Generating 4-Level and Multitone FSK Using a Quadrature Modulator Page 1 of 9 Generating 4-Level and Multitone FSK Using a Quadrature Modulator by In a reent olumn (lik on the Arhives botton at the top of this page to link to it) I desribed how to use a quadrature modulator to generate quiet arriers at several frequenies. Then that olumn examined what s needed to generate a frequeny-shift keyed (FSK) data signal. This time I ll extend the onept to inlude m-ary FSK and multitone FSK. 2- and 4-Level FSK To refresh your memory, Fig 1 shows the basi quadrature modulator. Our task is to derive the I and Q waveforms that ause the modulator to generate the desired RF signal. I I-Arm + RF os( RF t) V out Q-Arm 90 o +/- Q Fig 1 -- Arhiteture of the quadrature modulator In binary or 2-Level FSK (2L-FSK), the system enodes a Zero as one RF frequeny (f 0 ) and a One as a seond RF frequeny (f 1 ). The symbol rate (R S ) equals the bit rate (R B ). Extending the onept, in 4-Level FSK (4L-FSK) two data bits generate one of four possible RF tones. Beause two bits make up eah symbol, the symbol rate is half the bit rate. Fig 2 shows the bit-to-symbol mapping for generating 2L-FSK. The same figure shows the bit-tosymbol mapping this artile uses to generate 4L-FSK, where again eah symbol (frequeny) requires two bits to uniquely speify one of four possible frequenies.
Generating 4-Level and Multitone FSK Using a Quadrature Modulator Page 2 of 9 Symbol 2-Level FSK "0" "1" 4-Level FSK "00" "01" "10" "11" Frequeny f 0 f 1 f 0 f 1 f 2 f 3 f RF f RF Fig 2 Symbol (frequeny)-to-bit map of 2-Level FSK and of 4-Level FSK Choosing a symbol-to-bit mapping seems like a simple exerise, but you must onsider many options and tradeoffs, espeially for large, omplex symbol domains suh as 64-QAM. The arbitrary bit-to-symbol map the author seleted to generate the example 4L-FSK for this artile is: Lowest frequeny: f 0 = f RF - 3R S maps to symbol 00 f 1 = f RF - R S maps to symbol 01 f 2 = f RF + R S maps to symbol 10 Highest frequeny: f 3 = f RF + 3R maps to symbol 11 Other mappings are possible, inluding the Grey ode. To make the best deision, you must examine the demodulator and figure out how it s most likely to make a symbol error, and then map aordingly. Ideally, you would like one symbol error to generate only one bit error. The tehnique I desribed last month applies sinewaves at frequeny f m to the I- and Q-ports of a quadrature modulator to produe signals that are displaed from f RF by f m. The phase relationship of the two sinewaves applied to the I and Q ports determines whether the output signal is above or below the RF arrier. For the purposes of this olumn s example, let s separate eah tone from its neighbor by twie the symbol rate. That distane is more than you need for reliable detetion at the reeiver, but the resulting graphis look more intuitive. Given this ondition, you must generate a sinewave at the symbol rate and at three times the symbol rate as in Fig 3.
Generating 4-Level and Multitone FSK Using a Quadrature Modulator Page 3 of 9 I 00 I 01 I I 10 I 11 RF os( RF t) + V out Q 00 Q 01 90 o + Q 10 Q Q 11 Fig 3 Generating 4-Level FSK with a quadrature modulator. The symbol you wish to transmit determines whih I and Q to apply at the modulator inputs. The symbol 00 requires I 00 and Q 00 ; a 01 needs I 01 and Q 01 ; a 10 wants I 10 and Q 10 ; while I 11 and Q 11 produe symbol 11. When the transmitted symbol is to be 00, apply I 00 to the modulator s I port and Q 00 to its Q port. This ombination produes a tone at f 0 = f RF - 3R S. Similarly, applying I 01 and Q 01 produes a tone at f 1 = f RF - R S ; I 10 and Q 10 produe a tone at f 2 = f RF + R S ; and I 11 and Q 11 produe a tone at f 3 = f RF + 3R S. You apply eah set of I and Q waveforms for one symbol time, then hange aording to the next symbol. Fig 4 shows a random symbol stream and the I and Q waveforms you must generate to enode that stream as a 4L-FSK waveform. This method presents the I and Q ports with either one or three omplete yles of a sinusoidal wave over the duration of eah symbol.
