Modulation Techniques :
Modulation Techniques Made by : Eng/ Mohamed Mostafa Modulation :
Modulation Why modulation?
Notice the sidebands Extending to
Infinity due to side lobes generated
By sharp edges. Digital Modulation :
Digital Modulation Why Digital Modulation
The move to digital modulation provides more information capacity
Compatibility with digital data services
Higher data security
Better quality communications
Quicker system availability.
Constraints:
• available bandwidth
• permissible power
• inherent noise level of the system Digital Modulation :
Digital Modulation Effect of Number Of Levels:
Higher levels always means dividing the pattern into more decision levels.
Two levels Four Levels
The more the increment of the non-linearity of the power amplifier, the worse the shift from the original threshold levels. we need Higher linearity for Higher number of levels.
have higher SNR than those who only use two level schemes for similar BER. Considerations in Choice of Modulation Scheme :
Considerations in Choice of Modulation Scheme Criteria to take into account when choosing the digital modulation method:
Power efficiency, i.e., the Eb/N0 ratio for a specific error probability
Bandwidth efficiency, i.e., the data rate per unit bandwidth
The bit error rate or bit error probability of a modulation scheme is inversely related to Signal energy per bit / noise power spectral density Eb/No
Performance on multipath fading channels and under non-linear distortion
Implementation cost and complexity
Conflicting requirements that cannot be satisfied simultaneously Considerations in Choice of Modulation Scheme :
Considerations in Choice of Modulation Scheme Trading off simplicity and bandwidth
Simple hardware can be used in transmitters and receivers to communicate information. However, this uses a lot of spectrum which limits the number of users. Alternatively, more complex transmitters and receivers can be used to transmit the same information over less bandwidth. The transition to more and more spectrally efficient transmission techniques requires more and more complex hardware. Complex hardware is difficult to design, test, and build. Considerations in Choice of Modulation Scheme :
Considerations in Choice of Modulation Scheme Bandwidth Efficiency
bandwidth efficiency limits Nyquist Techniques :
Nyquist Techniques
There is no ISI Nyquist Techniques :
Nyquist Techniques Raised Cosine Family BPSK :
BPSK What is PSK?
PSK modulation encodes data on a sine wave by shifting the phase of the carrier signal to represent the binary data stream.
A single carrier frequency can carry data with the relative phase of the waveform indicating the bit value of the data.
E.g., a logic “0” can be represented as a 0 degree phase shift and a logic “1” by 180 degree. FSK (BFSK) :
FSK (BFSK) Non-coherant BFSK
In its most general form, the binary FSK scheme uses two signals with different frequencies to represent binary 1 and 0.
where Φ1 and Φ2 are initial phases at t = 0, and T is the bit period of the binary data.
These two signals are not coherent since Φ1 and Φ2 are not the same in general.
The waveform is not continuous at bit transitions. This form of FSK is therefore called noncoherent or discontinuous FSK. FSK (BFSK) :
FSK (BFSK) Coherant BFSK
Phase discontinuities CPFSK :
CPFSK Continuous phase
Space and mark frequencies can be chosen so that the periods both cross zero.
Smooth transitions result in less bandwidth.
This is improved in minimum shift keying (MSK) in which mark and space frequencies are integer multiples of the bit clock frequency, MSK :
MSK MSK or “fast” FSK is a special type of continuous phase FSK
In MSK the frequency separation between the two tones is Δf= f=1/(2T b)
Δf= f=1/(2T b) is the minimum frequency separation that is necessary to ensure orthognality between the two tones over the signaling interval of length Tb
The power efficiency of MSK is similar to the power efficiency of BPSK
The bandwidth efficiency of MSK is twice the bandwidth efficiency of BPSK FSK :
FSK error probability of coherently demodulated FSK
The error probability for a given signal-to-noise ratio decrease as M increases, contrary to other modulation scheme (i.e. PSK and QAM), but on the other hand the bandwidth efficiency decrease as M increases GMSK :
GMSK GMSK is a derivative of MSK
In GMSK the baseband binary data is first Gaussian pulse shaped before frequency modulating a carrier ⇒ smoother phase trajectory
The 3dB bandwidth bandwidth-bit duration product of the Gaussian filter (BTb) is a parameter that measures the performance of GMSK
A lower value of BTb implies a narrower bandwidth but more ISI ⇒ bandwidth efficient but power inefficient
A higher value of BT b implies a wider bandwidth but less ISI ⇒ bandwidth inefficient but power efficient M-ary Modulation :
M-ary Modulation A group of n bits is transmitted in each signaling interval T=log 2(M)Tb
In M-ASK a group of n bits is transmitted using M= 2^n different amplitudes
In M-PSK a group of n bits is transmitted using M= 2^n different phases
In M-FSK a group of n bits is transmitted using M= 2^n different frequencies
Quadrature amplitude modulation (QAM) uses a combination of amplitude and phase modulation to convey the information Generation of M-Ary Digital Signals :
Generation of M-Ary Digital Signals In M-ASK the in-phase component is an M-level NRZ baseband signal and the quadrature component is zero
In M-PSK the in-phase and quadrature components are M-level NRZ baseband signals
In M-QAM the in-phase and quadrature components are √M-level NRZ baseband signals
The amplitude of the in-phase/quadrature component is given by the I/Q value of the point of the constellation to be transmitted GSM :
GSM GMSK :
GMSK What is GMSK
A Gaussian-shaped impulse response filter generates a signal with low side lobes and narrower main lobe than the rectangular pulse. Since the filter theoretically has output before input, it can only be approximated by a delayed and shaped impulse response that has a Gaussian - like shape. This modulation is called Gaussian Minimum Shift Keying (GMSK). GMSK :
GMSK Why using GMSK?
