ELT Advanced Course in Digital Transmission. Lecture 1

Transcription

1 TUT ELT Advanced Course in Digital Transmission Markku Renfors Department of Electronics and Communications Engineering Tampere University of Technology Lecture. Introduction to the topic areas of the course - Elements of advanced digital transmission systems - Connections of the topics of the course to the general context 2. Review of digital transmission techniques - Mostly based on the lecture notes of the course TLT Digital Transmission (page numbers on later pages refer to this material) - The main ideas and concepts summarized on pp Summary and examples of optimum demodulation principles (sampled matched filter, whitened matched filter) on pp Frequency-domain equalization techniques, DFT-S- OFDM principle, PAPR considerations on pp. 5-

2 TUT 2 Elements of advanced digital transmission systems System model for basic single-carrier transmission o Linear digital transmission system model (Digital Transmission Lecture notes, pp ) as the basis - Transmit filter - channel - receive filter - Nyquist pulse shaping principle for zero ISI o I/Q modulation & demodulation (pp ) are included in practical radio systems. Here we mostly utilize the equivalent baseband model. Synchronization issues and RF imperfections related to practical I/Q modulation and demodulation are not a concern in this course. Generic Receiver Configuration Received signal Signal demodulation Sufficient statistic Detection Output decision Signal demodulator o Converts the received signal into an N-dimensional vector in the signal space. o Signal-space concepts (pp ) are widely used in the studies. o Optimum demodulation principles developed on pp Sufficient statistic - Correlation receiver/matched filter receiver - Sampled matched filter model o The noise at the sampled matched filter output is correlated, i.e., not white. (More precisely, it is white only under very special conditions.) The whitened matched filter model (pp ) is an optimal demodulation method where also the noise is uncorrelated. o Some enhancements to this model are included on pages 6-4 below.

3 TUT 3 Received signal Signal demodulation Sufficient statistic Detection Output decision Detector o Decides which of the M possible signal waveforms was transmitted. - For a single isolated symbol: No ISI effects; theoretical case which gives some performance bounds - For a block of symbols or continuous sequence detection: ISI effects included. o Based on the maximum likelihood estimation theory, introduced on pp (pages 70, summarize the essential knowledge of the general theory for the detection case ) o Maximum likelihood sequence detector and its implementation using the Viterbi algorithm provide the optimum practical detection method (see pp in the Digital Transmission lecture notes) o Linear and decision feedback equalization are suboptimal solutions with lower complexity. These are described on pp o Frequency domain equalization has lower complexity in case of highly frequency-selective channels. These ideas are introduced below. Multicarrier modulation, OFDM o A key ingredient in most of the recent broadband wireless system developments Error-Control Coding o Efficient feedforward error control coding (FEC) techniques are a key element in today s wireless communication systems. Turbo-codes and LDPC codes are widely utilized. o In advanced designs, decoding is often closely coupled with the detection part, with extensive exchange of soft information and iterative detection/decoding schemes.

4 TUT 4 Time-frequency selective channel characteristics and diversity o Mobile channels are heavily both time and frequency selective. - The data transmitted in a particular time-frequency bin is easily lost in the channel o To cope with time-frequency selective channels, the following schemes may be considered: - Diversity, i.e., send each data element at multiple timefrequency bins. Diversity can be obtained, e.g., through Wideband modulation (CDMA, single carrier) Repetition of data symbols, with interleaving, along frequency or time axis or, more generally, through coding - Adaptive modulation & coding (AMC) based on feedback information about the channel state Scheduling different users signals optimally to different time-frequency resource blocks Precoding: Transmitted waveform can be adapted to the channel response, when this is known. This results in better performance than in the usual model where the transmitter doesn t know the channel. Channel reciprocity: If the same frequency channel is used for uplink and downlink, the transmitter is able to estimate the transmission channel state from the received signal, without feedback. However, due to practical difficulties, this has been only a theoretical possibility so far. - AMC-schemes are easier to implement for stationary or slowly fading channels, fast fading cases are more challenging. In diversity schemes, fast fading brings time diversity, which may even enhance the performance, compared to slowly fading cases. - Examples: 3GPP-LTE relies heavily on AMC principles and channel aware scheduling WiMAX (802.6e) includes both AMC-based transmission mode (called AMC23) and a transmission mode which relies on frequency diversity (called PUSC) o Multicarrier techniques are very useful in this context