Generating 4-Level and Multitone FSK Using a Quadrature Modulator Page 4 of 9 Fig 4 Waveforms present in a 4-Level FSK quadrature modulator. The top trae shows the symbol stream to enode. The bottom two traes show the I and Q waveforms you must apply to the modulator. Symbols 00 and 11 both require three yles of a sine wave, whereas symbols 01 and 01 require only a single sinewave yle. It s now interesting to examine the spetrum of suh a signal. You might expet to see only the four possible output frequenies, and indeed they are dominant, but sidelobes also arise. For instane, Fig 5 shows the spetrum of a 4L-FSK signal whose bit rate is 10k bps. The symbol rate is 5k symbols/se. You an see the four symbols (or tones) at -15 khz (-3R S ), -5 khz (-R S ), +5 khz (+R S ) and +15 khz (+3R S ). The sin(x)/x spetral shape surrounding eah tone is due to the suddenness with whih the system hanges symbols and the high frequenies that arise from a step funtion.
Generating 4-Level and Multitone FSK Using a Quadrature Modulator Page 5 of 9 Fig 5 Spetrum of a 4-Level FSK signal. The bit rate is 10 kbps while the symbol rate is 5k symbols/seond. The four tones are separated by 10 khz. We an learly see eah of the four tones generated by the modulator. To get a different view of the output waveform, examine Fig 6, whih shows the time-frequeny plot (spetrogram) of the 4L-FSK signal. The four tones at frequenies f 0, f 1, f 2 and f 3 are learly visible. A frequeny hange ours every 200 se, indiating a 5-kHz symbol rate just what you designed.
Generating 4-Level and Multitone FSK Using a Quadrature Modulator Page 6 of 9 Fig 6 Spetrogram (time-frequeny plot) of a 4-Level FSK signal. The symbol stream used for this plot was (00, 01, 10, 11, 00, 01, 10, 11), whih is enoded as (f 0, f 1, f 2, f 3, f 0, f 1, f 2, f 3,). Multitone FSK It s not diffiult to expand this sheme into other modulation methods that present some speifi advantages. For instane, the onept behind multitone FSK (also known as Orthogonally Multiplexed QAM or OMQAM) is to break down a high-speed bitstream into N lower-speed bitstreams, eah of whih you then enode as its own separate 2L-FSK hannel. If the bit rate of the high-speed hannel is R b, then the bit rate of eah of the N low-speed hannels is R b /N. One primary advantage of this modulation is a dereased symbol rate, whih fights multipath propagation effets. Another advantage is that this modulation spreads the information over a wide bandwidth. Any propagation nulls or narrowband interferene affets only a small number of hannels. Multitone FSK is used in adaptive HF modems, HDTV transmissions and some power line modems. This olumn desribes this type of modulation primarily by example. Fig 7 shows how you might break a user bit stream apart for an 8-level multitone FSK system. The demultiplexer absorbs a bitstream of R b bits/se and emits eight bitstreams, B 0 to B 7, eah running at R b /8 bits/se.
Generating 4-Level and Multitone FSK Using a Quadrature Modulator Page 7 of 9 Bit Stream (at R b bps) Demultiplexer Demultiplexed Bit Streams (at R b /8 bps) B 0 B 1 B 2 B 3 B 4 B 5 B 6 B 7 Fig 7 A demultiplexer takes in a user bitstream at R b bits/se and produes 8 low-speed bitstreams, eah at R b /8 bits/se. You now use eah low-speed R b /8 bitstream to frequeny-modulate one arrier at a rate of R b /8. For example, bitstream B 0 modulates a arrier entered at frequeny f B0. You want the modulator to emit frequeny f B0,0 when B 0 = 0 and to emit frequeny f B0,1 when B 0 = 1. Similarly, bit stream B 1 frequeny-modulates the arrier at f B1, ausing the modulator to emit frequeny f B1,0 when B 1 = 0 and frequeny f B1,1 when B 1 = 1. In general, bitstream B n auses the modulator to emit frequeny f Bn,0 when B n = 0 and frequeny f Bn,1 when B n = 1. Fig 8 illustrates this plan.
