The Throughput Potential of Cognitive Radio: A Theoretical Perspective
Summary (2 min read)
Introduction
- In a very broad sense, the term ‘cognitive radio’ can be used to refer to various solutions to this problem that seek to overlay, underlay or interweave the secondary user’s signals with the primary users’ signals in such a way that the primary users of the spectrum are as unaffected as possible.
- In the ‘underlay’ technique, simultaneous primary and secondary transmissions are allowed as in Ultrawideband (UWB) systems.
- The secondary radio spreads its signal over a bandwidth large enough to ensure that the amount of interference caused to the primary users is within tolerable limits.
- Spectrum utilization is thus improved by frequency re-use over the spectrum holes.
II. OVERLAY MODELS
- The overlay technique permits the secondary system to transmit simultaneously with the primary user.
- The secondary transmitter uses a part of its power to relay the primary user’s message to the primary receiver.
- Figure 2 shows the equivalent system model.
- The utility of overlay models lies in the fact that they characterize the ultimate limits of cognitive radio when the secondary user has access to side information and sophisticated coding techniques.
- THE INTERWEAVE MODEL Non-causal knowledge of the interference is difficult to obtain when the transmitters are not in close proximity of each other or do not share codebooks.
A. Two Switch Model
- A mathematical model for cognitive radio links can be obtained from a conceptual understanding of the interweave technique.
- Similarly, the cognitive receiver SR detects spectral holes when both B and C are inactive.
- Further, the secondary transmitter ST does not automatically have full knowledge of the primary user activity in the vicinity of the receiver SR and vice versa.
- Therefore the primary user activity sensed at the secondary transmitter and receiver change with time.
- The communication opportunities sensed at the secondary transmitter are modeled using a two-state switch st ∈ {0, 1}.
B. Capacity of the Two Switch Model
- A block static model with a coherence interval of Tc is assumed for the primary user activity , i.e., the switches at the secondary transmitter and receiver retain their state for a period of Tc channel uses (one block) after which they change to an i.i.d state.
- St is known only to the secondary transmitter and sr only to the secondary receiver, i.e., the secondary transmitter and receiver only have partial channel knowledge.
- Cognitive radio therefore corresponds to communication with partial side information.
- Capacity expressions with partial side information involve a input distribution maximization that is difficult to solve [10].
C. Sensitivity of Primary User Detection
- To explore the tradeoff between the sensitivity of primary user detection and the capacity of the cognitive radio link, the authors consider a secondary transmitter and secondary receiver separated by a distance d as shown in Figure 4.
- The authors assume perfect detection of primary users within the sensing regions.
- Figure 5 plots the secondary user throughput against the radius of the sensing regions.
- Rs for different primary user densities λ.
- Similar behavior is also observed even in cases where the primary user detection is not perfect.
IV. OVERLAY VS. INTERWEAVE: A QUANTITATIVE COMPARISON
- The authors present some numerical results comparing the theoretical performance limits of the overlay and interweave cognitive models discussed previously.
- Consider a communication scenario with the primary and secondary transmitter-receiver pairs located as shown in Figure 6.
- The primary user activity follows an i.i.d Bernoulli process with an average on-time of 40%.
- The fraction of overlay transmission time therefore decreases to 0 and both Cselfishoverlay and C selfless overlay approach Ctwo switch.
- When the primary and secondary transmitters are located close to each other (x ≈ 0), the secondary transmitter is able to obtain the primary message sooner and therefore Cselflessoverlay and C selfish overlay increase.
V. CONCLUSION
- The authors provide an overview of different techniques to cognitive radio that underlay, overlay and interweave secondary transmissions with the primary users’ signals.
- Models for cognitive radio links based on these techniques are studied.
- Numerical results comparing the throughputs of the different cognitive radio models show that the overlay technique can increase the throughput of secondary communications significantly over the interweave technique.
- This improvement, however, is critically dependent on the availability of interference knowledge at the secondary transmitter and quickly disappears as the distance between the primary and secondary transmitters increases.
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Cites background from "The Throughput Potential of Cogniti..."
...The plot suggest s that 8 degrees of freedom ( d([1]) = d([2]) = d([3]) = d([4]) = 2) can be achieved without channel extension....
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...In other words, given a set of randomly generated channel matrices and a degree-of-freedom allocation (d([1]), d([2]), · · · , d), it is not known if one can almost surely find transmit and receive filters that will satisfy the feasib ility conditions....