5 TUT 5 Multi-antenna techniques, spatial diversity, and spatial multiplexing o Using multiple antennas brings a new element to wireless communication system development, with a great potential to enhance the link quality and/or capacity at link level and, especially, at system level. o For example, using multiple receiver (or transmitter) antennas, it is possible to obtain diversity (so-called spatial diversity) even if there are no (time/frequency) diversity elements in the transmitted waveform. Peak-to-average power ratio o The peak-to-peak voltage range of a communications waveform has significant effect on the implementation of the transmitter and receiver electronics, the transmitter power amplifier in particular. o For example, in OFDM and CDMA systems, the peak value in reference to the RMS value, tends to be high. This has lead to the re-introduction of single-carrier transmission in the uplink of new wireless communication systems, like 3GPP-LTE. o This is a notable example of various implementation related issues, which also have to be taken into consideration when developing wireless communication systems in the waveform domain.

6 TUT 6 Summary of Optimum Signal Demodulation Principles () AWGN channel symbols in Transmit filter g(t) n(t) Receive filter f(t) =g*(-t) Root raised-cosine (RRC) filtering on both sides results in zero ISI: G( f) F( f) = P ( f) where P RC (f) satisfies the Nyquist criterion. (2) Channel with known distortion (Proakis Sect ) RC Sampling at symbol rate to detector Transmit filter Channel Receive filter Sampling at g d (t) b(t) f d (t) symbol rate Compensating the channel in the transmitter end is one possibility, which simplifies the receiver implementation. Alternatively, the channel compensation can be split equally between transmitter and receiver. The latter approach, resulting in smaller loss in SNR due to channel, is characterized by: PRC ( f) Gd ( f) =, f < ( + α) 2 / T B( f) F ( f) = G ( f) d d n(t) G ( f) B( f) F ( f) = P ( f) d d RC

7 TUT 7 (3) Channel with ISI & additive white Gaussian noise Sampled matched filter: Transmit filter g(t) Channel b(t) Received pulse shape: ht () = gt () bt () Matched filter: f( t) = h*( t) = g*( t) b*( t) channel matched filter : b*( t) Overall continuous-time frequency response with RRC pulse shaping in transmitter: X( f) = G( f) B( f) B*( f) G*( f) = G( f) B( f) = P ( ) ( ) RC f B f n(t) Receive filter f (t)= g* (-t)* b *(-t) Sampling at symbol rate Overall discrete-time impulse response: xk = g( t) b( t) b*( t) g*( t ) = Overall transfer function: X( z) = DzD ( ) *( z ) t kt Folded spectrum = Overall discrete-time frequency response: 2 2 j 2 k 2 k X( e ω ) G π ω B ω π = + + T k = T T

8 TUT 8 Frequency domain view to sampled matched filter model - The following discussion shows that the sampled matched filter model maximizes the SNR at each frequency of the folded spectrum. o Intuitively, this is the best we can do. o Compensating the channel frequency response is a separate task, carried out by the detector (i.e., channel equalizer) Folded spectrum: G(f)B(f)F(f) f-/t G(f-/T)B(f-/T)F(f-/T) Passband f Transition band - In the passband region, noise and signal are affected in the same way by the receive filter => SNR is not affected. - In the transition band o Coherent (constructive) combination of the two components is achieved if the phase responses are the same. The zerophase solution of matched filter satisfies this condition. o The SNR at each frequency is maximized when the two observations, after phase equalization, are weighted by the spectrum magnitude values. This is exactly what the matched filter is doing! We can also see that non-ideal processing (like symbol timing errors) in the demodulation part results in some loss of signal energy in the transition band.

9 TUT 9 Whitened Matched Filter The noise samples at the sampled matched filter output are correlated (i.e., the noise is not white): N0 2π k Φ nn( ω) = H ω+ = T k = T 2 jω ( ) De Only in case of ideal channel, the noise is uncorrelated. In the whitened matched filter (WMF) model, a noise whitening filter is included after the sampled matched filter: 2 Matched filter h*(-t) Sampling at symbol rate Noise-whitening filter /D*(z - ) The noise-whitening filter is obtained from the factorization of the sampled match filter based system transfer function: X z DzD z ( ) = ( ) *( ) With WMF, the system transfer function becomes D(z). Usually, there are many ways to do the factorization. The practical approach is to choose D(z) to be a minimum-phase transfer function. This means that - All the poles and zeros are within the unit circle - The energy is concentrated in the beginning of the system impulse response. (Check the corresponding demo about this issue.) About the optimality: The outputs of both sampled matched filter and whitened matched filter contain sufficient statistics, i.e., all information from the received continuous-time signal which can be utilized in detection.

