2013 Exam Flashcards
Key Adv. of FDE (5)
- vastly reduced eq. complexity
- complexity scales linearly w/ data rate + channel memory
- ISI avoided by insertion of G.I
- only a single complex multiplier required per subcarrier
- simple integration w/ MIMO
Why is pwr ampl. linearity important in design of OFDM transmitter? (5)
- OFDM waveform has a noise like t.d structure
- Results in a vary high dynamic range
- Pwr ampl. must maintain lin. ampl + phase o/p over a wide i/p envelope
- If not sufficiently linear, then non-linear intermodulation distortion results in spectral re-growth in adj. bands
- Severe non-linearity has in-band distortion of the Tx signal
matric calc. per symbol
for each symbol, there are ML states
ML+1
comparisons per symbol
One comp. per state
DS-SS PG Expression to Jamming Resistance of Wanted Signal
Rb - Signal Clock Rate
Rc - Chipping Rate
Gold Code Generator Diagram
- C/A code o/p is gold code for particular satellite, given by the states of G2
- Obtained using the shift + add property
Why are Gold Codes appropriate for GPS (5)
- Auto-correlation is a key property for spreading code acquisition + tracking
- Wanted code separation in a multi-user environment is given by the cross-correlation
- An arbitrary selection of spreading codes (m-sequences) will result in poor cross correlation due to reduction in index of discrimination
- Cross-correlation noise from an unwanted user can mask the auto-correlation function of a wanted user
- Gold codes have good auto + cross-correlation properties
Principles of MMSE
configures tap weights to statistically minimise the mean square error between the Tx + Rx data sequence
MMSE exp + simplified expr
If eqns are represented by wi, the eqn can be re-written as
By taking derivation of J w.r.t each equaliser tap + set to 0, a set of eqns can be generated whose soln minimises J
- creates an eq. w/ MMSE
In presense of noise (low SNR), ZF alg. will result in a …
… different set of tap weights that result in a higher MSE since channel inversion process amplifies noise
Iterative op. of steepest descent alg. (5)
- Eq. weights are updated in opposition to the gradient @ the current location on the error surface
- Ensures that the alg. iterates down the error surface towards a minimum value
- Current location - current eq. co-effs
- Eq. co-effs are updated iteratively by applying a correlation vector in the direction of the steepest downward slope
- Dist moved in each iteration is defined by the steepness of the slope, | Delta(k) | , w/ step size \mu
Why is computation of the true gradient difficult to achieve in a mobile antenna? (4)
R - autocorrelation matrix
p - cross-correlation matrix
w - eq. co-eff of vector
- R + p only computed through a large training seq.
- Block based calc. cannot begin until all of the training seq data has been received
- Acquiring R + p alows computation of optimum filter co-effs using Wiener-Hopf eqn
- In LMS alg, expectation function in the true grad. expr are replaced w/ approx instantaneous values
- Results in noisy est. of gradient which can be used in the iterative update eqn
Adv. + disadv. of using RLS to determine filter weights? (1,2)
Adv
-
Rapid ability to converge to the desired filter weights
- can optimally converge on each filter weight through the use of individual step sizes (Kalman Gain Matrix)
Disadv
- Complex maths
- Numerical instability @ low precision
Ill-Conditioned Channel Definition
If eigenvalue spread of the autocorrelation matrix is high
Why does the LMS alg. peform poorly in an ill-conditioned channel? (3)
- For an n-tap filter, there will be n eigenvalues
- A step size must be chosen that is a compromise between:
- large - support strong Eigenvalues
- small - support weak eigenvalues
- Small step size results in excessively long training times
Max # users in terms of Energy per Bit, Eb, + PG
State any assumptions made
Assumption - M.I from other CDMA users can be modelled as AWGN + dominates over thermal noise
