EE 6331, Spring, 2009 Advanced Telecommunication

EE 6331, Spring, 2009Advanced Telecommunication Zhu Han Department of Electrical and Computer Engineering Class 17 Mar. 31th, 2009

Outline Receiver Structure: Match filter revisit Eye Diagram Equalization Basics Surveys Linear DFE MLSE Zero Forcing, LMS RLS Fractionally spaced equalizer Turbo equalizer ECE6331

Receiver Structure • Matched filter: match source impulse and maximize SNR • grx to maximize the SNR at the sampling time/output • Equalizer: remove ISI • Timing • When to sample. Eye diagram • Decision • d(i) is 0 or 1 Noisena(t) gTx(t) gRx(t) d(i) ? ECE6331

Matched Filter: optimal receive filter for maximized Matched filter example • Received SNR is maximized at time T0 example: Receive filter (mathed filter) transmit filter ECE6331

Eye Diagram • The eye diagram is created by taking the time domain signal and overlapping the traces for a certain number of symbols. • The open part of the signal represents the time that we can safely sample the signal with fidelity ECE6331

Vertical and Horizontal Eye Openings • The vertical eye opening or noise margin is related to the SNR, and thus the BER • A large eye opening corresponds to a low BER • The horizontal eye opening relates the jitter and the sensitivity of the sampling instant to jitter • The red brace indicates the range of sample instants with good eye opening • At other sample instants, the eye opening is greatly reduced, as governed by the indicated slope ECE6331

Interpretation of Eye Diagram • 10 points in the final ECE6331

Jitter in Circuit design • Circuit design ECE6331

Raised Cosine Eye Diagram • The larger , the wider the opening. • The larger , the larger bandwidth (1+ )/Tb • But smaller  will lead to larger errors if not sampled at the best sampling time which occurs at the center of the eye. ECE6331

Eye Diagram Setup • Eye diagram is a retrace display of data waveform • Data waveform is applied to input channel • Scope is triggered by data clock • Horizontal span is set to cover 2-3 symbol intervals • Measurement of eye opening is performed to estimate BER • BER is reduced because of additive interference and noise • Sampling also impacted by jitter ECE6331

Eye Diagram • Eye diagram is a means of evaluating the quality of a received “digital waveform” • By quality is meant the ability to correctly recover symbols and timing • The received signal could be examined at the input to a digital receiver or at some stage within the receiver before the decision stage • Eye diagrams reveal the impact of ISI and noise • Two major issues are 1) sample value variation, and 2) jitter and sensitivity of sampling instant • Eye diagram reveals issues of both • Eye diagram can also give an estimate of achievable BER • Check eye diagrams at the end of class for participation ECE6331

Figure 4.34 (a) Eye diagram for noiseless quaternary system. (b) Eye diagram for quaternary system with SNR  20 dB. (c) Eye diagram for quaternary system with SNR  10 dB. EE 541/451 Fall 2007

Figure 4.35 (a) Eye diagram for noiseless band-limited quaternary system: cutoff frequency fo  0.975 Hz. (b) Eye diagram for noiseless band-limited quaternary system: cutoff frequency fo  0.5 Hz. ECE6331

Eye Diagram In Phase ECE6331

Linear Modulation with Nyquist Impulse Shaping QPSK diagram under limited bandwidth conditions  if system (tx and rx filter) meets 1st Nyquist : 4 sharp signal points (right diagram) ECE6331

Equalization, Diversity, and Channel Coding Three techniques are used independently or in tandem to improve receiver signal quality Equalization compensates for ISI created by multipath with time dispersive channels (W>BC) Change the overall response to remove ISI Diversity also compensates for fading channel impairments, and is usually implemented by using two or more receiving antennas Multiple received copies: Spatial diversity, antenna polarization diversity, frequency diversity, time diversity. Reduces the depth and duration of the fades experienced by a receiver in a flat fading (narrowband) channel Channel Coding improves mobile communication link performance by adding redundant data bits in the transmitted message Channel coding is used by the Rx to detect or correct some (or all) of the errors introduced by the channel (Post detection technique) Block code and convolutional code ECE6331

Equalization Techniques The term equalization can be used to describe any signal processing operation that minimizes ISI Two operation modes for an adaptive equalizer: training and tracking Three factors affect the time spanning over which an equalizer converges: equalizer algorithm, equalizer structure and time rate of change of the multipath radio channel TDMA wireless systems are particularly well suited for equalizers Symbol Mapper ISI Channel Equalizer Decision Device ECE6331

Channel Response Equalizer is usually implemented at baseband or at IF in a receiver f*(t): complex conjugate of f(t) nb(t): baseband noise at the input of the equalizer heq(t): impulse response of the equalizer ECE6331

