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SDM
University
SDM 201
QAM OFDM SDM
A Relative Performance Comparison
1) Sample Rates for Given Bandwidth
a) QAM, OFDM
i) Each generates a spectrum centered about 0Hz; this sets the maximum frequency of interest for sampling purposes at half the final (RF) bandwidth. Nyquist requires that the sampling rate be at least twice the maximum frequency of interest.
ii) Centering about 0Hz also eliminates the negative image of the up-/down-converted signal; the IF filtering need only eliminate the sampling image. This requires that the maximum frequency of interest be raised by at least half the transition band of an IF filter.
iii) Both QAM and OFDM use I and Q sampling, therefore two sample streams are generated, and the number of Samples processed per unit time would be:
b) SDM
i) SDM Wavelets use a pure real spectrum, with no negative components; this sets the maximum frequency of interest for sampling purposes at the final (RF) bandwidth. Nyquist requires that the sampling rate be at least twice the maximum frequency of interest.
ii) With the pure real spectrum of wavelets, the IF filtering needs to eliminate both the negative image and the sampling image of the up-/down-converted signal. This requires that the pure real spectrum start above 0Hz by at least half the transition band of the IF filter, and that the resulting maximum frequency of interest be raised by at least half the transition band.
c) The Net Result of the above is:
This expresses the concept that, at similar bandwidths, the SDM Wavelet Engine processes the same data per symbol as competing modulations.
2) Symbol Spacing (of consecutive symbols, also known as baud rate)
a) OFDM
i) OFDM's orthogonal carriers are susceptible to distortion by the frequency response of the transmission medium (essentially smearing one symbol into the next, creating Inter-Symbol Interference (ISI). In order to combat this, a cyclic prefix is generally pre-pended to the actual symbol data to allow this transient response to settle out before the data is processed. Depending on the transmission medium response, this cyclic prefix is 3-25% of the symbol data.
b) QAM
i) QAM's single-carrier transition encoding are also susceptible to ISI effects, but the nature of the single carrier lends itself somewhat better to equalization to eliminate the effects. No cyclic prefix is used.
c) SDM
i) SDM wavelets use wide, overlapping, symbols; the baud rate would be the same as for the equivalent band OFDM symbols, but without the requirement of a cyclic prefix. This increase in useful baud rate comes at the expense of a novel but relatively simple process at the front-end of the modulator/ demodulator, which reduces further processing to the same order-of-magnitude complexity of other modulations.
d) The Net Result of the above:
Wavelets are able to send more symbols per unit time for a similar bandwidth compared to OFDM; this specific advantage does not apply to QAM, but note the next comparison.
3) Occupied Bandwidth/Bandwidth efficiency
Any modulation is bounded not only by the bandwidth
it is limited to, but also by the requirement that there be no signal
energy at the edges of the occupied spectrum to avoid interference
with frequency-adjacent signals. The need to reduce this energy results
in a required increase in the occupied spectrum above the modulated
spectrum. This increase is referred to as Alpha.
This can be expressed as either:
The Occupied Bandwidth must be increased from the Modulation Bandwidth by Alpha.
…or…
The Modulation Bandwidth must be decreased from the Occupied Bandwidth by Alpha.
a) QAM
i) The single-carrier nature of QAM requires a reasonably flat response across its occupied spectrum. An external (to the modulation) filter is required to accomplish this, the combination of flat response a relatively low tolerance for in-band distortion results in an Alpha of (1.15).
b) OFDM
i) The multi-carrier nature of OFDM allows for the band response to be somewhat relaxed relative to QAM; this results in an effective Alpha of (1.05).
c) SDM
i) The nature of SDM wavelets allows for inherently steep band edges; no external filter is required to meet the edge requirements. However, the edge bands need to be left unoccupied, and the width of these bands relative to the total bandwidth then determine Alpha. At the expense of increased gate-count, Alpha can be almost arbitrarily small; practical designs have a range of (1.02) to (1.05).
d) The Net Result of the above:
Both OFDM and SDM are more efficient at using available spectrum. This result, combined with the previous, gives SDM an advantage over both QAM and OFDM.
4) Acquisition/Pilot Tones
a) QAM
i) The single carrier nature of QAM makes detection and acquisition of the signal inherent in the design of the demodulator.
b) OFDM
i) OFDM uses an FFT to demodulate the data carriers; this requires receiver synchronization with the symbol boundaries of the transmitter. To assist this, most OFDM systems dedicate at least some of the carriers to very simply modulated, non-data signals. These typically use 1-2% of the carriers, which results in reduced data throughput.
c) SDM
i) Novel acquisition techniques remove the need to dedicate bands for acquisition. Current design decisions result in a 0.1% cost in data throughput.
d) The Net Result of the above:
SDM has a 1 – 2% Data Capacity advantage over OFDM relative to acquisition requirements.
5) Equalization
a) QAM
i) Equalization of QAM signals, due to their single-carrier nature, is straightforward, requiring no loss of capacity. However, when extended over a wide bandwidth (high baud-rate), the complexity of “flattening” the spectrum can be quite severe.
b) OFDM
i) Typically, OFDM systems use a periodic Pilot/Reference signal to equalize each carrier. These signals are staggered amongst all of the non-pilot carriers, resulting in a 2-8% loss of data carrying capacity.
c) SDM
i) The single-axis modulation of SDM sub-bands allows for the data-modulated signals to be used for equalization, such that no capacity is sacrificed.
d) The Net Result of the above:
SDM has a 2 – 8% Data Capacity advantage over OFDM due to Equalization, and a clear complexity advantage at wide bandwidths over QAM.
6) Spectral Shaping & Fitting
a) QAM
i) QAM systems are not able to send or receive less than their design bandwidth.
b) OFDM
i) OFDM systems are not able to send less than their design bandwidth.
c) SDM
i) The extremely steep edges and deep out-of-band rejection of the sub-bands allow an SDM Wavelet Engine to shape its signals and response to the available spectrum, even to the extremely of being able to send a single band purely under software control. In Upstream cable applications, this allows am SDMWavelet Engine to shape its spectrum to whatever narrow-band interferers and gaps are present.
d) The Net Result of the above:
SDM has a unique advantage over both QAM and OFDM in using “sparse” and/or narrow available bandwidth; such conditions are typical in Cable Upstream applications.
7) Narrow Band interference
a) QAM
i) QAM systems are relatively susceptible to Narrow band signals, without the ability to reject them easily.
b) OFDM
i) OFDM systems’ susceptibility depends on the number of carriers used, and on the width of the interferer; however, very large (4K+) FFTs are needed to reduce the effect below 1%. In addition, the effect of the interference is greater than the relative width of the interferer; i.e. interference in 1% of the bandwidth effects at least 3% of the carriers
c) SDM
i) The extremely steep edges and deep out-of-band rejection of the sub-bands allow an SDM Wavelet Engine to reject narrow-band interferers from all but the directly co-located band. Similarly to OFDM, the “narrowness” of the band (conversely, the number of bands) is a design decision; generally a number on the scale of 100 is used, making one band a 1% effect. Unlike OFDM, increasing the width of the interferer up to 1% of the bandwidth does not increase the errors.
d) The Net Result of the above:
SDM localizes narrowband interference more effectively than either QAM or OFDM.
Comparison Table
* This comparison is for Overall
Core processing, only; Front End processing for
time domain equalizers for OFDM and QAM are not included
End of Wavelet 201
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