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Fundamentals of Wireless Communications and Its Recent Developments. 鍾偉和 助研究員 中央研究院 資訊科技創新研究中心 http://www.citi.sinica.edu.tw/pages/whc/vita_zh.html whc@citi.sinica.edu.tw. Research Center for Information Technology Innovation, Academia Sinica-Overview.

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## Fundamentals of Wireless Communications and Its Recent Developments

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**Fundamentals of Wireless Communications and Its Recent**Developments 鍾偉和 助研究員 中央研究院 資訊科技創新研究中心 http://www.citi.sinica.edu.tw/pages/whc/vita_zh.htmlwhc@citi.sinica.edu.tw**Research Center for Information Technology Innovation,**Academia Sinica-Overview • Formally Founded in 2007, Started Operation in Sept. 2008 • The 31st youngest research unit in Academia Sinica • Faculty Member and Research Staff • Tenure-track appointments(Research fellow): 14 • Research assistants (postdocs): 220+ • Jointly appointed faculty:50+ • Joint advisory with universities • Collaborations with industries**Outline**I. Introduction to communication system II. MIMO System III. Wireless Local Area Network(WLAN) IV. WiMax**Wireless Networks are Overloaded**• AT&T reported that mobile data traffic increases 5,000% in the past three years congested Demands keep increasing**I. Introduction to communication system**• Mathematical models for channels • Bandpass signals • Random process • Sampling theorem • Digital modulation • Types of Codes in communication system**Physical channel media**• magnetic-electrical signaled wire channel • modulated light beam optical (fiber) channel • antenna radiated wireless channel • Noise characteristic • thermal noise (additive noise) • signal attenuation • amplitude and phase distortion • multi-path distortion • Limitation of channel usage • transmitter power • receiver sensitivity • channel capacity (such as bandwidth)**Mathematical models forcommunication channels**1. Additive noise channel: where α is the attenuation factor, s(t) is the transmitted signal, and n(t) is the additive random noise process. (Note: Additive Gaussian noise channel: If n(t) is a Gaussian noise process.)**3. The linear time-variant filter channel with additive**noise: c(τ ;t) : τis the argument for filtering; tis the argument for time-dependence. (The time-invariant filter can be viewed as a special case of the time-variant filter. Cf. the next slide.)**The linear time-variant filter channel with additive noise:**c(τ;t) usually has the form where {ak(t)} represents the possibly time-variant attenuation factor for the L multipath propagation paths, and {τk} are the corresponding time delays. Hence,**Example : The linear time-variant filter channel with**additive noise:**Band-pass signals and systems**• Representation of band-pass: • Carrier modulation : carrier = • : Amplitude modulation • :Frequency modulation • : Phase modulation where m(t ) is the baseband signal.**The transmitted signal (after carrier modulation)**• is usually a real-valued bandpass signal. • Mathematical model of a real-valued narrowband bandpass signal:**For analytical convenience, the real-valued transmitted**bandpass signal is usually analyzed in terms of its complex-valued equivalent lowpass signal. • We need to Develop a mathematical representation (in time domain) of S+(f) and S−(f).**Previously, we discussed the representations of**deterministic signals. We now turn to discuss stochastically modeled signals, i.e., stochastic processes.**Random process**• Engineers : A random process is a collection of random variables that arise in the same probability experiment. • Mathematicians : A random process is a collection of random variables that are defined on a common probability space. It is usually denoted by**Complex-valued random processes**• Auto-correlation function**Cross-correlation function for two complex-valued random**processes: 23**Sampling theorem**Deterministic signal • Band-limited • A deterministic signal(or waveform) s(t) is said to be (absolutely) band-limited if • Sampling Theorem • A band-limited signal can be reconstructed by its samples if the sampling rate is greater than 2W (Nyquist rate). The reconstruction formula is The sinc function sinc(t) is evluated by sin(t)/t.**Random process**• Band-limited random process • Definition : A (WSS) random process Xt is said to be band-limited if • Hence, • Sampling representation of a random process • For a band-limited stationary stochastic process Xt**Memoryless modulation methods**• Digital pulse amplitude modulated (PAM) signals (Amplitude-Shift Keying or ASK) • Digital phase-modulated (PM) signals (Phase Shift Keying or PSK) • Quadrature amplitude modulated (QAM) signals • Multidimensional modulated signals • General • Orthogonal • Mutidimensional • Biorthogonal • Simplex signals**(M-level) pulse amplitude modulated (M-PAM) signals**• Channel symbol : • Example: M = 4 • The distance between two adjacent signal amplitude = 2d. • Bit interval = Tb = 1/R, symbol interval = T and k =log2M. Then symbol rate = symbol / sec = 1 / T = R / k (Note T = k Tb = k / R).