Telecommunications Systems in a Nutshell Laura Cottatellucci laura.cottatellucci@eurecom.fr
I. Outlines 2 Outlines 1. Point-to-Point Communications Systems 2. A Fundamental Communication Model: Multiple Access Channel 3. New Generation Wireless Networks: Interference Channel 4. Communications Trend and Game Theory
3 Point-to-Point Channel
II. Point-to-Point Communications Systems 4 Example 1: Optical System Laser Driver and Temperature Control Transmitter Optical Fiber Amplifier Discriminator Receiver
II. Point-to-Point Communications Systems 5 Example 2: Satellite Link Satellite Gateway Transmitter Gateway Receiver
II. Point-to-Point Communications Systems 6 Example 3: MIMO Antenna System ADSL Network Multiple Input Multiple Output (MIMO) antenna system Multi-antenna ADSL model Cable TV box
II. Point-to-Point Communications Systems 7 Example 4: Single Cell System Mobile Terminal Base Station
II. Point-to-Point Communications Systems 8 Scheme of a Point-to-Point Channel Digital Source (of Coded Bits) c[m] v[n] v(t) Labelling Pulse Shaper Digital Modulator Analog Modulator V(t) Physical Channel Digital Sink (of Coded Bits) Synchr and Channel Estimator Demodulator/ Matched Filter y(t) Y(t) Analog Demodulator
II. Point-to-Point Communications Systems 9 Digital Modulation Digital Modulator: It maps a sequence {c[m]} of bits onto analog signals (typically two). The analog signals are in baseband, i.e. their Fourier transform is nonzero in [ 1 2W, 1 2W Labeling: The input sequence c[m] is divided in groups of p bits. Each group (c[m], c[m + 1], c[m + p 1]) is mapped onto a symbol v[n] typically complex. Examples ]. 4-Phase Shift Keying (4-PSK) 01 00 1111 1011 1001 1101 0111 0011 0001 0101 16-Quadrature Amplitude Modulation (16-QAM) Gray Mapping 11 10 0110 0010 0000 0100 1110 1010 1000 1100
II. Point-to-Point Communications Systems 10 Pulse Shaper: It generates a continuous complex function v(t) = + n= v[n]ψ(t + nt ) = + n= v R [n]ψ(t + nt ) + j + n= v I [n]ψ(t + nt ) 1 v R (t) +sinc(t) sinc(t 1) sinc(t 2) +sinc(t 3) sinc(t 4) 0 v_r[0] v_r[1] v_r[2] v_r[3] v_r[4] 1 2 0 1 2 3 4
II. Point-to-Point Communications Systems 11 The pulse shape ψ(t) is chosen such that s(t) = ψ(t) ψ(t) = ψ(t τ)ψ(τ)d τ is a Nyquist pulse of parameter T, i.e. s(lt ) = I {l=0} and l Z. Square root Nyquist s(.) 2/T ψ(.) 2/T Roll off [1] Amos Lapidoth, A Foundation in Digital Communications, Cambridge, 2009. [2] John Proakis, Digital Communications, Mc Graw Hill, 4th Edition, 2001.
II. Point-to-Point Communications Systems 12 Digital Demodulation Under very favorable assumptions on the channel, the receiver recovers synchronization, estimates the channel, and demodulates by filtering the input signal by the pulse waveform (matched filter). The output of the matched filter is properly sampled. Synch. y R (t) Matched Filter ṽ R (t) = y R (t) ψ(t) ṽ R [n] ψ(t) Sampler at rate T y I (t) Matched Filter ṽ I (t) = y I (t) ψ(t) ṽ I [n] ψ(t)
II. Point-to-Point Communications Systems 13 Motivations Analog Modulation & Demodulation In many transmission means, signals at low frequency do not propagate well. Different telecommunication systems are maintained independent\orthogonal by assigning them orthogonal frequency band for transmission.