Generating 4-Level and Multitone FSK Using a Quadrature Modulator Page 8 of 9 Eight Independent Bitstreams at R b /8 bps B 0 B 1 B 2 B 3 B 4 B 5 B 6 B 7 "0" "1" f RF f B0 f B1 f B2 f B3 f B4 f B5 f B6 f B7 f B0,0 f B1,0 f B2,0 f B3,0 f B4,0 f B5,0 f B6,0 f B7,0 f B0,1 f B1,1 f B2,1 f B3,1 f B4,1 f B5,1 f B6,1 f B7,1 Frequeny Fig 8 The frequeny plan of an 8-Level multitone FSK modulator. Bitstream B 0 ontrols the frequeny of the tone entered about f B0, while bitstream B 1 ontrols the frequeny of the tone at f B1, et. During one symbol period, the modulator emits either f B0,0 or f B0,1. At the same time, it emits a tone at either f B1,0 or f B1,1, and so forth. The modulator always emits eight tones simultaneously during eah symbol period, and the stream assigned to eah tone determines its frequeny. When the system swithes over from one symbol to the next, its hange all eight tones simultaneously at the start of a new symbol. The symbol rate is R b /8 and the bit rate equals R b. For example, assume you need to transmit the symbol B 7 B 6 B 5 B 4 B 3 B 2 B 1 B 0 = 11000100. Fig 8 indiates you must simultaneously produe these eight tones: f B0,0 beause B 0 = 0 f B1,0 beause B 1 = 0 f B2,1 beause B 2 = 1 f B3,0 beause B 3 = 0 f B4,0 beause B 4 = 0 f B5,0 beause B 5 = 0 f B6,1 beause B 6 = 1 f B7,1 beause B 7 = 1
Generating 4-Level and Multitone FSK Using a Quadrature Modulator Page 9 of 9 Fig 9 shows the output spetrum required for this one symbol. Note that this spetrum is valid only for one symbol time. After the modulator has reated this 8-bit symbol, it must generate a new symbol based upon the next eight data bits. So the general problem boils down to, Given an arbitrary symbol [B 7 B 6 B 5 B 4 B 3 B 2 B 1 B 0 ], derive the orret I and Q. B 0 B 1 B 2 B 3 B 4 B 5 B 6 B 7 "0" "1" f RF f B0 f B1 f B2 f B3 f B4 f B5 f B6 f B7 f B0,0 f B1,0 f B2,0 f B3,0 f B4,0 f B5,0 f B6,0 f B7,0 f B0,1 f B1,1 f B2,1 f B3,1 f B4,1 f B5,1 f B6,1 f B7,1 Frequeny Fig 9 Multitone FSK spetrum required for symbol B 7 B 6 B 5 B 4 B 3 B 2 B 1 B 0 = 11000100 = f B7,1 f B6,1 f B5,0 f B4,0 f B3,0 f B2,1 f B1,0 f B0,0. The modulator must produe these eight tones simultaneously. There are two general methods for finding I and Q: first, the time-domain method, whih is intuitive and straightforward; seond, the FFT method, whih is omputationally effiient and more versatile. Next time, we ll look at the time-domain method in detail. Stay tuned. Author Biography was born and raised in Ohio, whih explains a lot. He went to the University of Akron for his undergraduate work in eletrial engineering and ompleted his MSEE at the Johns Hopkins University in 1988. He designed and taught several RFrelated ourses at Johns Hopkins University. He is also the author of Wireless Reeiver Design for Digital Communiations (ISBN-13: 978-1891121807) and of Radio Reeiver Design (ISBN-13: 978-1884932076) with Tom Vito. You an reah Kevin at mkevin@mlaning.om.