<<<All Things Wireless>>>
Bit Error Rate performance as a function of Signal to Noise Ratio.
LDPC codes were first proposed by Robert Gallager in 1960 but they did not get immediate recognition as they were quite cumbersome to code and decode. But in 1995 the interest in these codes was revived, after discovery of Turbo Codes. Both these codes achieve the Shannon Limit and have been adopted in many wireless communication systems including 5G.
Read moreConvolutional codes when decoded using Viterbi Algorithm (VA) provide significant gains over the no coding case. The performance is further improved by using soft metrics instead of hard metrics (Euclidean distance is used in this case instead of Hamming distance). In fact, the performance is even better than brute force ML decoded Hamming (7,4) Code discussed in the previous section.
Read moreIn this post we discuss Hamming (7,4) Code which transmits 4 information bits for every 7 bits transmitted, resulting in a code rate of 4/7. The 3 additional bits are called parity bits and these protect against single bit errors in the channel. This is called a systematic code since after performing the coding operation the information bits are preserved, parity bits are only appended to the information bits.
Read moreCarrier phase or frequency synchronization is a common problem in wireless communication systems. These two problems are interrelated as instantaneous frequency is just the rate of change of phase.
Read moreIt is widely believed that performance of non-coherent receivers is much worse than performance of coherent receivers in terms of Bit Error Rate (BER). Although this is true to some extent but as we show in this post the difference in performance is not that much in case of Minimum Shift Keying (MSK). In fact, there is only a difference of about one dB in an AWGN environment at high Signal to Noise Ratios (SNR). The difference is somewhat larger in flat fading environment but given the simplicity of implementation of a non-coherent receiver the trade-off might be worth it.
Read moreSome Background Before we delve deep into Minimum Shift Keying (MSK) and its performance in presence of co-channel interference the reader is advised to look at the following posts. Post 1 – MSK BER performance in AWGN and flat fading environment when viewed as extension of BPSK Post 2 – MSK Power Spectral Density and its BER performance in AWGN when viewed as a CPM Post 3 – MSK BER Performance in AWGN and flat fading environment when viewed as a CPM Co-channel interference is a phenomenon widely encountered in wireless communication systems and the main reason for that is […]
Read moreI – In the previous two posts we discussed MSK performance in an AWGN channel, first presenting the MATLAB/OCTAVE Code for one sample per symbol case [Post 1], and then extending it to the more general case of multiple samples per symbol [Post 2]. This helps us visualize the underlying beauty of Continuous Phase Modulation (CPM) which reduces out of band energy and consequently lowers Adjacent Channel Interference (ACI). We also briefly touched upon the case of MSK in Rayleigh fading, but did not go into the details. So here we take a deeper dive.
Read moreSome Background on MSK I – In the previous post we presented the mathematical model and code for BER calculation of a popular modulation scheme called MSK. However in the code we shared, we only considered one sample per symbol, which makes MSK look like BPSK. While BPSK symbols fall on the real axis, MSK symbols alternate between real and imaginary axes, progressing by π/2 phase during each symbol period. MSK signal thus has memory and this can help in demodulation using advanced techniques such as Viterbi Algorithm.
Read moreMinimum Shift Keying (MSK) is a type of Continuous Phase Modulation (CPM) that has been used in many wireless communication systems. To be more precise it is Continuous Phase Frequency Shift Keying (CPFSK) with two frequencies f1 and f2.
Read more