3. 3. Noncoherent Binary Modulation Techniques

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1 3. 3. Noncoherent Binary Modulation Techniques A digital communication receiver with no provision make for carrier phase recovery is said to be noncoherent. A. Noncoherent Orthogonal Modulation Scheme. For a binary signaling scheme that involves the use of two signals s 1 ( t ), s ( t ), 0 t T which are orthogonal with equal energy, let g 1 ( t ), g ( t ), denote the phase-shifted version of s 1 ( t ), s ( t ), res., which remain orthogonal and of equal energy. This scheme is referred to as noncoherent orthogonal modulation. 0 t T

2 At the receiver, the received signal x(t) can be expressed as follows x ( t ) = g g 1 ( t ) + n ( t ), ( t ) + n ( t ), s s 1 ( t ) ( t ) sent, sent, 0 0 t t T T The receiver tries to discriminate between s 1 (t) and s (t), regardless of the carrier phase. This goal can be achieved by the following receiver structure: x (t ) Matched to 1 (t) Matched to (t) Envelope detector Envelope detector Sample at t = T Sample at t = T l 1 Comparison device If l1 > l choose If l1 < l choose Figure 1. Binary receiver for noncoherent orthogonal modulation l s s 1 ( t ) ( t Gong

3 An noncoherent matched filter may be viewed as being equivalent to a quadrature receiver, as illustrated below. The quadrature receiver itself has two channel (recall that QPSK receiver). Let 1 (t) and (t) be the orthonormal set of s 1 (t) and s (t) and i ( ) be the version of i (t) that results from shifting the carrier phase by -90 degrees. The quadrature receiver is shown in Figure where i = 1,. ~ t In-phase channel x(t) (t) i T dt 0 Square -law device x Ii l i Square + rooter T dt 0 Square -law device x Qi ~ ( t ) i Qradrature channel Figure

4 Remark. The average probability of error for the noncoherent receiver, Figure 1, or equivalently Figure, is given by a simple formula P e 1 exp E = N0 (1) where E is the signal energy per symbol and N 0 / is the noise spectral density. We list this result here without proof. The proof can be found the text Gong 4

5 B. Noncoherent BFSK For the binary FSK case, the transmitted signal is Eb nc + i si ( t) = cos(f it), 0 t Tb i = 1, fi =, nc = integer, i = 1, T Tb b i.e., 1 s 1 0 s ( t) using frequency ( t)using frequency f f 1 Thus the noncoherent binary FSK is a special case of noncoherent orthogonal modulation with T = T b and E = Eb, where T b is the bit duration and E b is the signal energy per bit. From (1), we have the average probability of error (bit error rate) for noncoherent BFSK is P 1 E exp b N e = Gong 5

6 Matched to / cos f t T b 1 Envelope detector Sample at t = T b x(t) 0 t T b Matched to / cosf t T b 0 t T b Envelope detector Sample at t = T b l 1 Comparison device l If l1 > l choose If l1 < l choose 1 0 Figure 3. Noncoherent receiver for BFSK Remark. When comparing the error performance of noncoherent FSK with coherent PSK, it is seen that for the same P e, noncoherent FSK requires approximately 1 db more E b /N 0 than does BFSK (for P 10 4 e ), because coherent reference signals need not be generated. Therefore, almost all FSK receivers use noncoherent detection. In the following, we will see that the same phenomenon occurs for noncoherent DPSK and PSK.

7 C. Differential Phase-shift Keying (DPSK) Transmitter s two operations: (1) differential encoding of the input binary sequence and () phase-shift keying Generation of DPSK: For an input binary sequence b sequence { d k } is determined by { k }, a differential encoded d k = dk 1 bk or dk = dk 1 bk where denotes the modulo operation and the overbar denotes Gong 7

8 Table 1. Illustrating the generation of DPSK signal Differentially encoded sequence Corresponding phase shift index k: { b k } { d k } ref. bit dk = dk 1 bk { ( k)} Remark. DPSK is an another example of noncoherent orthogonal modulation, when it is considered over two bit intervals. In this case, from (1) we get the average probability of error for DPSK is P e 1 E exp = b N 0 since T = T b and E = E b.