**Transmitted energy of M-PAM signals**• Error consideration • The most possible error is the erroneous selection of an adjacent amplitude to the transmitted signal amplitude. • Therefore, the mapping (from bit pattern to channel symbol) is assigned to result in that the adjacent signal amplitudes differ by exactly one bit. (Gray encoding) • In such a way, the most possible bit error pattern caused by the noise is a single bit error. • Gray code (Signal space diagram : one dimension)**Euclidean distance**Euclidean distance: For Channel symbol, m = 1~M:**Single Side Band (SSB) PAM**• g(t) is real => G(f) is symmetric. • Consequently, the previous PAM is based on DSB transmission which requires twice the bandwidth. • Recall where is the Hilbert transform of g(t).**Transmitted energy of SSB M-PAM signals**• Recall : transmitted energy of DSB M-PAM signals Under the condition that DSB M-PAM and SSB M-PAM signals require the same transmitted energy, the latter consumes only half of the bandwidth of the former by the cost of an additional Hilbert transformer.**Phase-modulated (PM) signals**• Channel symbol • Example: M = 4**Transmission energy of PM signals**• Advantages of PM signals : equal energy for every channel symbol. • Error consideration • The most possible error is the erroneous selection of an adjacent phase of the transmitted signal. • Therefore, we assign the mapping from bit pattern to channel symbol as the adjacent signal phase differs by one bit. (Gray encoding). • In such a way, the most possible bit error pattern caused by the noise is a single-bit error.**(Two dimensional) signal space diagram for Gray code**• Euclidean distance**SSB for PM ?**• Note that the baseband signal is not a real number. (Hence, non - symmetric in spectrum.) So, there is no SSB version for PM. • This can be considered as a tradeoff, when being compared to PAM.**Types of Codes**• Channel codes • data transmission codes (error-correcting codes) • data translation codes (to meet channel constraints) • Source codes • lossless data compression codes • lossy data compression codes • Secrecy codes**Channel Codes**Concept: The purpose of channel encoder-decoder pair is to correct the error introduced by the channel (noise, fading, interference). The approach is to add redundancy (that is algebraic related to the information to be transmitted) in the channel encoder and to use this redundancy (and algebraic relation) at the decoder to reconstruct the channel input sequence as accurately as possible.**Shannon’s noisy channel coding theorem**• “With sufficient but finite redundancy properly introduced at the channel encoder, it is possible for the channel decoder to reconstruct the input sequence to any degree of accuracy desired, provided that the input rate to the channel encoder is less than a given value called channel capacity.” • General Design Criteria • For (digital) communication system users, BER is usually the most important performance measure. • Spectral efficiency (in bits/sec/Hz) is the ultimate concern from system engineering’s viewpoint. • Other general design criteria include: • Complexity (delay) • Cost • Weight • Heat dissipation • Fault tolerance**Spectral Efficiency**• Definition: η = data rate/required bandwidth (bits/s/Hz) • The Shannon-Hartley capacity of a band-limited AWGN channel of bandwidth W is given by C = W log2(1+S/N) where S/N=(EbR)/(N0W). • Hence the maximum spectral (bandwidth) efficiency ηmax is equal to ηmax = log2(1+S/N) =C/W≤R/W (bits/s/Hz)**Examples of simple channel codes**• Single-parity-check codes • add a single parity-check bit to a k-bit message word • code rate k/n = k/(k+1) = (n-1)/n • Repetition codes • repeat the information bit n times • code rate = 1/n**Example: (3,2) parity check code**• Definition: Hamming weight of a binary codeword is defined as the number of 1 in the codeword. • Definition: Hamming distance between two binary codeword is the number of places where they differ. • For the above example, w(000)=0, w(011)=2, w(101)=2, w(110)=2, d(011,101) = 2.**Example: (3,1) Repetition code**• Repetition decoding :To determine the value of a particular bit, we look at the received copies of the bit in the bitstream and choose the value that occurs more frequently. • Received bitstream c’ = 110, estimated m = 1.**A good code is one whose minimum distance is large. For the**previous example, the (3,2) parity check code has dmin = 2.**Convolutional Codes**• Encoding of information stream rather than information blocks • Easy implementation using shift register • Decoding is mostly performed by the Viterbi Algorithm • Errors in Viterbi decoding algorithms for convolutional codes tend to occur in bursts because they result from taking a wrong path in a trellis.

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