10 TUT 0 Example of matched filter models (a). Let us examine the sampled matched filter and whitened matched filter models in an example case where the channel impulse response is b(t)=δ(t)+0.2δ(t-t). (Such a symbol-spaced channel model is, of course, a very special case, and one has to be careful with the generality of the conclusions drawn from this example). Assume further that a root raised cosine filter p RRC (t) is used as the transmit filter. The channel noise is assumed to be white with power spectral density N 0. o What is the matched filter in this case? Received pulse shape: h( t) = prrc ( t) prrc ( t T) h ( t) = p ( ) 0.2 ( ) Matched filter: RRC t + prrc t T = 0.2 p ( t+ T) + p ( t) o What is the continuous time overall response (transmit filter channel - matched filter)? h( t) * h ( t) = 0.2 prc ( t + T) +.04 prc ( t) prc ( t T) Here prc () t is the raised cosine filter impulse response, p () t = p () t p () t = p ( t T) p ( t+ T). RRC RRC RC RRC RRC RRC RRC o What is the overall system impulse response with sampled matched filter? k = ( ) * ( ) = 0.2 k k k t= kt x ht h t δ δ δ o What is the noise power spectral density at the matched filter output? jωt jωt ( ) H( ω) H ( ω) N0 = 0.2e e PRC ( ω) N0 ( ( ω )) = cos T PRC ( ω) N0 o What is the noise power spectral density at the sampled matched filter output? jω jω jω X( e ) = 0.2e e = cos( ω) o What is the transfer function of the noise whitening filter? ( z ) ( ) X( z) = (0.2z+ )( z ) = DzD ( ) * z HWF ( z) = = D* 0.2z +

11 TUT o What is the overall system impulse response with whitened matched filter? Dz ( ) = + 0.2z dk = δk + 0.2δk (b). Repeat the exercise for channel impulse response b(t)=0.2 δ(t)+δ(t-t). Where are the differences? o What is the matched filter in this case? Received pulse shape: h( t) = 0.2 prrc ( t) + prrc ( t T) h ( t) = 0.2 p ( ) ( ) Matched filter: RRC t + prrc t T = p ( t+ T) p ( t) RRC o What is the continuous time overall response (transmit filter channel - matched filter)? SAME h( t) * h ( t) = 0.2 p ( t + T) +.04 p ( t) p ( t T) RRC RC RC RC o What is the overall system impulse response with sampled matched filter? SAME ( ) = ( ) * ( ) = 0.2 k k k t= kt xk ht h t δ δ δ o What is the noise power spectral density at the matched filter output? SAME jωt jωt ( ) H( ω) H ( ω) N0 = 0.2e e PRC ( ω) N0 ( ( ω )) = cos T PRC ( ω) N0 o What is the noise power spectral density at the sampled matched filter output? SAME jω jω jω X( e ) = 0.2e e = cos( ω) o What is the transfer function of the noise whitening filter? SAME X( z) = (0.2z+ )( z ) HWF ( z) = 0.2z +

12 TUT 2 o What is the overall system impulse response with whitened matched filter? SAME Dz ( ) = + 0.2z dk = δk + 0.2δk 2. We can consider also an equivalent model for the whitened matched filter case where the noise whitening filter is moved in front of the sampler and combined with the matched filter. What would be the frequency response of such a receiver filter with each of the above channel models? Do you have an interpretation for this model? () (2) jωt 0.2e + F( ω) = PRRC ( ω) = PRRC ( ω) jωt 0.2e + jωt e F( ω) = PRRC ( ω); P( ω) = PRRC ( ω) jωt 0.2e + The combination of matched filter and noise whitening filter effects as an allpass filter, i.e., it effects only the phases of the signal spectral components. Thus also the channel noise remains white, since the receiver filter doesn t have an effect on the noise power spectral density. In a way, this combination is equivalent to using an orthonormal basis in the correlation receiver model. Clearly, this result can be generalized to cases where the channel model is symbol-spaced. In these cases, DzD z = BzB z ( ) *( ) ( ) *( )