9 Remark. When comparing the error performance of () with that of coherent PSK, it is seen that for the same P e, DPSK requires approximately 1 db more E b /N 0 than does BPSK (for P 10 4 e ). It is easier to implement a DPSK system than a PSK system, since the DPSK receiver does not need phase Gong 9

10 4. 4. M-ary Modulation Techniques Error Probability of M-ary Digital PAM Signals Signal Representation of M-ary PSK Signal Representation of M-ary Gong 10

11 A. Error Probability of M-ary Digital PAM Signals Quaternary case: s ( t) = (3/ ), s ( t) = (1/ ), 1 a a s 3( t) = (1/ ) a, ands 4 ( t) = (3/ ) a, for 0 t T P e = 3 a erfc 4 T N 0 where d = a T is the minimum distance of the polar quaternary signal constellation. = 3 erfc 4 d N 0 m 1 = 00 m = 01 m 3 = 11 m 4 = 10 s Z 1 Z Z 3 Z = a T s1 a T 11 a T 1 = s31 = 3 a T s41= a T 0 a T 1( t ) Signal Constellation of Quaternary Signaling Scheme under Gray Code

12 Try for M = 8, which has the signal constellation as below (Gray code). Show that (1) () d 1 d Pe (000) = Pe (111) = erfc N 0 Pe (001) = Pe (011) = erfc N 0 Z 1 Z Z 3 Z 4 Z 5 Z 6 Z 7 Z s 11 = 7 d 3d s 1 = 5 d s d = d s d s51 = d s61 = d 41 = s71 = d s81 = d 31 d 0 0 d d 3d 1( t ) where d = a constellation. T which is the minimum distance of the above signal In general, for M-ary PAM, if the signal points then M M 1 d, L, d, d, d, d, L, d P e M 1 = erfc M d N 0 s 11, s1, L, sm 1 are

13 B. M-ary PSK Scheme: The phase of carrier takes on one of M possible values, namely, i = ( i 1 ) / M, i = 1,..., M A M-ary signal set is represented as s ( t) i E (i 1) = cos(f ct + ), i = 1,...,M, 0 t T M T where T is the symbol duration and E is the signal energy per symbol. The carrier frequency where n c is a fixed integer. f c = n c / Gong 13

14 Similar as we did for QPSK, each signal s i (t) can be represented by the following two orthogonal functions with unit energy: 1( t) = cos(f ct) and ( t) = sin(f ct) T T Thus, the signal constellation of M-ary PSK is two-dimensional. The M messages are equally spaced one circle of radius and center at the origin, see Figure 1 for an example of octa-psk. Figure 1. Signal Constellation for octa- PSK (M = 8). The decision boundaries are shown as dashed Gong 14

15 The coordinates of the received signal given s i (t) was transmitted is (i 1) x I = E cos + n M I, (i 1) xq = E cos + nq, i = 1,..., M M where n I and n Q are Gaussian random variables with zero mean and variance N 0 / (why?). Remark. The probability of correct reception is to integrate the shaded area. This probability can be bounded by some bound. Therefore, for large values of E/N 0, the probability of symbol error is approximately given by s / i M / M P e, M PSK Q E N 0 M sin 4, M (A)

16 C. M-ary FSK In an M-ary FSK scheme, the transmitted signals are defined by s i E ( t) = cos [ f0 + ( i 1) f ] t, 0 t T, i = 1,.., M T where f 0 T is taken as an integer for convenience and ( f ) min = 1/(T ) is the minimum frequency spacing such that adjacent signals are orthogonal (recall this result form MSK). For coherent M-ary FSK, the optimum receiver consists of a bank of M correlations or matched filters. At the sampling times t = kt, the receiver makes decisions based on the largest matched filter output. The probability of symbol error can be upper bounded by E P, ( M 1) Q (B) e M FSK N0 where E = Eb (log M ) is the energy per symbol and M is the size of the symbol set.

17 5. Multi-carrier Modulation and OFDM Applications of M-ary FSK: multicarrier modulation and OFDM Goal: for combating ISI Multicarrier modulation is a way to transmit digital data through bandlimited channel. Design of a bandwidth-efficient communication system in the presence of channel distortion or equivalently ISI, is to divide the available channel bandwidth into a number of equal-bandwidth subchannels, where the bandwidth of each channel is sufficiently narrow so that the frequency response characteristics of the subchannels are nearly equal. Such a division of the overall bandwidth into smaller subchannels is illustrated in Figure Gong 17

18 @G. Gong 18

19 Description: Number of Subchannels: N = W / f Then data symbol is transmitted by frequency-division multiplexing (FDM). This is known as a multicarrier modulation system. Orthogonality: Each subchannel is associated a carrier f i, where f i = f + ( i 1) f, i = 1,, N 0 L which is the mid-frequency in the ith subchannel. If the subcarriers are orthogonal over the symbol duration T, then it is referred to as orthogonal frequency-division multiplexing (OFDM). Thus OFDM is a special case of multicarrier Gong 19