A filter used to reduce the bandwidth of a baseband pulse train prior to modulation is called a pre-modulation filter. The Gaussian pre-modulation filter smoothes the phase trajectory of the MSK signal thus limiting the instantaneous frequency variations. The result is an FM modulated signal with a much narrower bandwidth.
Impulse response defined by a Gaussian Distribution – no overshoot or ringing (see lower figure) GMSK :
GMSK Efficiency
BT – refers to the filter’s -3dB BW and data
rate by:
For BT=0.3, adjacent symbols will interfere
with each other more than for BT=0.5
GMSK with BT=∞ is equivalent to MSK.
Trade-off between ISI and side-lobe
suppression. The higher the ISI, the more
difficult the detection will become. Modulation in GSM :
Modulation in GSM Power Spectrum of Selected Bit Error Rate of Selected
Binary Modulation Schemes Binary Modulation Schemes Modulation in GMSK :
Modulation in GMSK Two point modulation
not however, suitable for coherent
demodulation due to component
tolerance problems.
I and Q modulation
The modulated RF signal is created by mixing
the I and Q components up
to the frequency of the RF carrier,
where they are summed together. Slide 25:
Example of GMSK modulation {1,1,-1,1,1,-1,-1,1,-1,1,-1,-1, 1,1,-1,1,1,-1,-1,1,-1,1,-1,-1,............}
The first few Gaussian shaped pulses (BN = 0.5)
These individual shaped pulses are then added together to give b(t).
This function, b(t), is then integrated, with respect to t (time) from t to ∞, to give the function c(t). take Sine and Cosine functions of it to produce the I and Q-baseband signals.
I(t) = Cos[ c(t) ]
Q(t) = Sin[ c(t) ]
These two functions I(t) and Q(t) are then passed through the I/Q modulator which leads to the output signal m(t) Modulation in GSM :
Modulation in GSM In GSM, we use GMSK
Why?
Due to the very limited bandwidth (200kHz), we needed a modulation scheme that has higher Bandwidth efficiency.
The only way was to try to Eliminate the side lobes. As it can’t be eliminated, we’ve chosen the scheme with the lowest possible side lobes (MSK).Although MSK would appear to have some direct advantages due to its inherent improved spectral properties, direct generation of an MSK waveform utilizing a modulator both difficult and expensive. The multipliers required are expensive and the timing requirements quite tight. Numerous timing adjustments are necessary and the frequency deviation of 0.5T implies difficult, and perhaps impossible in some situations, filtering Modulation in GSM :
Modulation in GSM Solution – use a pre-modulation filter:
Straight-forward Approach: Low-Pass Filter
More Efficient/Realistic Approach: Gaussian Filter
In GMSK the baseband binary data is first Gaussian pulse shaped before frequency modulating a carrier ⇒ smoother phase trajectory
The 3dB bandwidth bandwidth-bit duration product of the Gaussian filter (BT b) is a parameter that measures the performance of GMSK
A lower value of BT b implies a narrower bandwidth but more ISI ⇒ bandwidth efficient but power inefficient
A higher value of BT b implies a wider bandwidth but less ISI ⇒ bandwidth inefficient but power efficient Modulation in GSM :
Modulation in GSM Separation between carriers must be sufficient to eliminate interference between adjacent channels, where The more the separation the less the co-channel interference but the less the available channels suited in the bandwidth.
It is found that a 200 kHz channel separation is suitable for all systems.
The channel data rate is 270 kbps
GMSK enables the transmission of 270kbit/s within a 200kHz channel. This gives a bit-rate of 1.35 bit/s per Hz.