13 TUT 3 3. When the channel is not symbol-spaced, the fairly simple relations between the channel impulse response and various impulse responses analyzed in Example are not valid anymore. Let us check this issue using the channel impulse response g(t)=0.2 δ(t)+δ(t-3t/2). In numerical studies, you can assume discrete-time RRC filters with 2x oversampling and a roll-off of 25 %. Short RRC filter length (like 5) recommended! o Do the first two steps of Problem analytically. o What is the matched filter in this case? Received pulse shape: h( t) = 0.2 hrrc ( t) + hrrc ( t 3 T/ 2) h ( t) = 0.2 h ( ) ( 3 / 2) Matched filter: RRC t + hrrc t T = h ( t+ 3 T/ 2) h ( t) RRC o What is the continuous time overall response (transmit filter channel - matched filter)? h( t) * h ( t) = 0.2 hrc ( t + 3 T/ 2) +.04 hrc ( t) hrc ( t 3 T/ 2) o Check numerically (with Matlab) the overall system impulse response with sampled matched filter. Explain what you see..2 RRC RC filtering introduces dispersion to the channel taps which are not symbol-spaced and extends the channel impulse response length

14 TUT 4 o Use Matlab to obtain the overall system impulse response with whitened matched filter. You can use the script facmi.m below. What do you learn from this exercise? We see here that RRC filtering increases the channel length, and the effective channel taps in the WMF model are not directly connected to the physical channel taps anymore h=rcosfir(0.25,7,2,); g=conv(h,[ ]); gs=g(2:2:end); figure(),stem(gs) figure(2),stem(facmi(gs)) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This function calculates an estimate of the minimum phase % factor h_min of a symmetric impulse response h. % qp is the order of the prediction error filter, chosen here as 0. % % Code made by M. Tupala, TUT/ICE, February 2006 % modified by M. Renfors, TUT/ICE, Sept function h_min= facmi(h) qp=0; qh=(length(h)+)/2; a_out=h; r=a_out; r(:qh-)=[]; % AC of h % Levinson-Durbin recursion if qp < qh r=r(:qp); else r=[r zeros(,qp-qh + )]; end p=levinson(r); p=(-p(2:end)); a2=flipud([ -(p)]').'; % Noise whitening part hm=filter(a2,,[a_out zeros(, qp)]).'; h_min=hm(end-qh+:end);

15 TUT 5 Example: PAPR in DFT-S-OFDM. As a simplified example case, we can consider the following (here somewhat unconventional parameter values are used to get straightforward baseband model): o K-symbol QPSK/QAM sequence is generated at baseband. (Use K=65 and binary PSK in the experiment) o The sequence is converted to frequency domain using K-point DFT o The K frequency bins are allocated to K consecutive subbands placed arbitrarily within M subbands of the used frequency channel. (In the following experiments, use M=205 an the allocation where the transmitted spectrum is centered at 0-frequency.) o The baseband equivalent waveform is obtained through an M-point IDFT. RRC-type pulse-shaping could be implemented using some additional processing in frequency domain. However, we can consider also using a (nominally) 0 roll-off, just according to the above scheme. (Since DFT-IDFT processing makes a relatively poor filter, this doesn t severely contradict our very basic claim that 0 roll-off in RC filtering is a bad idea!) Your task is to examine this idea by checking: o The PAPR of the modulated waveform o The eye diagram of the baseband waveform in case of an ideal channel. Here the receiver filtering ideally has no effect on the eye diagram, so it can be ignored. To get enough statistics, use something like 00 blocks of 65 data symbols. clear all close all PAPRmax=0; for loop=:00, a=sign(randn(,65)); b=fft(a); c=[b(:33),zeros(,205-65),b(34:65)]; d=ifft(c)*sqrt(205/2); PAPR=0*log0(max(abs(d).^2)/var(d)) PAPRmax=max(PAPRmax,PAPR); end PAPRmax e=kron(d(:3:end),[,zeros(,30)]); figure(),plot(d) hold on stem(e) figure(2) hold on for k=:64, plot(d((k-)*3+:(k+)*3)) end hold off % One block of BPSK signal % Generated baseband waveform % PAPR for current block % Maximum PAPR over 00 blocks % Time-domain baseband waveform % To check that we see the correct % symbol values in the waveform % Eye diagram

16 TUT 6 Maximum PAPR value is found to be about 8.8 db