20 Description (Cont.): ISI Reduction: the subcarriers are spaced by 1/T s Hz, where T s is the symbol duration of the subcarriers, then T ofdm, the symbol duration of the OFDM system is related by T s = NT ofdm By selecting N to be sufficiently large, the symbol interval T s of the subcarriers can be made significantly larger than the time duration of the channel-time dispersion. Hence, ISI can be made arbitrarily small by selection of N. In other words, each subchannel appears to have a fixed frequency response C(f k ), k = 0, 1,, N - Gong 0

21 @G. Gong 1

22 @G. Gong

23 @G. Gong 3

24 OFDM Implemented by IDFT and Gong 4

25 Disadvantage: A major problem with the multicarrier modulation in general and OFDM system in particular is the high peak-to-average power ratio (PAR) that is inherent in the transmitted signal. Applications: High-speed transmission over telephone lines, such as digital subcarrier lines. This type of OFDM modulator has also been called discrete multitone (DMT) modulator. OFDM is also used indigital audio broadcasting in Europe and other parts of the worldand in digital cellular communication Gong 5

26 6. 6. Comparisonof of Digital Modulation Systems A. Bit Error Probabilities from Symbol Error Probabilities There are two approaches to define an equivalent bit error probability, P b, or bit error rate (BER), from a symbol error probability, P s. It depends on (1) structure of the signal space, and () the mapping of the signal space points into equivalent bit Gong 6

27 Definition 1. We assume that in going from one signal point to an adjacent signal point, only one bit in the binary word representing the signal changes. In this case, P b = log P s M Remark. M-ary PSK, if a Gray code is employed and M- ary QAM are of the Gong 7

28 Definition. Denote n = log M. We assume that all symbol errors are equally likely. We define P b as the ratio of A, the average number of bit errors per n-bit symbols to n, number of bits per symbol. In the following, we will give an explicit formula for P b. Notice that - Each symbol is in error in an M-ary system with probability P s ( M - For a given symbol error, suppose that k bits are in error. There are n k 1 ) ways that this can happen, which results P b n A 1 n P s = = k n n k = 1 k ( M 1 ) = M P s ( M 1 ) P / s for large M.

29 Remark. M-ary FSK is of this case. B. Bandwidth Efficiencies of M-ary Digital Comm. Systems (DCS) Goal: Consider the bandwidth efficiencies in terms of bits per second per hertz (bps/hz) of bandwidth of various digital modulation schemes. For a M-ary DCS, let R b denote the bit rate and R s symbol rate. Then R b = (log M ) R s For a M-ary PSK, QAM, DPSK, the null to null bandwidth is B M, X = log R b M = R B M b =, X 0. 5 (log M ) (bps/hz)

30 For a M-ary FSK, consider the spacing between frequency is minimum. Then the bandwidth is B coh =, MFSK B coh R b = ( M + log = 3 ) R M log M, MFSK + M 3 b (bps/hz) Table 1. Bandwidth Efficiencies of M-ary Signals M : PSK DPSK QAM : FSK 1 Gong 30

31 Remark: (1) M-ary PSK and M-ary QAM have -dimensional signal space and they are both bandwidth efficient (or called spectral efficient). () MFSK has M-dimensional signal space and it is bandwidth inefficient. Note. The other parameter used in comparing performance (power efficiencies) of different schemes is E/N 0, the ratio of symbol energy to noise power spectral density. In other words, it is to make comparisons between different DSCs on the basis of the relative signal power needed to support a given received information rate assuming identical noise environment.

32 Shannon s system capacity C of an AWGN channel: C = W log (1 + P/WN 0 ) bits/s R > C / = R b / W 4 R = C Bandwidth limited region R < C M-PSK M-QAM M= 8 16 E b M-FSK Power limited region / N 0 ( db ) Figure 1. Band Width Efficiency Plane P e = 5 10

33 7. 7. Synchronization Synchronization at three levels: A. Carrier synchronization (or called carrier recovery): for estimation of carrier phase and frequency. When the coherent detection is used, the knowledge of both the frequency and phase of the carrier is necessary. In other words, there has to be phase concurrence between the incoming carrier and a replica of it in the receiver. This is achieved by employing a phase-locked loop (PLL). The following figure shows a block diagram for carrier synchronization for M-ary Gong 33

34 Received M-ary PSK signal Mth power-law Phase-locked loop BPF LPF If M =, this loop is called a squaring loop. VCO Frequency divide by M Figure 1. Mth Power Loop To data demodulator/detector

