About Homework. The rest parts of the course: focus on popular standards like GSM, WCDMA, etc.

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1 About Homework The rest parts of the course: focus on popular standards like GSM, WCDMA, etc. Good news: No complicated mathematics and calculations! Concepts: Understanding and remember! Homework: review the course materials learned in the class and we will have a test (close-book, 10 minutes) in next class. Six classes left. Five tests. Five scores. The best three out of the five scores will be taken as the final score of your homework. Answers of all tests and the homework of part 1 to 4 will be revealed in the final class (tutorial) on Nov. 9. p. 3

2 Part 4. Communications over Wireless Channels (Con't) p. 4

3 System Performance over Radio Links p. 5

4 Modulation: Review (1) Modulation: The transformation of a sequence of digital data into an analog waveform appropriate for transmission. Digital communications, information needed to be transmitted: discrete bit sequences Signal suitable for radio transmission: usually a continuous sinusoidal wave ( ) = sin ( π + ϕ ) s t A f t c amplitude frequency phase Digital information is transmitted by varying one or more parameters of the transmitted signal or waveform: Amplitude Amplitude Shift Keying (ASK) Frequency Frequency Shift Keying (FSK) Phase Phase Shift Keying (PSK) p. 6

5 () = sin ( π + ϕ ) s t A f t Info. bits: 0 1 ASK c Amp. of the carrier: 0 Α Info. bits: 0 1 FSK Freq. of the carrier: f f 1 Info. bits: 0 1 BPSK Phase of the carrier: π 0 p. 7

6 Signal Constellation Diagram Modulation: Review () () = sin ( π + ϕ ) s t A f t c Signal Constellation Diagram Information bits: QPSK Phase of the sine wave: QPSK π/ π 3π/ p. 8

7 4QAM 8QAM Examples of combined ASK-PSK signal const. diagram 16QAM Examples of rectangular ASK-PSK (QAM) signal const. diagram p. 9

8 Modulation: Review () Modulation techniques commonly used in mobile communications: GMSK (GSM), BPSK and QPSK (IS-95, WCDMA), 8-PSK (EDGE), 16QAM (HSPA), 64QAM (HSPA+, LTE) Bit and symbol: A symbol is the fundamental unit that is used to modulate the carrier waveform. QPSK: four symbols, two bits constitute a symbol, and this symbol is used to control the phase shift of the carrier frequency M-ary PSK/QAM: M symbols, log M bits form a symbol. In M-ary signaling, when the bit transmission rate is 1/T b bits per second, the symbol rate is 1/T b /log M symbols per second. Question: How many bits are transmitted by one symbol if 16QAM (or 64QAM) is employed? p. 10

9 (in AWGN channel) Es/N 0 : signal to noise ratio per symbol p. 11

10 Modulation: Review (3) Gray Encoding: Two adjacent symbols each consisting of m bits have exactly one bit position where the bits in the two symbols are different. Advantage: minimization of bit error when a symbol is incorrectly decoded as an adjacent symbol. Examples: Natural encoding Gray encoding Gray encoding p. 1

Modulation: Review (4) Differential encoding: For example, in differential PSK (DPSK), the carrier phase shift depends not only on the symbols transmitted at the current

11 Modulation: Review (4) Differential encoding: For example, in differential PSK (DPSK), the carrier phase shift depends not only on the symbols transmitted at the current instant but also on the carrier phase shift at the previous time instant. Original info. bits b i Bits after diff. encoding d i =d i-1 +b i Advantage: easy to detect Carrier p. 13

12 Transmitter Detection Methods (1) Wireless Channel Receiver Tx Rx 0 t 0 t' t BPSK signal: T s ( ) = sin ( π + ϕ ) s t A f t i c i Data info. is carried in ϕ i (=π) T s Transmission time: t' what we get at the receiver: ( ϕ + π ft' ) = ( ϕ + φ ) i c i f c Phase of the carrier frequency p. 14

13 Detection Methods () Problem: how to get ϕ i from (ϕ i +φ fc ) Coherent detection: With the help of a pilot tone or a sequence of pilot symbols, estimate the additional phase shift caused by carrier freq. φ fc, thus ϕ i can be obtained by subtracting φ fc from (ϕ i +φ fc ) Nocoherent detection: The transmitted symbol is detected without a knowledge of the phase of the carrier frequency. Differential encoding is required. p. 15

14 Example of coherent detection Transmitter Receiver pilot sym. data sym. pilot sym. data sym. 0 t 0 t' t T s T s t +T s Pilot symbol is a known symbol to the receiver phase of rec. pilot: π/ What is known to the rec.: the trans. pilot has a initial phase of zero Phase of the carrier freq. πf c t'=φ fc =π/-0 =π/ p. 16 phase of rec. data sym: (ϕ i +φ fc +πf c T s ) =3π/ π phase carrying info. bit: ϕ i =3π/-π/=π

