the channel variation on each subchannel. Our method is simpler than those **of** previous LMMSE proposals. Every symbol **in** each subchannel needs less than four complex multiplications **in** the equalization process, and no information about the channel correlation and noise power level is needed. Furthermore, although the LS method is more sensitive to noise than the LMMSE method, our second-stage algorithm is very effective **in** reducing the LS estimation error.

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Abstract— With the increasing number **of** wireless network **in**- frastructure deployment and the popularity **of** portable computing devices, more and more internet users are experiencing ubiquitous mobility using both these computing devices and the wireless net- works to access the Internet. Therefore, it is necessary to study the loss behavior **of** the multimedia applications such as Web Brows- ing, VoIP, Teleconferencing, over wireless networks. This paper applies a matrix-analytic approach to analyze the loss probability **of** multimedia services over a **Rayleigh** **fading** channel. Due to the versatility **of** Discrete-time Markovian arrival process (D-BMAP) as an input process, the queuing model **of** the Burst-error commu- nication channel is a D-BMAP/D/1/K queue, where K is the buffer capacity.

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The effectiveness of erasure side information generated by Vterhi's ratio threshold test (RTT) decision for frequency-hopped multiple access @"MA) systems with M-ary [r]

Because **of** the unique features **of** the RB, by using proper network architecture and using advanced modulation formats [3]–[5], RB-induced signal degradation can be mitigated.
This is particularly true for PON using centralized carrier distribution. Dense wavelength-division-multiplexed (DWDM) PONs employing centralized optical carrier distribution and wavelength-insensitive (colorless) reflective optical networking units (RONUs) are attractive since the wavelength referencing

The main contribution **of** this paper is that for better characterizations **of** synchronization errors under a practical communication environment, that is, **in** doubly-selective **fading** channels, we analyze joint e ﬀects **of** the mentioned three major synchronization errors, without the assumption **of** small STO. Another contribution is that compact forms can be derived from our work to gain further insights on the synchronization error e ﬀects. To this end, we first analyze the signal model **of** the combined synchronization errors **in** time-selective and frequency-selective **fading** channels by extending the works **in** [1–15]. Next, based on this model, the theoretical SINR is formulated. The derived SINR can be exploited to obtain all possible combinations **of** syn- chronization errors that meet the required SINR constraint, knowing that the allowable synchronization errors could help design suitable synchronization algorithms and shorten the design cycle. To gain further insights, some compact

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Based on the foregoing results, the determination **of** the shap- ing filter for the second stage reduces to the choice **of** a suit- able operating value for α. For this, we do not have a theoreti- cally optimal formula, but only some rules **of** thumb. Experience shows that underestimation **of** α would not cause significant en- hancement **of** total MSE when the true α is large enough. **In** contrast, if the true α is small, then overestimation **of** it would cause great increase **of** the MSE. This phenomenon is heuris- tically reasonable, because (true) α is defined to be equal to σ n 2 /σ 2 e . Assuming a smaller value for α than its true value is tantamount to assuming a less converged state, which may re- sult **in** some slowdown **in** the convergence speed but would not likely cause stability problems. On the other hand, assuming a larger value for α than its true value means being over-optimistic on the convergence status, which would more likely cause per- formance degradation. Therefore, we choose to use a reasonably small value **in** the place **of** α. By experiment, we find that a suit- able range **of** its values is 0.5–2, with unity being a good choice.

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Transmit Equal Gain Precoding **in** **Rayleigh** **Fading** Channels
Shang-Ho Tsai
Abstract—Precoding with limited feedback information can achieve satisfactory **performance** while the amount **of** feedback information is kept small. **In** this paper, we analyze the theoretical **performance** **of** equal gain precoder and find that its **performance** is at most 1.049 dB worse than the optimal precoder no matter how the number **of** transmit antennas increases. Moreover, we analyze the **performance** degradation **of** the equal gain precoder due to scalar quantization theoretically. The result shows that 2–3 bits per transmit antenna (excluding the first antenna) can achieve 0.5–0.25-dB **performance** gap compared with the same scheme without quantization. Furthermore, we found that the equal gain precoder **in** general can achieve comparable **performance** with the Grassmannian precoder **in** the same moderate feedback bits. Simulation results are provided to corroborate the theoretical results.

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II. **OFDM** S YSTEM AND S IGNAL M ODELS
**In** the following discussion, all the quantities indexed with l belong to the lth symbol. A simplified **OFDM** system model is shown **in** Fig. 1, where X l, k / ˜ X l, k is the transmitted/received frequency-domain data at the kth subcarrier, x l,n is the trans- mitted time-domain data after the IFFT, and ˜ x l,n is the received time-domain data, where −N G n < N , N is the number **of** subcarriers, and N G is the CP length. 1/T S is the sampling fre- quency, ε f is the CFO (normalized by the subcarrier spacing), f c is the CF, n Δ is the estimated STO, and ε f is the estimated CFO. On the transmitter side, N complex data symbols are modulated onto N subcarriers by using the IFFT. The last N G IFFT output samples are copied to form the CP that is inserted at the beginning **of** each **OFDM** symbol. By inserting the CP, a guard interval is created so that ISI can be avoided and the orthogonality among subcarriers can be sustained. The

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ABSTRACT
**In** this paper, the impact **of** the correlation on the **performance** **of** multiple-cell DS-CDMA cellular **systems** over correlated **fading** channels is investigated. A new closed-form formula for the joint probability density function (joint pdf) **of** the diversity combiner with arbitrary correlation coefficients **in** terms **of** the generalized Laguere polynomial and the new expressions **of** average bit-error rate (BER) for the DS-CDMA system are given **in** this paper. The results demonstrate that the BER is significantly dependent on the correlation characteristic **of** diversity branching for multiple-cell environments.

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An analytic expression for the bit error probability upper bounds of rate-| convolutional codes in conjunction with QPSK modulation and maximum-likelihood Viterbi decod- ing on the fully[r]