QPSK – RAYmaps

December 8, 2011June 4, 2014BER Performance, LTE, WiMAX

QAM Theoretical BER in AWGN

Quadrature Amplitude Modulation (QAM) is an important modulation scheme as it allows for higher data rates and spectral efficiencies. The bit error rate (BER) of QAM can be calculated through Monte Carlo simulations. However this becomes quite complex as the constellation size of the modulation schemes increases. Therefore a theoretical approach is sometimes preferred. The BER for Gray coded QAM, for even number of bits per symbol, is shown below. Gray coding ensures that a symbol error results in a single bit error. The code for calculating the theoretical QAM BER for k even (even number of bits per symbol) […]

June 2, 2011March 22, 2013BER Performance

Bit Error Rate of QPSK in Rayleigh Fading

So far we have considered the bit error rate (BER) of BPSK and QPSK in an AWGN channel. Now we turn our attention to a Rayleigh fading channel which is a more realistic representation of a wireless communication channel. We consider a single tap Rayleigh fading channel which is good approximation of a flat fading channel i.e. a channel that has flat frequency response (but varying with time). The complex channel coefficient is given as (a+j*b) where a and b are Gaussian random variables with mean 0 and variance 0.5. We use the envelope of this channel coefficient in our […]

June 2, 2011June 3, 2014BER Performance

Bit Error Rate of QPSK

Simulating a QPSK system is equivalent to simulating two BPSK systems in parallel. So there is no difference in bit error rate(BER). Since the simulation is at baseband we multiply the in-phase and quadrature streams by 1 and j respectively (instead of cos and sin carriers). At the receiver we just use the real and imag functions to separate the two symbol streams. The BER is the average BER of the two parallel streams. As in the case of BPSK we can show that the baseband representation (using 1 and j) is equivalent to using the passband representation (using cosine […]