This is rather low bit-rate but acceptable as the channel used has high interference level in the air. Modulation in GSM :
Modulation in GSM Frequency Allocation
GSM 900 uses the circa 900Mhz band
The frequency band used is 890-915MHz (mobile transmit) and 935-960MHz (base transmit). Modulation in GSM :
Modulation in GSM To allow maximum number of users access, each band is subdivided into 124 carrier frequencies spaced 200 kHz apart, using FDMA techniques.
Each of these carrier frequencies is further subdivided into time slots using TDMA.
TDMA (Time Division Multiple Access) has 8 time slots (i.e. transmitting for one eighth of the time). Hence, one radio channel can support 8 'full rate' traffic.
A more economical 'half rate' scheme with 16 traffic channels is being introduced.
TDMA provides each user with the carrier frequency for approximately 0.577ms. Modulation in GSM :
Modulation in GSM Frequency hopping may he optionally employed in order to avoid 'deadspots' and to minimize interference from other signals. The hopping rate is one hop per TDMA frame (4.6µs), or 217 hops per second.
The method of modulation used Is Gaussian Minimum Shift Keying (GMSK), with a BT value of 0.3 at a gross data rate of 270 kb/s.
Time-bandwidth product of 0.3 was chosen as a compromise between spectral efficiency and intersymbol interference. With this value, 99% of the power spectrum is within a bandwidth of 250 kHz, and since GSM spectrum is divided into 200 kHz channels for multiple access, there is very little interference between the channels.
The speed at which GSM can transmit at, with BT =0.3, is 271 kb/s. (It cannot go faster, since that would cause intersymbol interference). UMTS :
UMTS M-ary PSK :
M-ary PSK phase diagram and signal constellation diagram for the case of M = 8 are shown below M-ary PSK :
M-ary PSK Example
Advantages of M-PSK
M-ary signaling schemes transmit log2M bits at a time.
Bandwidth requirement of M-ary signaling schemes is reduced. M-ary PSK :
M-ary PSK Modulation of M-ary PSK
We’ll convert the sequence into parallel. The number of bits in each time equals Log2 M. Now we have number of phases equal M. According to the input we’ll get an output with the phase θi.
Now we have 2 outputs Cos θi and Sin θi. Both will be multiplied by it’s own carrier (Same amplitude with 90 degrees phase shift) and The result is s(t) M-ary PSK :
M-ary PSK error probability of coherently demodulated PSK/M-ary PSK
the error probability for a given signal-to-noise ratio increase as M increases, contrary to other modulation scheme (i.e.FSK), but on the other hand the bandwidth efficiency increases as M increases QPSK :
QPSK What’s QPSK?
Quadrature Phase Shift Keying (QPSK) is a form of Phase Shift Keying in which two bits are modulated at once, selecting one of four possible carrier phase shifts (0, 90, 180, or 270 degrees). QPSK allows the signal to carry twice as much information as ordinary PSK using the same bandwidth. (This is a general example, not the one used by UMTS) QPSK :
QPSK Shape and Constellation Diagram QPSK :
QPSK Example
consider a random binary data sequence: 10111011000110…
designate the bits as ‘odd’ (bo) and ‘even’ (be) so that one modulation symbol consists of one odd bit and the adjacent even bit. The above sequence can be split into an odd bit sequence (1111001…) and an even bit sequence (0101010…).
Now we can recognize the binary bit stream as a sequence of signal points which are to be transmitted:
{(10), (11), (10), (11), (00), (01), (10), … QPSK :
QPSK Generation of QPSK
Block Diagram of QPSK modulator
A Better Block diagram that can be better in practical QPSK :
QPSK Generation of QPSK
Why?
The output of the multiplier in the I-path is similar to a BPSK modulated signal where the modulating sequence has been derived from the odd sequence. Similarly, the output of the multiplier in the Q-path is a BPSK modulated signal where the modulating sequence is derived from the even sequence and the carrier is a sine wave. If the even and odd bits are independent of each other while occurring randomly at the input to the modulator, the QPSK modulated signal can indeed be viewed as consisting of two independent BPSK modulated signals with orthogonal carriers. QPSK :
QPSK Example Modulation in UMTS :
Modulation in UMTS Why taking ∏/4-shift QPSK over QPSK?
QPSK
Highest shift
= pi/2
∏/4-OQPSK
Highest shift
= pi/4
So, when the shift = pi/2 higher delay & sharper edge. OQPSK, ∏/4-shifted QPSK :
OQPSK, ∏/4-shifted QPSK Variants of QPSK
Conventional QPSK has transitions through zero (i.e.. 180o phase transition). Highly linear amplifier required.