35 B. Symbol Synchronization (or called clock recovery) The receiver has to know the instant of time at which the modulation can change its state., i.e., the starting and finishing times of the individual symbols, so that it may determine when to sample and when to quench the product integrator. The estimation of these times is called symbol synchronization or clock recovery. Note. There are typically a very large number of carrier cycles per symbol period, this second level of synchronization is much coarser than phase synchronization (PS), and is usually done with different circuitry than that used for Gong 35

36 One of methods that can achieve this goal is to employ a closed-loop symbol synchronizer. Among the class of closed-loop symbol synchronizers, the early/late-gate synchronizer is the most popular one which shown in Figure 3. g(t) a a T t 0 T T T 0 T T 0 T 0 + T (a) Rectangular pulse g(t) (b) Output of filter matched to g(t) Gong 36

37 Late gate d = 0T T d dt y 1 Absolute value y1 VCO Loop filter F() e = y y1 + timing T d 0 dt y Absolute value y Early gate Figure 3. Early/late-gate data synchronizer

38 C. Frame Synchronization Almost all digital data steams have some sort of frame structure. This is to say that the data stream is organized into uniformly sized groups of bits. For a receiver to make sense of the incoming data stream, the receive needs to be synchronized with the data streams frame structure. This is called frame synchronization. This is usually accomplished with the aid of some special signaling procedure from the transmitter. The simplest frame synchronization aid is the frame marker, for example, in T1 system, for a total of 193 bit, one bit is to used as the frame Gong 38

39 The frame marker could be a single bit, or a short pattern of bits that the transmitter injects periodically into the data stream. The receiver must know the pattern and the injection interval. See Figure Gong 39

40 n bits K bits n bits K bits Data stream n bits K bits n bits K bits Receiver generated frame marker replica Figure 4. Frame marker Gong 40

41 The receiver, having achieved symbol synchronization, correlated the known pattern with the incoming data stream at the known injection interval. If the receiver is not in synchronization with the framing pattern, the accumulated correlation will be low, otherwise, it should be nearly perfect, blemished only by an occasional detection error. A good synchronization codeword is one that has the property that the absolute value of its correlation sidelobes is small. The bit sequences with the property that their largest sidelobe has a magnitude of unity are known as Barker sequences. Unfortunately, the Barker sequences only exist for the length less than Gong 41

42 8. Applications to Digital Cellular Communication Systems In this section, we will present an overview of two types of digital cellular communications systems that are currently in use. One is the GSM ( Global System for Mobile Communication) systems that is widely used in Europe and other parts of the world. It employs time-division multiple access (TDMA) to accommodate multiple users. The second is the CDMA system based on Interim Standard 95 (IS-95) that is widely used in North America and some countries in the Far East. Remark. The extended versions of GSM and IS-95 are UMTS (Universal Mobile Telecommunications Systems, 1998 or W-CDMA) and CDMA 000, respectively.

43 analog speech RPE- LPC speech coder 13 kbps Channel coder.8 kbps Block interleaver Channel measurement bits Burst assembler and encryption 7 other users TDMA multiplexer 70.8 kbps GMSK modulator Frequency hopping synthesizer To transmitter (a) Modulator PN code generator Received signal LPF and A/O converter Buffer Matched filter Channel equalizer Decryption and deinterleaving Channel decoder Speech synthesis Frequency synthesizer (b) Demodulator PN code generator Functional block diagram of modulator and demodulator for GSM

44 Summary of Parameters in GSM System System Parameters Uplink frequency band Downlink frequency band Number of carriers/band Multiple-access method Number of users/carrier Date rate/carrier Speech-coding rate Speech encoder Coded-speech rate Modulation Interleaver Frequency-hopping rate Specification MHz MHz 15 TDMA Kbps 13 KHz RPE-LPC.8 kbps GMSK with BT = 0.30 Block 17 Gong 44

45 Multiple Access Methods

46 The CDMA Cocktail Party This is great stuff Where is she Who called How long will this take Who knows Where is the meeting You know that How can I get there Can I go home? Where is the office

47 Code Division Multiplexing Access (CDMA) Code Division Multiplexing Access (CDMA) Multiple users share a common channel simultaneously by using different codes Narrowband user information is spread into a much wider spectrum by the spreading code The signal from other users will be seen as a background noise: multiple access interference (MAI) The limit of the maximum number of users in the system is determined by interference due to multiple access and multipath fading: Adding one user to CDMA system will only cause graceful degradation of quality Theoretically, no fixed maximum number of Gong 47

