Signal Processing
Happy holidays! 🙂
Wishing every one merry Christmas and a great year 2009 and beyond.
I will list down some of the books which I have on my desk. They help me with the math and simulations
Digital Communication: Third Edition, by John R. Barry, Edward A. Lee, David G. Messerschmitt
We have discussed quite a few receiver structures for a 2×2 MIMO channel namely,
(a) Zero Forcing (ZF) equalization
(b) Minimum Mean Square Error (MMSE) equalization
(c) Zero Forcing equalization with Successive Interference Cancellation (ZF-SIC)
(d) ZF-SIC with optimal ordering and
(e) MIMO with MMSE SIC and optimal ordering
From the above receiver structures, we saw that MMSE equalisation with optimally ordered Successive Interference Cancellation gave the best performance. In this post, we will discuss another receiver structure called Maximum Likelihood (ML) decoding which gives us an even better performance. We will assume that the channel is a flat fading Rayleigh multipath channel and the modulation is BPSK.
We have installed Google FriendConnect on dspLog.com. With Google Friend Connect, you can:
(a) You can interact with other members who have similiar interests. You will come to know the list of other sites (apart from dspLog.com) where the members have joined. You can add a member as a friend and so on.
(b) You can invite friends from orkut, Google Talk and other social networks and contact lists to join.
(c) You need not create a new account. You can sign in with your Google, Yahoo, AIM or OpenID account.
If you wish to join dspLog community via FriendConnect, please click ‘Join this Site‘ button on the sidebar.
This post attempts to build further on the MIMO equalization schemes which we have discussed –
(a) Minimum Mean Square Error (MMSE) equalization,
(b) Zero Forcing equalization with Successive Interference Cancellation (ZF-SIC) and
(c) ZF-SIC with optimal ordering.
We have learned that successive interference cancellation with optimal ordering improves the performance with Zero Forcing equalization. In this post, we extend the concept of successive interference cancellation to the MMSE equalization and simulate the performance. We will assume that the channel is a flat fading Rayleigh multipath channel and the modulation is BPSK.
In previous posts, we had discussed equalization of a 2×2 MIMO channel with Zero Forcing (ZF) equalization and later, Zero Forcing equalization with successive interference cancellation (ZF-SIC). In this post, we will explore a variant of ZF-SIC called Zero Forcing Successive Interference Cancellation with optimal ordering. We will assume that the channel is a flat fading Rayleigh multipath channel and the modulation is BPSK.
In signal processing blocks like power estimation used in digital communication, it may be required to represent the estimate in log scale. This post explains a simple linear to log conversion scheme proposed in the DSP Guru column on DSP Trick: Quick-and-Dirty Logarithms. The scheme makes implementation of a linear to log conversion simple and small in a digital hardware like FPGA.
The post on MIMO with Zero Forcing equalizer discussed a probable way of equalizing a 2×2 MIMO channel. The simulated results with the 2×2 MIMO system with zero forcing equalizer showed matching results as obtained in for a 1×1 system for BPSK modulation in Rayleigh channel. In this post, we will try to improve the bit error rate performance by trying out Successive Interference Cancellation (SIC). We will assume that the channel is a flat fading Rayleigh multipath channel and the modulation is BPSK.
Continue reading “MIMO with Zero Forcing Successive Interference Cancellation equalizer”
In a previous post, we had discussed a 2×2 MIMO transmission using BPSK modulation in Rayleigh channel with a Zero Forcing equalizer. The simulated results with the 2×2 MIMO system with zero forcing equalizer showed matching results as obtained in for a 1×1 system for BPSK modulation in Rayleigh channel. In this post, we will discuss a different equalization approach called Minimum Mean Square Error (MMSE) equalization. We will assume that the channel is a flat fading Rayleigh multipath channel and the modulation is BPSK.
An important milestone for the dspLog happened on Oct 21st 2008. On this day last year, the blog migrated from the Blogger platform to the independently hosted platform at www.dsplog.com ! Belated birthday wishes for the blog!!! 🙂
Looking back, the first year was satisfying – both in terms of contents and traffic. We started off by discussing symbol error rates for various modulation schemes in AWGN. slowed moved tobit error rates, then to OFDM, multipath channel and recently towards multi-antenna schemes. The traffic slowly gorwed and now we have around 300+ subscribers. Continue reading “Happy Birthday – dspLog”
We had discussed three Single Input Multiple Output (SIMO also known as receive diversity) schemes – Selection combining, Equal Gain Combining, Maximal Ratio Combining and a Multiple Input Single Output (MISO, also known as transmit diversity) scheme – Alamouti 2×1 STBC. Let us now discuss the case where there a multiple transmit antennas and multiple receive antennas resulting in the formation of a Multiple Input Multiple Output (MIMO) channel. In this post, we will restrict our discussion to a 2 transmit 2 receive antenna case (resulting in a 2×2 MIMO channel). We will assume that the channel is a flat fading Rayleigh multipath channel and the modulation is BPSK.
In the recent past, we have discussed three receive diversity schemes – Selection combining, Equal Gain Combining and Maximal Ratio Combining. All the three approaches used the antenna array at the receiver to improve the demodulation performance, albeit with different levels of complexity. Time to move on to a transmit diversity scheme where the information is spread across multiple antennas at the transmitter. In this post, lets discuss a popular transmit diversity scheme called Alamouti Space Time Block Coding (STBC). For the discussion, we will assume that the channel is a flat fading Rayleigh multipath channel and the modulation is BPSK.
We have quite a few articles discussing bit and symbol error rates for popular digital modulation schemes in Additive White Gaussian Noise (AWGN) channel. This post summarizes the articles discussing the theoretical and simulated error rates for the digital modulation schemes like BPSK, QPSK, 4–PAM, 16PSK and 16QAM. Further, Bit Error Rate with Gray coded mapping, bit error rate for BPSK over OFDM are also discussed.
The links to the individual articles and the Matlab/Octave simulation models are listed below. Alternatively, I have made a e-book discussing all the below mentioned articles to a single PDF file. If you wish, you can download the free e-book by subscribing to the free email newsletter.
Continue reading “Download free e-book on error probability in AWGN”
This is the third post in the series discussing receiver diversity in a wireless link. Receiver diversity is a form of space diversity, where there are multiple antennas at the receiver. The presence of receiver diversity poses an interesting problem – how do we use ‘effectively‘ the information from all the antennas to demodulate the data. In the previous posts, we discussed selection diversity and equal gain combining (EGC).
In this post, we will discuss Maximal Ratio Combining (MRC). For the discussion, we will assume that the channel is a flat fading Rayleigh multipath channel and the modulation is BPSK.
Continue reading “Maximal Ratio Combining (MRC)”
This is the second post in the series discussing receiver diversity in a wireless link. Receiver diversity is a form of space diversity, where there are multiple antennas at the receiver. The presence of receiver diversity poses an interesting problem – how do we use ‘effectively‘ the information from all the antennas to demodulate the data. In the previous post, we discussed selection diversity. In this post, we will discuss equal gain combining (EGC). For the discussion, we will assume that the channel is a flat fading Rayleigh multipath channel and the modulation is BPSK.