Block Diagram ECE6331

Equalization If the channel is frequency selective, the equalizer enhances the frequency components with small amplitudes and attenuates the strong frequencies in the received frequency response For a time-varying channel, an adaptive equalizer is needed to track the channel variations ECE6331

Basic Structure of Adaptive Equalizer Transversal filter with N delay elements, N+1 taps, and N+1 tunable complex weights These weights are updated continuously by an adaptive algorithm The adaptive algorithm is controlled by the error signal ek ECE6331

Minimize Estimation Error Classical equalization theory : using training sequence to minimize the cost function E[e(k) e*(k)] Recent techniques for adaptive algorithm : blind algorithms Constant Modulus Algorithm (CMA, used for constant envelope modulation) Spectral Coherence Restoral Algorithm (SCORE, exploits spectral redundancy or cyclostationarity in the Tx signal) ECE6331

Math Derivation • Error signal where • Mean square error • Expected MSE where ECE6331

Math Derivation • Optimum weight vector • Minimum mean square error (MMSE) • Minimizing the MSE tends to reduce the bit error rate • Example 7.1, 7.2 • Training Sequence then Data transmission within each frame Training Sequence Data transmission Training Sequence Data transmission ECE6331

Classification of Equalizer if d(t) is not the feedback path to adapt the equalizer, the equalization is linear if d(t) is fed back to change the subsequent outputs of the equalizer, the equalization is nonlinear ECE6331

Linear transversal equalizer LTE, made up of tapped delay lines ECE6331

ARMA Model (FIR, IIR) ECE6331

Linear Transversal Equalizer :frequency response of the channel :noise spectral density ECE6331

Lattice Filter ECE6331

Characteristics ofLattice Filter Advantages Numerical stability Faster convergence Unique structure allows the dynamic assignment of the most effective length Disadvantages The structure is more complicated ECE6331

Nonlinear Equalization Used in applications where the channel distortion is too severe Three effective methods Decision Feedback Equalization (DFE) Maximum Likelihood Symbol Detection Maximum Likelihood Sequence Estimator (MLSE) ECE6331

Nonlinear Equalization--DFE • Basic idea : once an information symbol has been detected and decided upon, the ISI that it induces on future symbols can be estimated and substracted out before detection of subsequent symbols • Can be realized in either the direct transversal form or as a lattice filter ECE6331

DFE ECE6331 EE 552/452 Spring 2007

Predictive DFE Predictive DFE (proposed by Belfiore and Park) Consists of an FFF and an FBF, the latter is called a noise predictor Predictive DFE performs as well as conventional DFE as the limit in the number of taps in FFF and the FBF approach infinity The FBF in predictive DFE can also be realized as a lattice structure The RLS algorithm can be used to yield fast convergence ECE6331

Predictive DFE ECE6331

MLSE MLSE tests all possible data sequences (rather than decoding each received symbol by itself ), and chooses the data sequence with the maximum probability as the output Usually has a large computational requirement First proposed by Forney using a basic MLSE estimator structure and implementing it with the Viterbi algorithm The block diagram of MLSE receiver MLSE requires knowledge of the channel characteristics in order to compute the matrics for making decisions MLSE also requires knowledge of the statistical distribution of the noise corrupting the signal ECE6331

MLSE ECE6331

Algorithm for Adaptive Equalization Equalization is related to previous frames. Performance measures for an algorithm Rate of convergence Misadjustment Computational complexity Numerical properties Factors dominate the choice of an equalization structure and its algorithm The cost of computing platform The power budget The radio propagation characteristics ECE6331

Algorithm for Adaptive Equalization The speed of the mobile unit determines the channel fading rate and the Dopper spread, which is related to the coherent time of the channel directly The choice of algorithm, and its corresponding rate of convergence, depends on the channel data rate and coherent time The number of taps used in the equalizer design depends on the maximum expected time delay spread of the channel The circuit complexity and processing time increases with the number of taps and delay elements Three classic equalizer algorithms : zero forcing (ZF), least mean squares (LMS), and recursive least squares (RLS) algorithms ECE6331

Summary of algorithms ECE6331

Turbo Equalizer Separating the equalization and decoding is suboptimal knowledge about the structure on the transmitted symbols imposed by the error correcting code is not exploited by the equalizer. turbo equalization is an iterative equalization/decoding process. involves using output from the decoder to re-equalize the received data. normally based on: interference canceller, or APP equalizer. P-1 P + Output Data Forward Filter MAP Decoder Soft encoded symbols DFE with hard input feedback Feedback Filter Decision Device ECE6331

Turbo Decoder Performance. 0 iteration=DFE ECE6331

EE 6331, Spring, 2009 Advanced Telecommunication