48 Code Division Multiplexing Access (CDMA) (Cont.) Code Division Multiplexing Access (CDMA) (Cont.) Received signal PSD Despread signal PSD for user 1 user 1 user M Despreading user M signal power Interference power Bandwidth Bandwidth user 1 user user 3 user 4 user user 3 user 4 CDMA is an interference-limited multiple access scheme The signal from other users will be seen as a background noise: Gong access interference (MAI) 48

49 CDMA System Design Voice Coding Forward Link Generation CODEC bps 4800 bps 400 bps 100 bps R = 1/ Convolutional Encoder and Repetition User Address Mask (ESN) Block Interleaver Long Code PN Generator 19. ksps 1.88 Mcps Decimator 19. ksps Power Control Bit Decimator MUX Wt Hz 1.88 Mcps I PN QPN Cell Power Control VOCODER Voice Coding Reverse Link Generation I PN CODEC bps 4800 bps 400 bps 100 bps R = 1/3 8.8 Convolutional ksps Encoder and Repetition 8.8 Block ksps Interleaver User Address Mask Walsh Cover 307. khz 1.88 Long Mcps Code PN Generator Data Burst Randomizer 1.88 Mcps QPN 1/ PN Chip Dela D Mobile

50 The CDMA Rate Families IS-95 defines the 9600 bps family of rates (Rate Set 1) 9600, 4800, 400, and 100 bps Can select one of the four rates every 0 ms frame bps family of rates (Rate Set ) 14400, 700, 3600, and 1800 bps Can select one of the four rates every 0 ms frame Extended rates (extended Rate Set 1) Adds 1900, 38400, and bps At most four rates can be active Can select one of the four active rates every 0 ms frame

51 Variable-Rate Vocoder 0 ms Packets Full Rate 8.55 kbps 64 kbps PCM Encoder Decoder 1/ Rate 4 kbps 1/4 Rate kbps Decoder Encoder 64 kbps PCM 1/8 Rate 0.8 kbps

52 Link Waveform CDMA Forward Link Waveform Pilot Channel Sync Channel Paging Channel Traffic Channel QTSO CDMA REVERSE Link Waveform Access Channel Traffic Channel QTSO

53 PN code generator I channel Pilot channel and other traffic channels in same cell Hadamard (Walsh) sequence Baseband shaping + filter Data 9.6 kbps 4.8 kbps.4 kbps 1. kbps Mask Rate ½, L = 9 Convolution encoder with repetition Long code generator Decimator Block inter- Carrier leaver generator Block diagram of IS-95 forward link Baseband shaping Gong 53 filter PN code generator Q channel -90 deg. Pilot channel and other traffic channels in same cell To transmitter

54 Reverse CDMA Channel REVERSE CDMA CHANNEL (1.3 MHz channel received by base station) Access Ch 1 Access Ch n Traffic Ch 1 Traffic Ch m Addressed by Long Code PNs

55 Reverse Traffic Channel Structure for Rate Set 1 Reverse Traffic Channel Add Frame Information Quality Indicators (1, 8, 0, Bits (17, 80, 40, or 8.6 kbps or 0 bits/frame) 4.0 kbps 16 bits/frame).0 kbps 0.8 kbps Add 8 bit Encoder Tail 9.6 kbps 4.8 kbps.4 kbps 1. kbps Convolutional Encoder r=1/3, K=9 Code Symbol 8.8 ksps 14.4 ksps 7. ksps 3.6 ksps Symbol Repetition Code Symbol 8.8 ksps 8.8 ksps Block Interleaver Code Symbol I-channel Sequence 1.88 Mcps 64-ary Orthogonal Modulator Modulation Symbol (Walsh chip) 4.8 ksps (307. kcps) Frame Data Rate Data Burst Randomizer PN chip 1.88 Mcps Long Code Generator 1/ PN chip Delay = ns D Q-channel Sequence 1.88 Mcps I Q Baseband Filter Baseband Filter I(t) cos(f c t) Q(t) sin(f c t) s(t) Long Code Mask

56 Summary of Parameters in IS-95 System System Parameters Uplink frequency band Downlink frequency band Number of carriers/band Multiple-access method Number of users/carrier Chip rate Speech coder Speech rate Interleaver Channel encoder Modulation Signature sequences PN sequence Specification MHz MHz 0 CDMA Mbps Variable rate, CELP 9600, 4800, 40, 100 Block R=1/,L=9(D), R=1/, L=9(U) BPSK with QPSK spreading (D) 64-ary orthogonal with QPSK spreading (U) Hadamard (Walsh) of length (long code), 15 (spreading codes)

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