Example of noncoherent detection 0 Transmitter Original bits: 1 0 0 1 0 Differentially

t 0 t' ϕ0 π fct ' Receiver + ϕ + π f ( T + t ) Phase difference: = 1 0 + c s known: π 1 c s

15 Example of noncoherent detection 0 Transmitter Original bits: Differentially encoded bits: DBPSK: original bit 0: no phase change original bit 1: phase change t 0 t' ϕ0 π fct ' Receiver + ϕ + π f ( T + t ) Phase difference: = c s known: π 1 c s ' ( ) [ ] ϕ1+ π fc Ts + t' ϕ0 + π fct' ϕ ϕ π ft Phase diff.: 0 0 π 0 Detected bits: t p. 17

16 Error Probabilities for AWGN Channels (Comparison) The SNR difference required to achieve the same P b of 10 5 : Is a fraction of db only: between - phase PSK and -phase DPSK is a fraction of db. Is more than db: between 4-phase PSK and 4-phase DPSK is more than db. New mobile radio communication systems (e.g., 3G, HSPA) turn to use coherent detection rather than noncoherent detection. A pilot signal (for both uplink and downlink) is used to contain the phase information. Copied from Proakis s Digital Communications p. 18

17 Bit Error Probability Comparison between Coherent and Noncoherent Detection Performances in Rayleigh Fading Performances for BPSK and DBPSK using coherent and noncoherent detection techniques, respectively Coherent detection Noncoherent detection A 3dB loss in E b /N 0 is incurred by using noncoherent detection over coherent detection, even though binary signaling is considered. Another piece of evidence showing that coherent detection is preferred for mobile radio communications E b /N 0 (db) p. 19

18 Detection Methods (3) Summary of coherent and noncoherent detection noncoherent detection is easy to implement; no need for pilot, higher transmission efficiency coherent detection is more complicated than noncoherent detection because it needs pilot to track the phase of carrier freq. coherent detection always provides better performance than noncoherent detection p. 0

19 Bit Error Probability Diversity Techniques (Motivation) Performances for BPSK systems using coherent detection and operating on AWGN channels or Rayleigh-fading channels AWGN channels Rayleigh-fading channels Observation: Performance of communications over a Rayleigh fading is very poor in comparison to the one over an unfaded AWGN channel. Motivation: The need to enhance the performance. Diversity: One method to enhance the performance is the use of diversity techniques E b /N 0 (db) p. 1

20 Illustration of Time Diversity Amp. Rayleigh Fading Channel One single info. data Repetition Interleaving Simplest way to enhance the perf. Further enhance by time diversity t Easy to be corrupted by the channel and detection error occurs Likely to experience deep fading concurrently The probability that all copies experience deep fading is greatly reduced t p.

21 Diversity Techniques (Principle) Diversity Redundancy in transmission or reception. Principle: Consider the case that the same signal is transmitted two times. When the first replica of the signal is transmitted on a channel that is in deep fade, the information contained in the signal can hardly be able to be recovered. In the next time instant, the second replica of the signal is transmitted. At that time, the channel is in good condition, the information inside the signal can be recovered with low/acceptable bit error probability. 1st time of transmission Channel in deep fade, signal very weak time diversity t nd time of transmission Channel in good condition, signal very strong p. 3

22 Diversity Techniques (1) Condition to obtain time diversity: t > ( t ) c Reason: The fading characteristics of a channel at two time instants separated by more than the coherence time of the channel are slightly correlated. By transmitting the same signal on multiple discrete time instants mutually separated by more than the coherence time, diversity effects can be observed. Method to exploit Previous examples: repetition code More power error-correcting codes: convolutional code, turbo code, LDPC code Summary Advantage: Easy to implement. Disadvantage 1: Need to ensure that two successive bits are separated with sufficient time separation. Interleaving is required. Disadvantage : If the channel is very slowly varying, time diversity is ineffective. Relevance to mobile communications: Error-correcting coding is always implemented in mobile communication systems. It is already implicitly used to exploit time diversity. p. 4

23 Diversity Techniques () Frequency diversity: At the transmitter, the same information is transmitted via two or multiple signals at different frequencies. Condition to obtain freq. diversity: f > ( f ) c Summary Disadvantage: More transmit power is required. Signal bandwidth is expanded. Relevance to mobile communications: Another form frequency diversity, known as multipath diversity, is frequently employed in CDMA mobile communication systems. e jπf0t freq. separation f f 0 f 1 f n e jπfnt signal spectrum p. 5

24 Diversity Techniques (3) Multipath diversity: Freq. domain: freq. selective channel: f sig >( f) c coherence bandwidth signal spectrum f sig f t p. 6 Time domain: Multipath channel. Multipath components are independently faded. By combining these component, deep fades can be avoided. Method to exploit: direct-sequence spread-spectrum techniques (i.e., CDMA techniques) plus RAKE receiver Summary Advantage: Efficient utilization of the implicit freq. diversity offered by the wideband signal. Disadvantage: Wideband signals are generally more difficult to handle. Relevance to mobile communications: cdmaone, WCDMA and cdma000