In Offset QPSK, the transitions on the I and Q channels are staggered. Phase transitions are therefore limited to 90o
π/4-QPSK the set of constellation points are toggled each symbol, so transitions through zero cannot occur. This scheme produces the lowest envelope variations. Modulation in UMTS :
Modulation in UMTS Practical QPSK used in UMTS
Raised cosine (phase shifted by pi/4)
4 Symbols, 2 bits/symbol
Signal shifts between the phase
states are separated by 90 degrees
Since the two carriers, cos(ct) and
sin(ct) are orthogonal they do not
interfere with each other
Any symbol can transition to any other
symbol Modulation in UMTS :
The UTRAN air interface uses QPSK modulation in the downlink, although HS-PDSCH may also employ 16 Quadrature Amplitude Modulation (16 QAM). 16 QAM requires good radio conditions to work well. The modulation chip rate is 3.84 Mcps. The original proposal called for a chip rate of 4.096 Mcps, but this was modified later to make it closer to the CDMA2000 chip rate.
With 16 QAM also the amplitude of the signal matters. In QPSK one symbol carries two data bits; in 16 QAM each symbol includes four bits. Thus, a QPSK system with a chip rate of 3.84 Mcps could theoretically transfer 2 × 3.84 = 7.68 Mbps, and a 16 QAM system could transfer 4 × 3.84 Mbps = 15.36 Mbps Modulation in UMTS LTE :
LTE QAM :
QAM What’s QAM?
QAM is the encoding of information into a carrier wave by variation of the amplitude of both the carrier wave and a 'quadrature' carrier that is 90° out of phase with the main carrier in accordance with two input signals. Alternately, this can be regarded (using complex number notation) as simple amplitude modulation of a complex-valued carrier wave by a single complex-valued signal.
What this actually means is that the amplitude and the phase of the carrier wave are simultaneously changed according to the information you want to transmit. QAM :
QAM Generating QAM
We chose 16 as an example this time. That is, we consider combining bits in groups of four, yielding 16 possible values. These values change every 4T so we can expect a bandwidth that is one-fourth that of BPSK. If we use 16 ary- PSK, the points in signal space would be equally spaced on the circumference of a circle, and the angular spacing between adjacent points would be 22.5 degrees. In this case, both the amplitude and the phase vary , so the points no longer lie on the circumference of a single circle. The signal space diagram consist of 16 points in a uniform square array. The Individual signals are of the form: QAM Modulator :
QAM Modulator Matched Delay matches delay through 90o phase shifter (required but often omitted on block diagrams) QAM Demodulator :
QAM Demodulator Automatic gain control
Scales analog input voltage to appropriate level for A/D
Increase gain when received signal level is low
In-phase/quadrature (I/Q) demodulation
Recover baseband in-phase/quadrature signal
Lowpass filters are matched filters & extract baseband Receiver
Filter A/D Symbol
Clock
Recovery LPF LPF Carrier Detect AGC X X 90o r0(t) r1(t) r(t) r(m) I(m) Q(m) Equalizer L I(n) L Q(n) L samples/symbol BER :
BER error probability of coherently demodulated QAM
As can be seen below as the signal set size increases so does the probability of error.
Where P(e) is the probability of error and Eb / No is the ratio of bit energy to noise power spectral density. 16 QAM :
16 QAM there are four I values and four Q values. This results in a total of 16 possible states for the signal. It can transition from any state to any other state at every symbol time. Since 16 = 2^4, four bits per symbol can be sent. This consists of two bits for I and two bits for Q. The symbol rate is one fourth of the bit rate. So this modulation format produces a more spectrally efficient transmission.
Four Bits Per SymbolSymbol Rate = 1/4 Bit Rate 64 QAM :
64 QAM In this case there are six I values and six Qvalues resulting in a total of 36 possible states (6x6=36). This is too many states for a power of two (the closest power of two is 32). So the four corner symbol states, which take the most power to transmit, are omitted. This reduces the amount of peak power the transmitter has to generate. Since 25 = 32, there are five bits per symbol and the symbol rate is one fifth of the bit rate. Five Bits Per SymbolSymbol Rate = 1/6 Bit Rate LTE Modulation :
LTE Modulation Frequency allocation: famous allocated bands from 1.7 to 2.5 GHz
Scalable BW: 1.25, 2.5, 5.0, 10.0 and 20.0 MHz
Subcarrier spacing: Δf = 15 kHz.
Spectrum efficiency: Downlink: 5bits/s/Hz
Uplink: 2.5bits/s/Hz
Peak data rate:
Downlink: (2 Ch MIMO) peak rate of 100 Mbps in 20 MHz channel
Uplink: (single Ch Tx) peak rate of 50 Mbps in 20 MHz channel