II. Point-to-Point Communications Systems 14 Analog Modulation Analog Modulator: It converts the baseband complex signal v(t) = v R (t) + jv I (t) of bandwidth [ W/2, +W/2] onto the passband signal bandlimited to W around the carrier frequency f c. V (t) = v R (t)cos2πf c t v I (t)sin2πf c t Baseband signal v(t) in the frequency domain Fv(t) W/2 W/2 FV (t) f c Passband signal V (t) in the frequency domain f c
II. Point-to-Point Communications Systems 15 Analog Demodulation Analog Modulator: The passband real received signal Y (t) bandlimited to W around the carrier frequency f c is converted to a baseband signal of bandwidth [ W/2, +W/2]. If H(t) is the channel frequency response bandlimited to W around the carrier frequency f c, and h(t) is complex baseband representation y(t) = v(t) h(t) Y (t) cos(2πf c t) y R (t) W/2 W/2 Y (t) 90 o Phase Shift Y (t) sin(2πf c t) y I (t) W/2 W/2
II. Point-to-Point Communications Systems 16 Physical Channel The channel kernel k(t; τ) at time τ is the output of the channel when an impulse signal s(t) = δ(t τ) is applied at time τ. If the output of the channel to an impulse signal input δ(t τ) at any time τ is the shift of its output at time 0 by a time shift τ, i.e. k(t, τ) = k(t τ, 0) = h(ξ) with ξ = t τ, the channel is time invariant. h(ξ) is the channel impulse response. 0.8 0.6 0.4 0.2 Time Invariant Channel k(t,0) k(t,1) k(t,2) k(t,3) k(t,4) k(t,5) 1.5 1 Time Variant Channel k(t,0) k(t,1) k(t,2) k(t,3) k(t,4) k(t,5) 0 6 5 4 τ 3 2 1 0 0 2 4 t 6 8 10 0.5 5 0 4 3 τ 2 1 0 0 2 4 t 6 8 10
II. Point-to-Point Communications Systems 17 The Fourier transform of the impulse response h(ξ) is called frequency response. The output of a linear time invariant channel with impulse response h(t) to an input signal x(t) is y(t) = x(t) h(t) = x(θ)h(t θ)d θ The output of a linear time variant channel with kernel k(t; τ) to an input signal x(t) is y(t) = x(θ)k(t, θ)d θ = x(θ)h(t θ, θ)d θ where h(ξ, τ) = k(ξ + τ, τ) is the time variant impulse response.
II. Point-to-Point Communications Systems 18 If the frequency response of a channel is constant, the channel is said frequency flat. Otherwise, it is said frequency selective. Remarks Up to a multiplicative factor, a frequency flat channel keeps invariant the shape of a pulse signal and does not introduce intersymbol interference. A frequency selective channel modifies the shape of a pulse signal and, typically, introduces intersymbol interference. Most of the existing systems deals with frequency selectivity at a demodulator level by performing channel equalization. If a channel is time variant, it is called fading channel. Channel estimation is more challenging. Channel fading properties have fundamental impact on the system design and performance.
II. Point-to-Point Communications Systems 19 Baseband model of a Point-to-Point Channel Digital Source (of Coded Bits) Labelling Baseband Point-to-Point Channel c[m] v[n] Digital Sink (of Coded Bits) ṽ[n] = L h[k]v[n k] + w[n] k=0 v[n] is the sequence of complex transmitted signals (labeling output) (h[0], h[1],... h[l]) is a complex vector discrete representation of a baseband impulse response accounting for all devices and transmission means from the pulse shaper input to the matched filter output. w[n] is an additive white complex Gaussian noise sequence modeling the thermal noise in all the system devices.
II. Point-to-Point Communications Systems 20 If L = 0 the channel is frequency flat and ṽ[n] = hv[n] + w[n] A fundamental performance measure: Signal-to-Noise Ratio SNR = average received signal energy per (complex) symbol time noise energy per (complex) symbol time = h 2 E v[n] 2 N 0 The expectation is taken over the modulation set. Often E v[n] 2 = 1. Error probability at a detector output is an SNR function depending on the modulation. N 0 is the power spectral density of the noise random process. The power spectrum density of a random process is the Fourier transform of its autocorrelation. For a white process, the power spectrum density is constant. A symbol is transmitted at constant rate T 1.
II. Point-to-Point Communications Systems 21 Basic Point-to-Point Communication Problem Source??? Point to Point??? Channel Sink A source transmits via a noisy channel to a sink Problem: Reliable transmission, i.e. we want to recreate the transmitted information with as little distortion as possible at the sink, at high speed.