25 Diversity Techniques (4) Receive diversity: At the receiver, two or more antennas separated sufficiently are used for signal reception. The separation is such that the correlation of signals received at different antennas is small. Advantage: Transmit power does not need to be increased. Disadvantage: More antennas are needed. May not be possible at mobile stations. Relevance to mobile communications: Very popular for use at base stations. large enough Combiner Transmitter p. 7 Receiver

26 Diversity Techniques (5) Transmit diversity: At the transmitter, multiple antennas are used to transmit the same information signal. The antennas are sufficiently separated to ensure low correlation in fading. The carrier phases of all the signals are adjusted such that the signals are coherently added at the receive antenna. Advantage: Can be used at base station. While diversity can be exploited, only one receive antenna is required. Disadvantage: Phase adjustment is required. Closed-loop control is required. Relevance to mobile communications: The benefit of capacity enhancement outweighs the implementation difficulty. WCDMA has approved the use of transmit diversity. large enough Phase Adjustment Receiver p. 8 Transmitter

27 Diversity Combining Order of diversity It is the number of replicas of the same signal available in a diversity system. When the order of diversity is one, the system is a non-diversity system. The higher the order, the better the system performance Selection combining (SC) The replicas are compared and the largest one in magnitude or SNR is selected for demodulation or detection. Maximal ratio combining (MRC) The replicas are weighted and coherently added together so that the resultant SNR is maximized. Equal-gain combining (EGC) The replicas are coherently added to form an estimate that is used for demodulation of detection. p. 9

28 Example of Diversity Combining Receive Diversity (SIMO) receive antennas: sufficiently spaced, independent fading channel is known how to obtain receive diversity: selection combining, gain combining s hs r=hs+n Tx Tx Single Input Single Output (SISO) Rx Rx SIMO E{} s = 0, E{} n = 0, P { } 1, { } sig = E s = σ = E n = 1, h = 0.5 : { } { n } E hs h Psig signal-to-noise ratio (SNR) at receiver: SNR= = = 0.5 E σ p. 30 ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU

29 Receive Diversity () Selection combining h 1 =0.5 h =1.1 r 1 =h 1 s+n 1 r =h s+n Tx h 3 =-0. r 3 =h 3 s+n 3 Rx p. 31 { } σ { } { } { } 1 3 E{ h 1s } h1 P 1 = sig = n1 } σ E{ h s } h P = sig = E{ n } σ E{ h 3s } h3 P 3 = sig = E{ n3 } σ P = E s = 1, = E n = E n = E n = 1 : sig SNR at receiver 1: SNR = 0.5 SNR at receiver : SNR = 1.1 SNR at receiver 3: SNR = 0.04 Choose the largest SNR! Received signal from antenna is retained! ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU

30 Receive Diversity (3) Maximal Ratio Combining (Gain combining) h 1 =0.5 h =1.1 r 1 =h 1 s+n 1 r =h s+n Tx h 3 =-0. r 3 =h 3 s+n 3 Rx p. 3 make use of all received signals weighting: the one with higher SNR should have a more important role in the final signal signal after weighting: y = w r + w r + w r = h r + h r + h r SNR after weighting: SNR= * * * * * * ( h h h ) s ( hn hn hn) = ( ) E h h h s h + h + h P = E h n h n h n + + σ * * * { } ( 1 3 ) ( 1 3 ) ( h1 h h3 ) h + h + h Psig = = 1.50 σ ELEC 7073 Digital Communications III, Dept. of E.E.E., HKU sig Maximal ratio combining (MRC)

31 Bit Error Probability for MRC Systems A higher order of diversity gives a better performance. Non-diversity systems A higher order system yields a BER curve that has a steeper slope of BER reduction. The advantage of E b /N 0 reduction for a higher order diversity system diminishes. That is, diminishing return is observed. Copied from Proakis s Digital Communications p. 33

32 Summary What is the purpose of modulation? Three basic types of modulation schemes according to the parameters of the carrier adjusted to transmit digital information. Familiar with popular modulation schemes like BPSK, DBPSK, QPSK, 16QAM. How to represent a modulation scheme using signal constellation diagram? Concepts of bit and symbol. How to do Gray encoding and differential encoding? What are coherent detection and noncoherent detection? What are their advantages and disadvantages, respectively? Understand the principle of diversity. What are time diversity, frequency diversity and space diversity? Understand the operation of selection combining and maximal ratio combining. p. 34

Amplitude Frequency Phase

Amplitude Frequency Phase Chapter 4 (part 2) Digital Modulation Techniques Chapter 4 (part 2) Overview Digital Modulation techniques (part 2) Bandpass data transmission Amplitude Shift Keying (ASK) Phase Shift Keying (PSK) Frequency