Rud, The Lyons book is a good introduction to the FFT and FIR filters but I haven't read the other book. "Multirate Signal Processing" (ISBN 0-13-146511-2) has information on more complex DSP systems. "Digital Communications" (ISBN 0-07-051726) is fairly old, but a good introductory book and there should be a new issue out by now. "Quadrature Amplitude Modulation" (ISBN 0470 09468 0) has lots of information on single carrier and OFDM modems. "Trellis and Turbo Coding" (ISBN 0-471-22755-2 has useful information on several error-correcting codes.
QPSK encodes 2 bits so if 1 is used for error-correction only 1 is left for user data. 8PSK has 8 states so only 3 bits are encoded and if one is 1 for error-correction information, 2 are left for data. OFDM using the FFT and IFFT restricts the type of modulation used on each subcarrier as the sidebands for all subcarriers are interleaved and the sidebands for each subcarrier must have nulls at the frequencies of all other subcarriers. From what I've read, the phase or amplitude can only be changed at the beginning of each sampling period. If the subcarriers are placed further apart than the symbol rate for each subcarrier, a separate filter could be implemented for each subcarrier and the FFT need not be used. The modulation restriction is removed, but the bandwidth is 1.5-2 times greater. A subcarrier phase modulated at a 62.5 Hz rate has a peak at the center frequency and one set of sidebands on either side of that frequency with nulls every 62.5 Hz. The sidebands for each subcarrier look a lot like the spectrum of an FM signal with the distance between the first nulls 125 Hz. The first-order sidebands between the first nulls on each side of the subcarrier frequency have most of the energy so some of the higher-order sidebands can be filtered out. If a subcarrier isn't modulated, it occupies close to 0 Hz. WIth 8 subcarriers, all of the first-order sidebands occupy 562.5 Hz. If unmodulated subcarriers are placed 62.5 Hz above or below the first and last subcarriers, it makes little difference in the total occupied bandwidth. 73, John KD6OZH ----- Original Message ----- From: Rud Merriam To: digitalradio@yahoogroups.com Sent: Thursday, October 25, 2007 03:48 UTC Subject: RE: [digitalradio] OFDM Proposal: Details John, One more time, thanks. A lot to mull over in your message. I am working from Lyons for DSP and Sklar for the digital communications. Plus whatever I can scare up on the web. Any other suggestions for reference materials? Two big gaps are going from the DSP in Lyons to practical implementation and between the DSP and digital. Lyons does not really talk about communications and Sklar does not go into the DSP enough for me. Sklar also seems to be a little behind the curve on DSP and recent developments. Sklar does cover the Ungerboek material so I will review it again. I don't follow the "one bit with QPSK and 2 using 8PSK" since QPSK will carry 2 bits and 8PSK 4 bits. I was also reviewing some other material. From it I was considering using 1/4 Pi DQPSK to avoid crossing through the origin during phase changes. There would be room for a 9th sub carrier and still fit in 500 Hz. Why wouldn't sub carriers above and below the data sub carriers not count for the bandwidth used? More than 9 sub carriers exceeds 500 Hz. Rud Merriam K5RUD ARES AEC Montgomery County, TX http://TheHamNetwork.net -----Original Message----- From: digitalradio@yahoogroups.com [mailto:[EMAIL PROTECTED] On Behalf Of John B. Stephensen Sent: Wednesday, October 24, 2007 8:37 PM To: digitalradio@yahoogroups.com Subject: Re: [digitalradio] OFDM Proposal: Details Differential PSK should be more reliable in the presence of frequency drift and Doppler spread. There are two ways to do this: 1) compare the phase with the previous phase of the same subcarrier or 2) compare the phase with the phase of the next higher or lower subcarrier. In the first case, the first symbol transmitted is always all zeroes. In the second case, there would have to be at least one pilot subcarrier that is unmodulated. If you want pilot subcarriers, it should be possible to put them 62.5 Hz above and below the outermost data subcarriers as they take no extra space if they are not modulated. A good way to do FEC is to use trellis-coded modulation (TCM). One bit is added to the data stream for each subcarrier. This, 1 data bit is sent using QPSK and 2 data bits are sent using 8PSK. The advantage of sending the data and ECC bits on one subcarrier is that the error-correcting code can be designed so that no extra bandwith is needed and that the addition of the extra bit actually decreases the required SNR rather than increasing it as you would first expect by increasing the number of points in the constellation. Ungerboek came up with a set of codes that can decrease the required SNR by 3-6 dB (with no fading) when going from QPSK with no ECC to 8PSK with ECC. The improvement is larger when fading occurs. The amount of improvement provided by TCM depends on the complexity of the state machine used to generate the ECC bit. However, a simple algorithm with 4 states provides a 3 dB improvement. A Viterbi decoder is used to calculate the most probable set of state transitions that the incoming signal has taken from symbol to symbol and then backtracks to determine the most likely combination over an entire data frame. It can also make decisions based on the actual value of the incoming signal rather than on 3 already decoded buts. This adds another 2 dB of improvement. Its probably useful to place the audio subcarrier frequencies in the 500-1000 Hz range or higher so that harmonics of low frequency subcarriers don't interfere with higher-frequency subcarriers. 73, John KD6OZH ----- Original Message ----- From: Rud Merriam To: digitalradio@yahoogroups.com Sent: Wednesday, October 24, 2007 10:03 UTC Subject: [digitalradio] OFDM Proposal: Details For your amusement and consternation here are my latest thoughts on doing an OFDM protocol. Symbol rate: 62.5 Hz (128 samples @ 8000 Hz) Guard interval: 2, 4, 8 ms adaptive to conditions Subchannels: 8 (62.5 125 187.5 250 312.5 375 437.5 500) Bandwidth: 437.5 Hz Raw BPS: 1778, 1600, 1333 adaptive (guard band change) Base frequency: undetermined MODULATION (somewhat firm) Waveform: DQPSK with constellation at 45, 135, 225, 315 degrees Generation: 8 separate generators providing continuous waves through the guard bands Phase change: start of symbol period Shaping: post generation raised cosine over symbol and guard period DEMODULATION (somewhat speculative) FT: 128 bin every 32 samples for locating subchannels Synchronization: square of subchannels identified by FT to locate bottom subchannel by 125 Hz signal Frequency drift: subchannel selection based on output of synchronization Phase detection: phase averaged over symbol period, differential with last symbol A main goal is to keep the bandwidth within 500 Hz. The symbol rate is as suggested by John KD6OZH. First testing will probably be with his 8 ms guard band but I would like to make it adaptive to short that period if multipath conditions allow. DQPSK to get more throughput and because getting the absolute phase is a challenge. Any suggestion to use absolute phase would be appreciated since that gains a couple dB. The Fourier transform is mainly to identify the potential subchannel locations to allow adjusting for frequency drift. Once high energy bins are determined the signal is filtered at various of those frequencies and the square used to detect the doubled lowest frequency (125 Hz). That also locates the symbol period for synchronization. Actually, the possible frequency includes the guard band so it may be one of three values. By determining that value the guard band period is also determined and the actual guard band removed. Rud Merriam K5RUD ARES AEC Montgomery County, TX http://TheHamNetwork.net