II. Point-to-Point Communications Systems 22 Comm. Problem and Source-Channel Separation Source Source Encoder Channel Point to Point Channel Source Encoder Channel Decoder Decoder Sink Source Coding Theorem: For a given source and distortion measure there exists a minimum rate R = R(d) (bit per emitted source symbol) which is necessary and sufficient to describe this source with distortion not exceeding d. Channel Coding Theorem: Given a channel there exists a maximum rate (bits per channel use) at which information can be transmitted reliably, i.e. with vanishing error probability, over the channel. The maximum rate is called the capacity of the channel and is denoted by C.
II. Point-to-Point Communications Systems 23 Comm. Problem and Source-Channel Separation (2) Source-Channel Separation Coding Theorem: Given a channel of capacity C, a source can be reconstructed with a distortion at most of d at the receiver if R(d) < C, i.e. if the rate required to represent the given source with the allowed distortion is smaller than the channel capacity. Conversely, no scheme can do better. Under the assumptions of the source-channel separation theorem The approach of separating source and channel coding is optimum.
II. Point-to-Point Communications Systems 24 Coded Communications over Point-to-Point Channels Communication Model Digital Source u Channel Encoder v Point to Point Channel ṽ Channel Decoder û Digital Sink u = (u 0, u 1,... u k 1 ) : binary k-tuple called message v = (v 0, v 1,... v n 1 ) : n-tuple of discrete symbols called codeword ṽ = (ṽ 0, ṽ 1,... ṽ n 1 ) : n-tuple of discrete symbols at the channel output û = (û 0, û 1,... û k 1 ) : binary k-tuple called decoded message R = k n [bit/symbol] is the code rate The code rate is the number of bits entering in the encoder per transmitted symbol.
II. Point-to-Point Communications Systems 25 Fading Channel and Capacity A channel varies very quickly over one or few symbols and it cannot be estimated at the receiver. Non-coherent communications with very poor performance. A channel almost constant over blocks of symbols and almost ergodic over a codeword transmission is a fast fading channel. Coherent communications with channel knowledge at the receiver. Channel not known at the transmitter (only statistics known): Transmission feasible at rate below the ergodic capacity and constant power allocation. Channel known at the transmitter: Capacity increased by optimal power allocation (e.g. time). waterfilling over
II. Point-to-Point Communications Systems 26 A channel almost constant over a codeword transmission is a slow fading channel. Coherent communications with channel knowledge at the receiver. Channel known at the transmitter: Transmission at a rate below channel capacity C = W log 2 (1 + SNR) Channel not known at the transmitter (only statistics known): Transmission feasible at rate below the outage capacity, i.e. the maximum rate at which it is possible to transmit with a predefined outage probability. Gaussian modulation.
27 Multiple Access Channel
III. Multiple Access Channel 28 A MAC Example: Single Cell System Mobile Terminal Base Station
III. Multiple Access Channel 29 E-Cloud Based Wireless Network: A MAC Example Distributed Antenna System Remote Radio Heads are connected to the e-cloud via optical fibers
III. Multiple Access Channel 30 Orthogonal Multiple Access Schemes: TDMA Time Division Multiple Access Frame Time Structured in frames Time Slot Frames structured in time slots. Each user is allocated one time slot. v[t], v[t+1]. v[t+p] Guard period for synchronization (optional) Time slot structured in symbols.
