# Root raised cosine pulse shaping filter

What are disadvantages of root raised cosine pulse shaping filter in digital communications and why does it need to be improved?

• Can you please state a more specific question, and a bit more background about what you already know? Also, why are those two (three?) papers relevant? – MBaz Mar 15 '17 at 1:25
• Root raised cosine nyquist filter have in-band ripple and out-of-band attenuation and causes timing jitter, ISI. Rcosine can be improved by increasing delay or by increasing sample rate but that will increase real-time implementation cost. But still when I look for material online Root raised cosine nyquist filter is widely used in digital communication system. Knowing more reasons why Root raised cosine nyquist filter is not the most ideal filter to use will help me understand better. – momo Mar 15 '17 at 2:09
• The RRC's ripples cause neither timing jitter nor ISI. I don't know what you are referring to as "out of band attenuation". And, you still haven't asked a specific question. – MBaz Mar 15 '17 at 2:20
• I had discussed a few things about RRC filters at this post, not completely answering your question but may offer some insights into why it is used dsp.stackexchange.com/questions/31485/…. The main challenge is balancing time and frequency requirements, sensitivity to timing jitter (if the decision point is very steep), how much spectral containment (probably the biggest motivator to have such a filter) and how much rejection can be achieved. – Dan Boschen Mar 15 '17 at 3:16

The primary reason that root raised cosine filters are used is because they can be expressed in closed form and they are simple to understand. There are far better root Nyquist filters out there.

Usually they are optimized through least squares or remez exchange to improve stopband attenuation or some other channel specific criterion.

The ISI-free response (obtained through the cascade of a root Nyquist, the channel, and another root Nyquist) is only accurate in a flat channel (although it is also a good approximation in an almost flat channel). The shortcomings of root Nyquist filters have largely been addressed by DMT/OFDM, SC-FDM, and other proposed (and still experimental) technologies. These technologies result in ISI-free responses even for channels that the root Nyquist filters do not.

However, all of this is very dependent on channel models. If you really want to study the advantages and disadvantages then you need to provide a channel model, because the limitations and drawbacks of any method will be dependent on the channel model you are considering.

• I don’t have channel model right now. I am only using rrc pulse shaping filter and observing in-band ripple. The ripple varies w.r.t delay or sample per symbol. I want to measure in-band ripple peak to peak. So I can add inverted amount of ripple to cancel in-band ripple for my rrc pulse shaping filter. – momo Mar 15 '17 at 22:49
• I think you should reword your question (or ask another one) then, because you don't even mention passband ripple. If that's what you are interested in, then asking a more direct question regarding passband ripple will get you a better answer. I think my answer addresses your question as it stands now. – hops Mar 16 '17 at 0:17

A single root-raised filter is not a Nyquist filter. It must be matched with a root-raised at the received end, which is its power. It allows for a transmit filter to limit channel bandwidth then inserts a receive filter to attenuate out-of-band channel noise. The transmit + receive then achieves a raised-cosine which IS a Nyquist filter to pass the signal on to the demodulator.

When the plain raised-cosine is used at the transmit, then the receive must remain amplitude and group-delay accurate across the band to keep the eye open. This is typically a higher order filter.

• I had also always thought (not certain) that the RRC allowed for a "matched filter" in the receiver, which optimizes SNR, while still achieving in cascade the Nyquist zero-ISI desired filter response. – Dan Boschen Mar 15 '17 at 3:07
• @DanBoschen The RRC pulse is defined as the pulse $p(t)$ such that $p(t)\ast p(t)$ is an RC pulse, so yeah, it's pretty much designed to be used with a matched filter in the receiver. – MBaz Mar 15 '17 at 14:32