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...SinceIw = ∑K k=1 I [k⋆] w , we have min U[1],U[2],··· ,U[K] Iw = min U[1],U[2],··· ,U[K] K ∑ k=1 I [k⋆]w = K ∑ k=1 [ min U[k] I [k⋆]w ] = K ∑ k=1 ←− P [k] d[k] [ min U[k] I [k⋆] ] In other words, given the values ofV[j], j ∈ {1, 2, · · · , K}, Step 4 minimizes the value ofIw over all possible choices of U[k], k ∈ {1, 2, · · · , K}....
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...Let (d([1]), d([2]), · · · d) denote the number of transmit streams of the users....
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...Since avoiding interference to unintended receivers is the defining feature of cognitive radio [2] the unselfish approach is a cognitive approach....
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483 citations
Cites background from "The Throughput Potential of Cogniti..."
...Second, in the underlay network model, the coexistence of primary and secondary users is allowed and hence the network is also termed as a spectrum sharing network [8],[9],[10]....
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...The defining assumption made in the current overlay models is that the primary message is known to the secondary transmitter in prior [9]....
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References
12,172 citations
"The Throughput Potential of Cogniti..." refers methods in this paper
...While cognitive radio is most commonly identified with the interweave technique [2], [6], recent literature [7]–[9] considers cognitive communication using the overlay approach....
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3,814 citations
"The Throughput Potential of Cogniti..." refers background or methods in this paper
...The ’interweave’ technique is based on the idea of opportunistic communication [2]....
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...While cognitive radio is most commonly identified with the interweave technique [2], [6], recent literature [7]–[9] considers cognitive communication using the overlay approach....
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1,939 citations
1,157 citations
"The Throughput Potential of Cogniti..." refers background or methods in this paper
...The defining assumption made in the overlay models [7], [9] is that the secondary transmitter has noncausal knowledge of the primary user’s transmissions, i.e., the primary message W1 is known a priori to the secondary transmitter....
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...The cognitive transmitter ST can therefore only sense whether or not primary users A or B are active, i.e., ST detects spectral holes when both A and B are inactive....
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...While cognitive radio is most commonly identified with the interweave technique [2], [6], recent literature [7]–[9] considers cognitive communication using the overlay approach....
[...]
279 citations
"The Throughput Potential of Cogniti..." refers background in this paper
...The solution to this problem is, fundamentally, to take a collaborative approach to sensing [9]‐[ 11 ]....
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Frequently Asked Questions (10)
Q2. What is the possible throughput of the two switch interweave model?
Since the transmitter in the two switch interweave model does not transmit when the primary user is active, the achievable throughput Ctwo switch is independent of x.
Q3. What is the defining assumption in the overlay technique?
The defining assumption made in the overlay models [7], [9] is that the secondary transmitter has noncausal knowledge of the primary user’s transmissions, i.e., the primary message W1 is known a priori to the secondary transmitter.
Q4. What is the primary receiver's use of dirty paper coding?
the secondary transmitter uses dirty paper coding on its own message to eliminate interference at the secondary receiver.
Q5. What is the primary message knowledge used to null the interference at the secondary receiver?
The primary message knowledge at the secondary transmitter is used to effectively null the interference at the secondary receiver by using dirty paper coding [7].
Q6. What is the genie bound on the capacity of the cognitive link?
Suppose the genie provides the receiver with the transmitter state st once every Tc channel uses in the genie variable G. Since the receiver has knowledge of both the transmitter state and receiver state, the authors have Cst,(sr,G) = Cst,∗.
Q7. What is the primary transmitter’s role in the overlay technique?
In this approach, the secondary transmitter uses a part of its power to relay the primary user’s message to the primary receiver.
Q8. What is the correlation between the transmitter and receiver state?
The correlation between the transmitter state st and the receiver state sr is a measure of the distributed nature of the system - if the transmitter and receiver are far apart, the more distributed the primary activity and therefore the lower the correlation.
Q9. What is the cost of acquiring non-causal interference knowledge?
The cost of acquiring this non-causal interference knowledge is the fraction of time ν that must be spent listening to the primary user’s transmissions.
Q10. What is the difference between the selfish approach and interweave techniques?
Since all the available power in the selfish approach is used for secondary transmissions, the Cselfishoverlay curves represent an upperbound on the secondary user’s capacity.