III. Multiple Access Channel 31 Orthogonal Multiple Access Schemes: FDMA Frequency Division Multiple Access One band per user Subchannel Power F F 4 F 3 F 2 1 1 4 F6 F 5 5
III. Multiple Access Channel 32 CDMA System in Uplink Transmitter 1 Multiple Access Channel v 1 [m] Upsampler Filter Pulse Shap. v 1 [m]ϕ 1m (t) N s 1m [n] ψ(t) a 1 δ(t τ 1 ) y(t) Transmitter K n(t) v K [m] Upsampler Filter Pulse Shap. v K [m]ϕ Km (t) N s Km [n] ψ(t) a K δ(t τ K ) Spreading Waveform: ϕ j,m (t) = N 1 n=0 s nj[m]ψ(t nt c )
III. Multiple Access Channel 33 Multiple Access Channel: Baseband System Model y[n] = K h k [n]v k [n] + w[n] k=1 K users Frequency flat fading channel. If h k [n] = h k for all n the channel is time invariant. sinc(t) is the symbol pulse. Additive white Gaussian noise w[n] with power spectral density N 0. Performance measure: Signal-to-Interference plus Noise Ratio SINR k = = average received signal energy per (complex) symbol time interference plus noise energy per (complex) symbol time h k 2 E v k [n] 2 h l 2 E v l [n] 2 + N 0 l=1 l k
34 Interference Channel
IV. Interference Channel 35 An Example: Heterogeneous Networks Coexisting Macro Cells and Femto Cells Femto BS Femto UT Macro Terminal Femto Cell Macro Base Station Macro Cell
IV. Interference Channel 36 An Example: Cognitive Radio Networks Secondary Terminal A1. Coexistence of a primary wireless network (WN) with licensed band and a secondary WN with unlicensed band. Secondary Terminal Secondary Multi-antenna Base Station Primary Terminal C2. Interference over the M primary terminals (PT) should Primary Terminal Secondary Terminal Primary Terminal Secondary Terminal not exceed given thresholds κ m. C3. SINR at secondary terminal k should not be lower that γ k. P4. Transmissions over the primary WN are transparent to a secondary WN presence. P5. Transmissions over the secondary WN occur if C2 and C3 are satisfied. Slight abuse of denomination compared to the basic definition of interference channel.
IV. Interference Channel 37 Basic Baseband Interference Model g 1 Tx 1 Rx 1 h 12 Information from Tx 1 and Tx 2 intended for Rx 1 and Rx 2, respectively. Two interfering communications. h 21 g 2 sinc( ) is the chip pulse. Frequency flat direct and interfering links. Tx 2 Rx 2 ṽ 1 [n] = g 1 [n]v 1 [n] + h 21 [n]v 2 [n] + w 1 [n] ṽ 2 [n] = g 2 [n]v 2 [n] + h 12 [n]v 1 [n] + w 2 [n] SINR i [n] = g i [n] 2 E v i [n] 2 h ji [n] 2 E v j [n] 2 + N 0 i, j = 1, 2, i j
38 Communications Trend
V. Communications Trend 39 Distributed Intelligence in Networks Centralized control with dumb terminals Shared control among peers with dumb terminals Distributed control among rational peers Distributed control among heterogeneous networks of intelligent nodes Cellular system with frequency reuse Multi-cellullar systems with shared bandwidth Ad hoc networks Cognitive networks Toward interaction of rational intelligent peers with distributed control capabilities
V. Communications Trend 40 Optimization and Equilibrium From local optimization To larger/global optimization From equilibrium among few intelligent nodes To equilibrium among all intelligent nodes Optimization (centralized/decentralized) inflexible and arbitrary decision based on fairness or efficiency criteria; neglecting single users standpoints. Equilibrium Working point resulting from distributed decisions of rational interacting nodes.
V. Communications Trend 41 Issues Working on Equilibria Many independent decision makers defining their policies according to their own goals......does an equilibrium point (EP) exist?...does an EP is unique?...if an EP is not unique, which additional constraint to enforce to let a system converge to a single EP?...is the equilibrium stable or do slight system perturbations cause chaos?...how far is the value of social utility (sum of single users utilities) from a global optimum?...
V. Communications Trend 42 Noncooperative versus Cooperative Games Central control OPTIMUM versus Game-driven communications systems or EQUILIBRIUM OPTIMUM & EQUILIBRIUM? COOPERATIVE GAMES!
43 Thank you for your attention! Questions???
44 Essential Bibliography [1 ] Amos Lapidoth, A Foundation in Digital Communications, Cambridge, 2009. [2 ] John Proakis, Digital Communications, Mc Graw Hill, 4th Edition, 2001. [3 ] Sergio Benedetto, Ezio Biglieri and Valentino Castellani, Digital Transmission Theory, Prentice Hall, 1987. [4 ] David Tse and Pramod Viswanath, Fundamentals of Wireless Communications, Cambridge University Press, 2005. [5 ] Thomas Cover and Joy Thomas, Elements of Information Theory, John Wiley & Sons, 1991.